diff --git a/cmd/cloudflared/tunnel/configuration.go b/cmd/cloudflared/tunnel/configuration.go index 36257cc7..f8930357 100644 --- a/cmd/cloudflared/tunnel/configuration.go +++ b/cmd/cloudflared/tunnel/configuration.go @@ -4,6 +4,7 @@ import ( "crypto/tls" "fmt" "io/ioutil" + mathRand "math/rand" "os" "path/filepath" "strings" @@ -220,6 +221,19 @@ func prepareTunnelConfig( ) transportProtocol := c.String("protocol") + + needPQ := c.Bool("post-quantum") + if needPQ { + if FipsEnabled { + return nil, nil, fmt.Errorf("post-quantum not supported in FIPS mode") + } + // Error if the user tries to force a non-quic transport protocol + if transportProtocol != connection.AutoSelectFlag && transportProtocol != connection.QUIC.String() { + return nil, nil, fmt.Errorf("post-quantum is only supported with the quic transport") + } + transportProtocol = connection.QUIC.String() + } + protocolFetcher := edgediscovery.ProtocolPercentage cfg := config.GetConfiguration() @@ -230,6 +244,9 @@ func prepareTunnelConfig( } log.Info().Msgf("Generated Connector ID: %s", clientUUID) features := append(c.StringSlice("features"), defaultFeatures...) + if needPQ { + features = append(features, supervisor.FeaturePostQuantum) + } if c.IsSet(TunnelTokenFlag) { if transportProtocol == connection.AutoSelectFlag { protocolFetcher = func() (edgediscovery.ProtocolPercents, error) { @@ -291,7 +308,7 @@ func prepareTunnelConfig( } warpRoutingEnabled := isWarpRoutingEnabled(cfg.WarpRouting, isNamedTunnel) - protocolSelector, err := connection.NewProtocolSelector(transportProtocol, warpRoutingEnabled, namedTunnel, protocolFetcher, supervisor.ResolveTTL, log) + protocolSelector, err := connection.NewProtocolSelector(transportProtocol, warpRoutingEnabled, namedTunnel, protocolFetcher, supervisor.ResolveTTL, log, c.Bool("post-quantum")) if err != nil { return nil, nil, err } @@ -330,6 +347,15 @@ func prepareTunnelConfig( return nil, nil, err } + var pqKexIdx int + if needPQ { + pqKexIdx = mathRand.Intn(len(supervisor.PQKexes)) + log.Info().Msgf( + "Using experimental hybrid post-quantum key agreement %s", + supervisor.PQKexNames[supervisor.PQKexes[pqKexIdx]], + ) + } + tunnelConfig := &supervisor.TunnelConfig{ GracePeriod: gracePeriod, ReplaceExisting: c.Bool("force"), @@ -355,6 +381,8 @@ func prepareTunnelConfig( MuxerConfig: muxerConfig, ProtocolSelector: protocolSelector, EdgeTLSConfigs: edgeTLSConfigs, + NeedPQ: needPQ, + PQKexIdx: pqKexIdx, } orchestratorConfig := &orchestration.Config{ Ingress: &ingressRules, diff --git a/cmd/cloudflared/tunnel/fips.go b/cmd/cloudflared/tunnel/fips.go new file mode 100644 index 00000000..03ae6d26 --- /dev/null +++ b/cmd/cloudflared/tunnel/fips.go @@ -0,0 +1,3 @@ +package tunnel + +var FipsEnabled bool diff --git a/cmd/cloudflared/tunnel/subcommands.go b/cmd/cloudflared/tunnel/subcommands.go index d3549856..71435465 100644 --- a/cmd/cloudflared/tunnel/subcommands.go +++ b/cmd/cloudflared/tunnel/subcommands.go @@ -140,6 +140,13 @@ var ( EnvVars: []string{"TUNNEL_TRANSPORT_PROTOCOL"}, Hidden: true, }) + postQuantumFlag = altsrc.NewBoolFlag(&cli.BoolFlag{ + Name: "post-quantum", + Usage: "When given creates an experimental post-quantum secure tunnel", + Aliases: []string{"pq"}, + EnvVars: []string{"TUNNEL_POST_QUANTUM"}, + Hidden: FipsEnabled, + }) sortInfoByFlag = &cli.StringFlag{ Name: "sort-by", Value: "createdAt", @@ -602,6 +609,7 @@ func buildRunCommand() *cli.Command { forceFlag, credentialsFileFlag, credentialsContentsFlag, + postQuantumFlag, selectProtocolFlag, featuresFlag, tunnelTokenFlag, diff --git a/connection/protocol.go b/connection/protocol.go index b8b7d5ce..ddf9bb76 100644 --- a/connection/protocol.go +++ b/connection/protocol.go @@ -1,6 +1,7 @@ package connection import ( + "errors" "fmt" "hash/fnv" "sync" @@ -130,6 +131,7 @@ type autoProtocolSelector struct { refreshAfter time.Time ttl time.Duration log *zerolog.Logger + needPQ bool } func newAutoProtocolSelector( @@ -139,6 +141,7 @@ func newAutoProtocolSelector( fetchFunc PercentageFetcher, ttl time.Duration, log *zerolog.Logger, + needPQ bool, ) *autoProtocolSelector { return &autoProtocolSelector{ current: current, @@ -148,6 +151,7 @@ func newAutoProtocolSelector( refreshAfter: time.Now().Add(ttl), ttl: ttl, log: log, + needPQ: needPQ, } } @@ -187,6 +191,9 @@ func getProtocol(protocolPool []Protocol, fetchFunc PercentageFetcher, switchThr func (s *autoProtocolSelector) Fallback() (Protocol, bool) { s.lock.RLock() defer s.lock.RUnlock() + if s.needPQ { + return 0, false + } return s.current.fallback() } @@ -199,9 +206,14 @@ func NewProtocolSelector( fetchFunc PercentageFetcher, ttl time.Duration, log *zerolog.Logger, + needPQ bool, ) (ProtocolSelector, error) { // Classic tunnel is only supported with h2mux if namedTunnel == nil { + if needPQ { + return nil, errors.New("Classic tunnel does not support post-quantum") + } + return &staticProtocolSelector{ current: H2mux, }, nil @@ -211,6 +223,9 @@ func NewProtocolSelector( fetchedProtocol, err := getProtocol([]Protocol{QUIC, HTTP2}, fetchFunc, threshold) if err != nil && protocolFlag == "auto" { log.Err(err).Msg("Unable to lookup protocol. Defaulting to `http2`. If this fails, you can attempt `--protocol quic` instead.") + if needPQ { + return nil, errors.New("http2 does not support post-quantum") + } return &staticProtocolSelector{ current: HTTP2, }, nil @@ -221,10 +236,10 @@ func NewProtocolSelector( protocolFlag = HTTP2.String() fetchedProtocol = HTTP2Warp } - return selectWarpRoutingProtocols(protocolFlag, fetchFunc, ttl, log, threshold, fetchedProtocol) + return selectWarpRoutingProtocols(protocolFlag, fetchFunc, ttl, log, threshold, fetchedProtocol, needPQ) } - return selectNamedTunnelProtocols(protocolFlag, fetchFunc, ttl, log, threshold, fetchedProtocol) + return selectNamedTunnelProtocols(protocolFlag, fetchFunc, ttl, log, threshold, fetchedProtocol, needPQ) } func selectNamedTunnelProtocols( @@ -234,6 +249,7 @@ func selectNamedTunnelProtocols( log *zerolog.Logger, threshold int32, protocol Protocol, + needPQ bool, ) (ProtocolSelector, error) { // If the user picks a protocol, then we stick to it no matter what. switch protocolFlag { @@ -248,7 +264,7 @@ func selectNamedTunnelProtocols( // If the user does not pick (hopefully the majority) then we use the one derived from the TXT DNS record and // fallback on failures. if protocolFlag == AutoSelectFlag { - return newAutoProtocolSelector(protocol, []Protocol{QUIC, HTTP2, H2mux}, threshold, fetchFunc, ttl, log), nil + return newAutoProtocolSelector(protocol, []Protocol{QUIC, HTTP2, H2mux}, threshold, fetchFunc, ttl, log, needPQ), nil } return nil, fmt.Errorf("Unknown protocol %s, %s", protocolFlag, AvailableProtocolFlagMessage) @@ -261,6 +277,7 @@ func selectWarpRoutingProtocols( log *zerolog.Logger, threshold int32, protocol Protocol, + needPQ bool, ) (ProtocolSelector, error) { // If the user picks a protocol, then we stick to it no matter what. switch protocolFlag { @@ -273,7 +290,7 @@ func selectWarpRoutingProtocols( // If the user does not pick (hopefully the majority) then we use the one derived from the TXT DNS record and // fallback on failures. if protocolFlag == AutoSelectFlag { - return newAutoProtocolSelector(protocol, []Protocol{QUICWarp, HTTP2Warp}, threshold, fetchFunc, ttl, log), nil + return newAutoProtocolSelector(protocol, []Protocol{QUICWarp, HTTP2Warp}, threshold, fetchFunc, ttl, log, needPQ), nil } return nil, fmt.Errorf("Unknown protocol %s, %s", protocolFlag, AvailableProtocolFlagMessage) diff --git a/connection/protocol_test.go b/connection/protocol_test.go index 9eef7b6c..b3bda44a 100644 --- a/connection/protocol_test.go +++ b/connection/protocol_test.go @@ -219,7 +219,7 @@ func TestNewProtocolSelector(t *testing.T) { for _, test := range tests { t.Run(test.name, func(t *testing.T) { - selector, err := NewProtocolSelector(test.protocol, test.warpRoutingEnabled, test.namedTunnelConfig, test.fetchFunc, testNoTTL, &log) + selector, err := NewProtocolSelector(test.protocol, test.warpRoutingEnabled, test.namedTunnelConfig, test.fetchFunc, testNoTTL, &log, false) if test.wantErr { assert.Error(t, err, fmt.Sprintf("test %s failed", test.name)) } else { @@ -237,7 +237,7 @@ func TestNewProtocolSelector(t *testing.T) { func TestAutoProtocolSelectorRefresh(t *testing.T) { fetcher := dynamicMockFetcher{} - selector, err := NewProtocolSelector(AutoSelectFlag, noWarpRoutingEnabled, testNamedTunnelProperties, fetcher.fetch(), testNoTTL, &log) + selector, err := NewProtocolSelector(AutoSelectFlag, noWarpRoutingEnabled, testNamedTunnelProperties, fetcher.fetch(), testNoTTL, &log, false) assert.NoError(t, err) assert.Equal(t, H2mux, selector.Current()) @@ -267,7 +267,7 @@ func TestAutoProtocolSelectorRefresh(t *testing.T) { func TestHTTP2ProtocolSelectorRefresh(t *testing.T) { fetcher := dynamicMockFetcher{} // Since the user chooses http2 on purpose, we always stick to it. - selector, err := NewProtocolSelector("http2", noWarpRoutingEnabled, testNamedTunnelProperties, fetcher.fetch(), testNoTTL, &log) + selector, err := NewProtocolSelector("http2", noWarpRoutingEnabled, testNamedTunnelProperties, fetcher.fetch(), testNoTTL, &log, false) assert.NoError(t, err) assert.Equal(t, HTTP2, selector.Current()) @@ -297,7 +297,7 @@ func TestHTTP2ProtocolSelectorRefresh(t *testing.T) { func TestProtocolSelectorRefreshTTL(t *testing.T) { fetcher := dynamicMockFetcher{} fetcher.protocolPercents = edgediscovery.ProtocolPercents{edgediscovery.ProtocolPercent{Protocol: "quic", Percentage: 100}} - selector, err := NewProtocolSelector(AutoSelectFlag, noWarpRoutingEnabled, testNamedTunnelProperties, fetcher.fetch(), time.Hour, &log) + selector, err := NewProtocolSelector(AutoSelectFlag, noWarpRoutingEnabled, testNamedTunnelProperties, fetcher.fetch(), time.Hour, &log, false) assert.NoError(t, err) assert.Equal(t, QUIC, selector.Current()) diff --git a/fips/fips.go.linux-amd64 b/fips/fips.go.linux-amd64 index e6b3585b..5075f298 100644 --- a/fips/fips.go.linux-amd64 +++ b/fips/fips.go.linux-amd64 @@ -2,4 +2,11 @@ package main -import _ "crypto/tls/fipsonly" +import ( + _ "crypto/tls/fipsonly" + "github.com/cloudflare/cloudflared/cmd/cloudflared/tunnel" +) + +func init () { + tunnel.FipsEnabled = true +} diff --git a/go.mod b/go.mod index 3cec487f..02c0bf76 100644 --- a/go.mod +++ b/go.mod @@ -12,6 +12,7 @@ require ( github.com/getsentry/raven-go v0.0.0-20180517221441-ed7bcb39ff10 github.com/gobwas/ws v1.0.4 github.com/golang-collections/collections v0.0.0-20130729185459-604e922904d3 + github.com/google/gopacket v1.1.19 github.com/google/uuid v1.3.0 github.com/gorilla/mux v1.8.0 github.com/gorilla/websocket v1.4.2 @@ -33,10 +34,10 @@ require ( go.opentelemetry.io/otel/trace v1.6.3 go.opentelemetry.io/proto/otlp v0.15.0 go.uber.org/automaxprocs v1.4.0 - golang.org/x/crypto v0.0.0-20220427172511-eb4f295cb31f + golang.org/x/crypto v0.0.0-20220722155217-630584e8d5aa golang.org/x/net v0.0.0-20220812174116-3211cb980234 golang.org/x/sync v0.0.0-20210220032951-036812b2e83c - golang.org/x/sys v0.0.0-20220728004956-3c1f35247d10 + golang.org/x/sys v0.0.0-20220808155132-1c4a2a72c664 golang.org/x/term v0.0.0-20210927222741-03fcf44c2211 google.golang.org/protobuf v1.28.0 gopkg.in/coreos/go-oidc.v2 v2.2.1 @@ -53,6 +54,7 @@ require ( github.com/certifi/gocertifi v0.0.0-20200211180108-c7c1fbc02894 // indirect github.com/cespare/xxhash/v2 v2.1.2 // indirect github.com/cheekybits/genny v1.0.0 // indirect + github.com/cloudflare/circl v1.2.1-0.20220809205628-0a9554f37a47 // indirect github.com/coredns/caddy v1.1.1 // indirect github.com/cpuguy83/go-md2man/v2 v2.0.0 // indirect github.com/davecgh/go-spew v1.1.1 // indirect @@ -67,7 +69,6 @@ require ( github.com/gobwas/httphead v0.0.0-20200921212729-da3d93bc3c58 // indirect github.com/gobwas/pool v0.2.1 // indirect github.com/golang/protobuf v1.5.2 // indirect - github.com/google/gopacket v1.1.19 // indirect github.com/grpc-ecosystem/grpc-gateway/v2 v2.7.0 // indirect github.com/grpc-ecosystem/grpc-opentracing v0.0.0-20180507213350-8e809c8a8645 // indirect github.com/kylelemons/godebug v1.1.0 // indirect @@ -107,3 +108,12 @@ replace github.com/lucas-clemente/quic-go => github.com/chungthuang/quic-go v0.2 replace github.com/prometheus/golang_client => github.com/prometheus/golang_client v1.12.1 replace gopkg.in/yaml.v3 => gopkg.in/yaml.v3 v3.0.1 + +// Post-quantum tunnel RTG-1339 +replace ( + // branch go1.18 + github.com/marten-seemann/qtls-go1-18 => github.com/cloudflare/qtls-pq v0.0.0-20220824105406-fb955667e0af + + // branch go1.19 + github.com/marten-seemann/qtls-go1-19 => github.com/cloudflare/qtls-pq v0.0.0-20220824104809-96561a41e0af +) diff --git a/go.sum b/go.sum index 2c4d11fb..7f2012a8 100644 --- a/go.sum +++ b/go.sum @@ -99,6 +99,7 @@ github.com/beorn7/perks v1.0.1 h1:VlbKKnNfV8bJzeqoa4cOKqO6bYr3WgKZxO8Z16+hsOM= github.com/beorn7/perks v1.0.1/go.mod h1:G2ZrVWU2WbWT9wwq4/hrbKbnv/1ERSJQ0ibhJ6rlkpw= github.com/bradfitz/go-smtpd v0.0.0-20170404230938-deb6d6237625/go.mod h1:HYsPBTaaSFSlLx/70C2HPIMNZpVV8+vt/A+FMnYP11g= github.com/buger/jsonparser v0.0.0-20181115193947-bf1c66bbce23/go.mod h1:bbYlZJ7hK1yFx9hf58LP0zeX7UjIGs20ufpu3evjr+s= +github.com/bwesterb/go-ristretto v1.2.2/go.mod h1:fUIoIZaG73pV5biE2Blr2xEzDoMj7NFEuV9ekS419A0= github.com/cenkalti/backoff/v4 v4.1.2/go.mod h1:scbssz8iZGpm3xbr14ovlUdkxfGXNInqkPWOWmG2CLw= github.com/census-instrumentation/opencensus-proto v0.2.1/go.mod h1:f6KPmirojxKA12rnyqOA5BBL4O983OfeGPqjHWSTneU= github.com/certifi/gocertifi v0.0.0-20200211180108-c7c1fbc02894 h1:JLaf/iINcLyjwbtTsCJjc6rtlASgHeIJPrB6QmwURnA= @@ -117,8 +118,14 @@ github.com/chzyer/test v0.0.0-20180213035817-a1ea475d72b1/go.mod h1:Q3SI9o4m/ZMn github.com/client9/misspell v0.3.4/go.mod h1:qj6jICC3Q7zFZvVWo7KLAzC3yx5G7kyvSDkc90ppPyw= github.com/cloudflare/brotli-go v0.0.0-20191101163834-d34379f7ff93 h1:QrGfkZDnMxcWHaYDdB7CmqS9i26OAnUj/xcus/abYkY= github.com/cloudflare/brotli-go v0.0.0-20191101163834-d34379f7ff93/go.mod h1:QiTe66jFdP7cUKMCCf/WrvDyYdtdmdZfVcdoLbzaKVY= +github.com/cloudflare/circl v1.2.1-0.20220809205628-0a9554f37a47 h1:YzpECHxZ9TzO7LpnKmPxItSd79lLgrR5heIlnqU4dTU= +github.com/cloudflare/circl v1.2.1-0.20220809205628-0a9554f37a47/go.mod h1:qhx8gBILsYlbam7h09SvHDSkjpe3TfLA7b/z4rxJvkE= github.com/cloudflare/golibs v0.0.0-20170913112048-333127dbecfc h1:Dvk3ySBsOm5EviLx6VCyILnafPcQinXGP5jbTdHUJgE= github.com/cloudflare/golibs v0.0.0-20170913112048-333127dbecfc/go.mod h1:HlgKKR8V5a1wroIDDIz3/A+T+9Janfq+7n1P5sEFdi0= +github.com/cloudflare/qtls-pq v0.0.0-20220824104809-96561a41e0af h1:JMpOQAaXjRRBkUX73fTNe9mConJLFl6FsIp9fHdLm7Y= +github.com/cloudflare/qtls-pq v0.0.0-20220824104809-96561a41e0af/go.mod h1:aIsWqC0WXyUiUxBl/RfxAjDyWE9CCLqvSMnCMTd/+bc= +github.com/cloudflare/qtls-pq v0.0.0-20220824105406-fb955667e0af h1:bhCmedjwrOSyzLtHVeQ+KhimcNTSfs0P5T7kbRQS+gA= +github.com/cloudflare/qtls-pq v0.0.0-20220824105406-fb955667e0af/go.mod h1:mW0BgKFFDAiSmOdUwoORtjo0V2vqw5QzVYRtKQqw/Jg= github.com/cncf/udpa/go v0.0.0-20191209042840-269d4d468f6f/go.mod h1:M8M6+tZqaGXZJjfX53e64911xZQV5JYwmTeXPW+k8Sc= github.com/cncf/udpa/go v0.0.0-20200629203442-efcf912fb354/go.mod h1:WmhPx2Nbnhtbo57+VJT5O0JRkEi1Wbu0z5j0R8u5Hbk= github.com/cncf/udpa/go v0.0.0-20201120205902-5459f2c99403/go.mod h1:WmhPx2Nbnhtbo57+VJT5O0JRkEi1Wbu0z5j0R8u5Hbk= @@ -401,10 +408,6 @@ github.com/marten-seemann/qtls-go1-16 v0.1.5 h1:o9JrYPPco/Nukd/HpOHMHZoBDXQqoNtU github.com/marten-seemann/qtls-go1-16 v0.1.5/go.mod h1:gNpI2Ol+lRS3WwSOtIUUtRwZEQMXjYK+dQSBFbethAk= github.com/marten-seemann/qtls-go1-17 v0.1.2 h1:JADBlm0LYiVbuSySCHeY863dNkcpMmDR7s0bLKJeYlQ= github.com/marten-seemann/qtls-go1-17 v0.1.2/go.mod h1:C2ekUKcDdz9SDWxec1N/MvcXBpaX9l3Nx67XaR84L5s= -github.com/marten-seemann/qtls-go1-18 v0.1.2 h1:JH6jmzbduz0ITVQ7ShevK10Av5+jBEKAHMntXmIV7kM= -github.com/marten-seemann/qtls-go1-18 v0.1.2/go.mod h1:mJttiymBAByA49mhlNZZGrH5u1uXYZJ+RW28Py7f4m4= -github.com/marten-seemann/qtls-go1-19 v0.1.0-beta.1 h1:7m/WlWcSROrcK5NxuXaxYD32BZqe/LEEnBrWcH/cOqQ= -github.com/marten-seemann/qtls-go1-19 v0.1.0-beta.1/go.mod h1:5HTDWtVudo/WFsHKRNuOhWlbdjrfs5JHrYb0wIJqGpI= github.com/mattn/go-colorable v0.1.8 h1:c1ghPdyEDarC70ftn0y+A/Ee++9zz8ljHG1b13eJ0s8= github.com/mattn/go-colorable v0.1.8/go.mod h1:u6P/XSegPjTcexA+o6vUJrdnUu04hMope9wVRipJSqc= github.com/mattn/go-isatty v0.0.12 h1:wuysRhFDzyxgEmMf5xjvJ2M9dZoWAXNNr5LSBS7uHXY= @@ -621,8 +624,8 @@ golang.org/x/crypto v0.0.0-20201112155050-0c6587e931a9/go.mod h1:LzIPMQfyMNhhGPh golang.org/x/crypto v0.0.0-20210817164053-32db794688a5/go.mod h1:GvvjBRRGRdwPK5ydBHafDWAxML/pGHZbMvKqRZ5+Abc= golang.org/x/crypto v0.0.0-20210920023735-84f357641f63/go.mod h1:GvvjBRRGRdwPK5ydBHafDWAxML/pGHZbMvKqRZ5+Abc= golang.org/x/crypto v0.0.0-20210921155107-089bfa567519/go.mod h1:GvvjBRRGRdwPK5ydBHafDWAxML/pGHZbMvKqRZ5+Abc= -golang.org/x/crypto v0.0.0-20220427172511-eb4f295cb31f h1:OeJjE6G4dgCY4PIXvIRQbE8+RX+uXZyGhUy/ksMGJoc= -golang.org/x/crypto v0.0.0-20220427172511-eb4f295cb31f/go.mod h1:IxCIyHEi3zRg3s0A5j5BB6A9Jmi73HwBIUl50j+osU4= +golang.org/x/crypto v0.0.0-20220722155217-630584e8d5aa h1:zuSxTR4o9y82ebqCUJYNGJbGPo6sKVl54f/TVDObg1c= +golang.org/x/crypto v0.0.0-20220722155217-630584e8d5aa/go.mod h1:IxCIyHEi3zRg3s0A5j5BB6A9Jmi73HwBIUl50j+osU4= golang.org/x/exp v0.0.0-20190121172915-509febef88a4/go.mod h1:CJ0aWSM057203Lf6IL+f9T1iT9GByDxfZKAQTCR3kQA= golang.org/x/exp v0.0.0-20190306152737-a1d7652674e8/go.mod h1:CJ0aWSM057203Lf6IL+f9T1iT9GByDxfZKAQTCR3kQA= golang.org/x/exp v0.0.0-20190510132918-efd6b22b2522/go.mod h1:ZjyILWgesfNpC6sMxTJOJm9Kp84zZh5NQWvqDGG3Qr8= @@ -708,9 +711,9 @@ golang.org/x/net v0.0.0-20210503060351-7fd8e65b6420/go.mod h1:9nx3DQGgdP8bBQD5qx golang.org/x/net v0.0.0-20210525063256-abc453219eb5/go.mod h1:9nx3DQGgdP8bBQD5qxJ1jj9UTztislL4KSBs9R2vV5Y= golang.org/x/net v0.0.0-20210726213435-c6fcb2dbf985/go.mod h1:9nx3DQGgdP8bBQD5qxJ1jj9UTztislL4KSBs9R2vV5Y= golang.org/x/net v0.0.0-20210917221730-978cfadd31cf/go.mod h1:9nx3DQGgdP8bBQD5qxJ1jj9UTztislL4KSBs9R2vV5Y= +golang.org/x/net v0.0.0-20211112202133-69e39bad7dc2/go.mod h1:9nx3DQGgdP8bBQD5qxJ1jj9UTztislL4KSBs9R2vV5Y= golang.org/x/net v0.0.0-20211209124913-491a49abca63/go.mod h1:9nx3DQGgdP8bBQD5qxJ1jj9UTztislL4KSBs9R2vV5Y= golang.org/x/net v0.0.0-20211216030914-fe4d6282115f/go.mod h1:9nx3DQGgdP8bBQD5qxJ1jj9UTztislL4KSBs9R2vV5Y= -golang.org/x/net v0.0.0-20220624214902-1bab6f366d9e h1:TsQ7F31D3bUCLeqPT0u+yjp1guoArKaNKmCr22PYgTQ= golang.org/x/net v0.0.0-20220624214902-1bab6f366d9e/go.mod h1:XRhObCWvk6IyKnWLug+ECip1KBveYUHfp+8e9klMJ9c= golang.org/x/net v0.0.0-20220812174116-3211cb980234 h1:RDqmgfe7SvlMWoqC3xwQ2blLO3fcWcxMa3eBLRdRW7E= golang.org/x/net v0.0.0-20220812174116-3211cb980234/go.mod h1:YDH+HFinaLZZlnHAfSS6ZXJJ9M9t4Dl22yv3iI2vPwk= @@ -818,10 +821,9 @@ golang.org/x/sys v0.0.0-20210908233432-aa78b53d3365/go.mod h1:oPkhp1MJrh7nUepCBc golang.org/x/sys v0.0.0-20211124211545-fe61309f8881/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg= golang.org/x/sys v0.0.0-20211216021012-1d35b9e2eb4e/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg= golang.org/x/sys v0.0.0-20220114195835-da31bd327af9/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg= -golang.org/x/sys v0.0.0-20220520151302-bc2c85ada10a h1:dGzPydgVsqGcTRVwiLJ1jVbufYwmzD3LfVPLKsKg+0k= golang.org/x/sys v0.0.0-20220520151302-bc2c85ada10a/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg= -golang.org/x/sys v0.0.0-20220728004956-3c1f35247d10 h1:WIoqL4EROvwiPdUtaip4VcDdpZ4kha7wBWZrbVKCIZg= -golang.org/x/sys v0.0.0-20220728004956-3c1f35247d10/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg= +golang.org/x/sys v0.0.0-20220808155132-1c4a2a72c664 h1:v1W7bwXHsnLLloWYTVEdvGvA7BHMeBYsPcF0GLDxIRs= +golang.org/x/sys v0.0.0-20220808155132-1c4a2a72c664/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg= golang.org/x/term v0.0.0-20201126162022-7de9c90e9dd1/go.mod h1:bj7SfCRtBDWHUb9snDiAeCFNEtKQo2Wmx5Cou7ajbmo= golang.org/x/term v0.0.0-20210615171337-6886f2dfbf5b/go.mod h1:jbD1KX2456YbFQfuXm/mYQcufACuNUgVhRMnK/tPxf8= golang.org/x/term v0.0.0-20210927222741-03fcf44c2211 h1:JGgROgKl9N8DuW20oFS5gxc+lE67/N3FcwmBPMe7ArY= diff --git a/supervisor/pqtunnels.go b/supervisor/pqtunnels.go new file mode 100644 index 00000000..f682828c --- /dev/null +++ b/supervisor/pqtunnels.go @@ -0,0 +1,100 @@ +package supervisor + +import ( + "bytes" + "crypto/tls" + "encoding/json" + "net/http" + "sync" +) + +// When experimental post-quantum tunnels are enabled, and we're hitting an +// issue creating the tunnel, we'll report the first error +// to https://pqtunnels.cloudflareresearch.com. + +var ( + PQKexes = [...]tls.CurveID{ + tls.CurveID(0xfe30), // X25519Kyber512Draft00 + tls.CurveID(0xfe31), // X25519Kyber768Draft00 + } + PQKexNames map[tls.CurveID]string = map[tls.CurveID]string{ + tls.CurveID(0xfe30): "X25519Kyber512Draft00", + tls.CurveID(0xfe31): "X25519Kyber768Draft00", + } + + pqtMux sync.Mutex // protects pqtSubmitted and pqtWaitForMessage + pqtSubmitted bool // whether an error has already been submitted + + // Number of errors to ignore before printing elaborate instructions. + pqtWaitForMessage int +) + +func handlePQTunnelError(rep error, config *TunnelConfig) { + needToMessage := false + + pqtMux.Lock() + needToSubmit := !pqtSubmitted + if needToSubmit { + pqtSubmitted = true + } + pqtWaitForMessage-- + if pqtWaitForMessage < 0 { + pqtWaitForMessage = 5 + needToMessage = true + } + pqtMux.Unlock() + + if needToMessage { + config.Log.Info().Msgf( + "\n\n" + + "===================================================================================\n" + + "You are hitting an error while using the experimental post-quantum tunnels feature.\n" + + "\n" + + "Please check:\n" + + "\n" + + " https://pqtunnels.cloudflareresearch.com\n" + + "\n" + + "for known problems.\n" + + "===================================================================================\n\n", + ) + } + + if needToSubmit { + go submitPQTunnelError(rep, config) + } +} + +func submitPQTunnelError(rep error, config *TunnelConfig) { + body, err := json.Marshal(struct { + Group int `json:"g"` + Message string `json:"m"` + Version string `json:"v"` + }{ + Group: int(PQKexes[config.PQKexIdx]), + Message: rep.Error(), + Version: config.ReportedVersion, + }) + if err != nil { + config.Log.Err(err).Msg("Failed to create error report") + return + } + + resp, err := http.Post( + "https://pqtunnels.cloudflareresearch.com", + "application/json", + bytes.NewBuffer(body), + ) + if err != nil { + config.Log.Err(err).Msg( + "Failed to submit post-quantum tunnel error report", + ) + return + } + if resp.StatusCode != 200 { + config.Log.Error().Msgf( + "Failed to submit post-quantum tunnel error report: status %d", + resp.StatusCode, + ) + } + resp.Body.Close() +} diff --git a/supervisor/tunnel.go b/supervisor/tunnel.go index 9b6f0db4..34f6cecc 100644 --- a/supervisor/tunnel.go +++ b/supervisor/tunnel.go @@ -36,6 +36,7 @@ const ( FeatureQuickReconnects = "quick_reconnects" FeatureAllowRemoteConfig = "allow_remote_config" FeatureDatagramV2 = "support_datagram_v2" + FeaturePostQuantum = "postquantum" ) type TunnelConfig struct { @@ -59,6 +60,11 @@ type TunnelConfig struct { Retries uint RunFromTerminal bool + NeedPQ bool + + // Index into PQKexes of post-quantum kex to use if NeedPQ is set. + PQKexIdx int + NamedTunnel *connection.NamedTunnelProperties ClassicTunnel *connection.ClassicTunnelProperties MuxerConfig *connection.MuxerConfig @@ -524,6 +530,9 @@ func (e *EdgeTunnelServer) serveH2mux( connIndex uint8, connectedFuse *connectedFuse, ) error { + if e.config.NeedPQ { + return unrecoverableError{errors.New("H2Mux transport does not support post-quantum")} + } connLog.Logger().Debug().Msgf("Connecting via h2mux") // Returns error from parsing the origin URL or handshake errors handler, err, recoverable := connection.NewH2muxConnection( @@ -575,6 +584,10 @@ func (e *EdgeTunnelServer) serveHTTP2( controlStreamHandler connection.ControlStreamHandler, connIndex uint8, ) error { + if e.config.NeedPQ { + return unrecoverableError{errors.New("HTTP/2 transport does not support post-quantum")} + } + connLog.Logger().Debug().Msgf("Connecting via http2") h2conn := connection.NewHTTP2Connection( tlsServerConn, @@ -613,6 +626,22 @@ func (e *EdgeTunnelServer) serveQUIC( connIndex uint8, ) (err error, recoverable bool) { tlsConfig := e.config.EdgeTLSConfigs[connection.QUIC] + + if e.config.NeedPQ { + // If the user passes the -post-quantum flag, we override + // CurvePreferences to only support hybrid post-quantum key agreements. + cs := make([]tls.CurveID, len(PQKexes)) + copy(cs, PQKexes[:]) + + // It is unclear whether Kyber512 or Kyber768 will become the standard. + // Kyber768 is a bit bigger (and doesn't fit in one initial + // datagram anymore). We're enabling both, but pick randomly which + // one to put first. (TLS will use the first one in the list + // and allows a fallback to the second.) + cs[0], cs[e.config.PQKexIdx] = cs[e.config.PQKexIdx], cs[0] + tlsConfig.CurvePreferences = cs + } + quicConfig := &quic.Config{ HandshakeIdleTimeout: quicpogs.HandshakeIdleTimeout, MaxIdleTimeout: quicpogs.MaxIdleTimeout, @@ -634,6 +663,10 @@ func (e *EdgeTunnelServer) serveQUIC( connLogger.Logger(), e.icmpProxy) if err != nil { + if e.config.NeedPQ { + handlePQTunnelError(err, e.config) + } + connLogger.ConnAwareLogger().Err(err).Msgf("Failed to create new quic connection") return err, true } diff --git a/supervisor/tunnel_test.go b/supervisor/tunnel_test.go index 2e646089..3f9ae62c 100644 --- a/supervisor/tunnel_test.go +++ b/supervisor/tunnel_test.go @@ -44,6 +44,7 @@ func TestWaitForBackoffFallback(t *testing.T) { mockFetcher.fetch(), resolveTTL, &log, + false, ) assert.NoError(t, err) @@ -104,6 +105,7 @@ func TestWaitForBackoffFallback(t *testing.T) { mockFetcher.fetch(), resolveTTL, &log, + false, ) assert.NoError(t, err) protoFallback = &protocolFallback{backoff, protocolSelector.Current(), false} diff --git a/vendor/github.com/cloudflare/circl/LICENSE b/vendor/github.com/cloudflare/circl/LICENSE new file mode 100644 index 00000000..67edaa90 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/LICENSE @@ -0,0 +1,57 @@ +Copyright (c) 2019 Cloudflare. All rights reserved. + +Redistribution and use in source and binary forms, with or without +modification, are permitted provided that the following conditions are +met: + + * Redistributions of source code must retain the above copyright +notice, this list of conditions and the following disclaimer. + * Redistributions in binary form must reproduce the above +copyright notice, this list of conditions and the following disclaimer +in the documentation and/or other materials provided with the +distribution. + * Neither the name of Cloudflare nor the names of its +contributors may be used to endorse or promote products derived from +this software without specific prior written permission. + +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT +OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, +SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT +LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, +DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY +THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT +(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE +OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + +======================================================================== + +Copyright (c) 2009 The Go Authors. All rights reserved. + +Redistribution and use in source and binary forms, with or without +modification, are permitted provided that the following conditions are +met: + + * Redistributions of source code must retain the above copyright +notice, this list of conditions and the following disclaimer. + * Redistributions in binary form must reproduce the above +copyright notice, this list of conditions and the following disclaimer +in the documentation and/or other materials provided with the +distribution. + * Neither the name of Google Inc. nor the names of its +contributors may be used to endorse or promote products derived from +this software without specific prior written permission. + +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT +OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, +SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT +LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, +DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY +THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT +(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE +OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. diff --git a/vendor/github.com/cloudflare/circl/dh/x25519/curve.go b/vendor/github.com/cloudflare/circl/dh/x25519/curve.go new file mode 100644 index 00000000..f9057c2b --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x25519/curve.go @@ -0,0 +1,96 @@ +package x25519 + +import ( + fp "github.com/cloudflare/circl/math/fp25519" +) + +// ladderJoye calculates a fixed-point multiplication with the generator point. +// The algorithm is the right-to-left Joye's ladder as described +// in "How to precompute a ladder" in SAC'2017. +func ladderJoye(k *Key) { + w := [5]fp.Elt{} // [mu,x1,z1,x2,z2] order must be preserved. + fp.SetOne(&w[1]) // x1 = 1 + fp.SetOne(&w[2]) // z1 = 1 + w[3] = fp.Elt{ // x2 = G-S + 0xbd, 0xaa, 0x2f, 0xc8, 0xfe, 0xe1, 0x94, 0x7e, + 0xf8, 0xed, 0xb2, 0x14, 0xae, 0x95, 0xf0, 0xbb, + 0xe2, 0x48, 0x5d, 0x23, 0xb9, 0xa0, 0xc7, 0xad, + 0x34, 0xab, 0x7c, 0xe2, 0xee, 0xcd, 0xae, 0x1e, + } + fp.SetOne(&w[4]) // z2 = 1 + + const n = 255 + const h = 3 + swap := uint(1) + for s := 0; s < n-h; s++ { + i := (s + h) / 8 + j := (s + h) % 8 + bit := uint((k[i] >> uint(j)) & 1) + copy(w[0][:], tableGenerator[s*Size:(s+1)*Size]) + diffAdd(&w, swap^bit) + swap = bit + } + for s := 0; s < h; s++ { + double(&w[1], &w[2]) + } + toAffine((*[fp.Size]byte)(k), &w[1], &w[2]) +} + +// ladderMontgomery calculates a generic scalar point multiplication +// The algorithm implemented is the left-to-right Montgomery's ladder. +func ladderMontgomery(k, xP *Key) { + w := [5]fp.Elt{} // [x1, x2, z2, x3, z3] order must be preserved. + w[0] = *(*fp.Elt)(xP) // x1 = xP + fp.SetOne(&w[1]) // x2 = 1 + w[3] = *(*fp.Elt)(xP) // x3 = xP + fp.SetOne(&w[4]) // z3 = 1 + + move := uint(0) + for s := 255 - 1; s >= 0; s-- { + i := s / 8 + j := s % 8 + bit := uint((k[i] >> uint(j)) & 1) + ladderStep(&w, move^bit) + move = bit + } + toAffine((*[fp.Size]byte)(k), &w[1], &w[2]) +} + +func toAffine(k *[fp.Size]byte, x, z *fp.Elt) { + fp.Inv(z, z) + fp.Mul(x, x, z) + _ = fp.ToBytes(k[:], x) +} + +var lowOrderPoints = [5]fp.Elt{ + { /* (0,_,1) point of order 2 on Curve25519 */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + }, + { /* (1,_,1) point of order 4 on Curve25519 */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + }, + { /* (x,_,1) first point of order 8 on Curve25519 */ + 0xe0, 0xeb, 0x7a, 0x7c, 0x3b, 0x41, 0xb8, 0xae, + 0x16, 0x56, 0xe3, 0xfa, 0xf1, 0x9f, 0xc4, 0x6a, + 0xda, 0x09, 0x8d, 0xeb, 0x9c, 0x32, 0xb1, 0xfd, + 0x86, 0x62, 0x05, 0x16, 0x5f, 0x49, 0xb8, 0x00, + }, + { /* (x,_,1) second point of order 8 on Curve25519 */ + 0x5f, 0x9c, 0x95, 0xbc, 0xa3, 0x50, 0x8c, 0x24, + 0xb1, 0xd0, 0xb1, 0x55, 0x9c, 0x83, 0xef, 0x5b, + 0x04, 0x44, 0x5c, 0xc4, 0x58, 0x1c, 0x8e, 0x86, + 0xd8, 0x22, 0x4e, 0xdd, 0xd0, 0x9f, 0x11, 0x57, + }, + { /* (-1,_,1) a point of order 4 on the twist of Curve25519 */ + 0xec, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, + }, +} diff --git a/vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.go b/vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.go new file mode 100644 index 00000000..8a3d54c5 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.go @@ -0,0 +1,30 @@ +//go:build amd64 && !purego +// +build amd64,!purego + +package x25519 + +import ( + fp "github.com/cloudflare/circl/math/fp25519" + "golang.org/x/sys/cpu" +) + +var hasBmi2Adx = cpu.X86.HasBMI2 && cpu.X86.HasADX + +var _ = hasBmi2Adx + +func double(x, z *fp.Elt) { doubleAmd64(x, z) } +func diffAdd(w *[5]fp.Elt, b uint) { diffAddAmd64(w, b) } +func ladderStep(w *[5]fp.Elt, b uint) { ladderStepAmd64(w, b) } +func mulA24(z, x *fp.Elt) { mulA24Amd64(z, x) } + +//go:noescape +func ladderStepAmd64(w *[5]fp.Elt, b uint) + +//go:noescape +func diffAddAmd64(w *[5]fp.Elt, b uint) + +//go:noescape +func doubleAmd64(x, z *fp.Elt) + +//go:noescape +func mulA24Amd64(z, x *fp.Elt) diff --git a/vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.h b/vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.h new file mode 100644 index 00000000..8c1ae4d0 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.h @@ -0,0 +1,111 @@ +#define ladderStepLeg \ + addSub(x2,z2) \ + addSub(x3,z3) \ + integerMulLeg(b0,x2,z3) \ + integerMulLeg(b1,x3,z2) \ + reduceFromDoubleLeg(t0,b0) \ + reduceFromDoubleLeg(t1,b1) \ + addSub(t0,t1) \ + cselect(x2,x3,regMove) \ + cselect(z2,z3,regMove) \ + integerSqrLeg(b0,t0) \ + integerSqrLeg(b1,t1) \ + reduceFromDoubleLeg(x3,b0) \ + reduceFromDoubleLeg(z3,b1) \ + integerMulLeg(b0,x1,z3) \ + reduceFromDoubleLeg(z3,b0) \ + integerSqrLeg(b0,x2) \ + integerSqrLeg(b1,z2) \ + reduceFromDoubleLeg(x2,b0) \ + reduceFromDoubleLeg(z2,b1) \ + subtraction(t0,x2,z2) \ + multiplyA24Leg(t1,t0) \ + additionLeg(t1,t1,z2) \ + integerMulLeg(b0,x2,z2) \ + integerMulLeg(b1,t0,t1) \ + reduceFromDoubleLeg(x2,b0) \ + reduceFromDoubleLeg(z2,b1) + +#define ladderStepBmi2Adx \ + addSub(x2,z2) \ + addSub(x3,z3) \ + integerMulAdx(b0,x2,z3) \ + integerMulAdx(b1,x3,z2) \ + reduceFromDoubleAdx(t0,b0) \ + reduceFromDoubleAdx(t1,b1) \ + addSub(t0,t1) \ + cselect(x2,x3,regMove) \ + cselect(z2,z3,regMove) \ + integerSqrAdx(b0,t0) \ + integerSqrAdx(b1,t1) \ + reduceFromDoubleAdx(x3,b0) \ + reduceFromDoubleAdx(z3,b1) \ + integerMulAdx(b0,x1,z3) \ + reduceFromDoubleAdx(z3,b0) \ + integerSqrAdx(b0,x2) \ + integerSqrAdx(b1,z2) \ + reduceFromDoubleAdx(x2,b0) \ + reduceFromDoubleAdx(z2,b1) \ + subtraction(t0,x2,z2) \ + multiplyA24Adx(t1,t0) \ + additionAdx(t1,t1,z2) \ + integerMulAdx(b0,x2,z2) \ + integerMulAdx(b1,t0,t1) \ + reduceFromDoubleAdx(x2,b0) \ + reduceFromDoubleAdx(z2,b1) + +#define difAddLeg \ + addSub(x1,z1) \ + integerMulLeg(b0,z1,ui) \ + reduceFromDoubleLeg(z1,b0) \ + addSub(x1,z1) \ + integerSqrLeg(b0,x1) \ + integerSqrLeg(b1,z1) \ + reduceFromDoubleLeg(x1,b0) \ + reduceFromDoubleLeg(z1,b1) \ + integerMulLeg(b0,x1,z2) \ + integerMulLeg(b1,z1,x2) \ + reduceFromDoubleLeg(x1,b0) \ + reduceFromDoubleLeg(z1,b1) + +#define difAddBmi2Adx \ + addSub(x1,z1) \ + integerMulAdx(b0,z1,ui) \ + reduceFromDoubleAdx(z1,b0) \ + addSub(x1,z1) \ + integerSqrAdx(b0,x1) \ + integerSqrAdx(b1,z1) \ + reduceFromDoubleAdx(x1,b0) \ + reduceFromDoubleAdx(z1,b1) \ + integerMulAdx(b0,x1,z2) \ + integerMulAdx(b1,z1,x2) \ + reduceFromDoubleAdx(x1,b0) \ + reduceFromDoubleAdx(z1,b1) + +#define doubleLeg \ + addSub(x1,z1) \ + integerSqrLeg(b0,x1) \ + integerSqrLeg(b1,z1) \ + reduceFromDoubleLeg(x1,b0) \ + reduceFromDoubleLeg(z1,b1) \ + subtraction(t0,x1,z1) \ + multiplyA24Leg(t1,t0) \ + additionLeg(t1,t1,z1) \ + integerMulLeg(b0,x1,z1) \ + integerMulLeg(b1,t0,t1) \ + reduceFromDoubleLeg(x1,b0) \ + reduceFromDoubleLeg(z1,b1) + +#define doubleBmi2Adx \ + addSub(x1,z1) \ + integerSqrAdx(b0,x1) \ + integerSqrAdx(b1,z1) \ + reduceFromDoubleAdx(x1,b0) \ + reduceFromDoubleAdx(z1,b1) \ + subtraction(t0,x1,z1) \ + multiplyA24Adx(t1,t0) \ + additionAdx(t1,t1,z1) \ + integerMulAdx(b0,x1,z1) \ + integerMulAdx(b1,t0,t1) \ + reduceFromDoubleAdx(x1,b0) \ + reduceFromDoubleAdx(z1,b1) diff --git a/vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.s b/vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.s new file mode 100644 index 00000000..b7723185 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.s @@ -0,0 +1,156 @@ +// +build amd64 + +#include "textflag.h" + +// Depends on circl/math/fp25519 package +#include "../../math/fp25519/fp_amd64.h" +#include "curve_amd64.h" + +// CTE_A24 is (A+2)/4 from Curve25519 +#define CTE_A24 121666 + +#define Size 32 + +// multiplyA24Leg multiplies x times CTE_A24 and stores in z +// Uses: AX, DX, R8-R13, FLAGS +// Instr: x86_64, cmov +#define multiplyA24Leg(z,x) \ + MOVL $CTE_A24, AX; MULQ 0+x; MOVQ AX, R8; MOVQ DX, R9; \ + MOVL $CTE_A24, AX; MULQ 8+x; MOVQ AX, R12; MOVQ DX, R10; \ + MOVL $CTE_A24, AX; MULQ 16+x; MOVQ AX, R13; MOVQ DX, R11; \ + MOVL $CTE_A24, AX; MULQ 24+x; \ + ADDQ R12, R9; \ + ADCQ R13, R10; \ + ADCQ AX, R11; \ + ADCQ $0, DX; \ + MOVL $38, AX; /* 2*C = 38 = 2^256 MOD 2^255-19*/ \ + IMULQ AX, DX; \ + ADDQ DX, R8; \ + ADCQ $0, R9; MOVQ R9, 8+z; \ + ADCQ $0, R10; MOVQ R10, 16+z; \ + ADCQ $0, R11; MOVQ R11, 24+z; \ + MOVQ $0, DX; \ + CMOVQCS AX, DX; \ + ADDQ DX, R8; MOVQ R8, 0+z; + +// multiplyA24Adx multiplies x times CTE_A24 and stores in z +// Uses: AX, DX, R8-R12, FLAGS +// Instr: x86_64, cmov, bmi2 +#define multiplyA24Adx(z,x) \ + MOVQ $CTE_A24, DX; \ + MULXQ 0+x, R8, R10; \ + MULXQ 8+x, R9, R11; ADDQ R10, R9; \ + MULXQ 16+x, R10, AX; ADCQ R11, R10; \ + MULXQ 24+x, R11, R12; ADCQ AX, R11; \ + ;;;;;;;;;;;;;;;;;;;;; ADCQ $0, R12; \ + MOVL $38, DX; /* 2*C = 38 = 2^256 MOD 2^255-19*/ \ + IMULQ DX, R12; \ + ADDQ R12, R8; \ + ADCQ $0, R9; MOVQ R9, 8+z; \ + ADCQ $0, R10; MOVQ R10, 16+z; \ + ADCQ $0, R11; MOVQ R11, 24+z; \ + MOVQ $0, R12; \ + CMOVQCS DX, R12; \ + ADDQ R12, R8; MOVQ R8, 0+z; + +#define mulA24Legacy \ + multiplyA24Leg(0(DI),0(SI)) +#define mulA24Bmi2Adx \ + multiplyA24Adx(0(DI),0(SI)) + +// func mulA24Amd64(z, x *fp255.Elt) +TEXT ·mulA24Amd64(SB),NOSPLIT,$0-16 + MOVQ z+0(FP), DI + MOVQ x+8(FP), SI + CHECK_BMI2ADX(LMA24, mulA24Legacy, mulA24Bmi2Adx) + + +// func ladderStepAmd64(w *[5]fp255.Elt, b uint) +// ladderStepAmd64 calculates a point addition and doubling as follows: +// (x2,z2) = 2*(x2,z2) and (x3,z3) = (x2,z2)+(x3,z3) using as a difference (x1,-). +// work = (x1,x2,z2,x3,z3) are five fp255.Elt of 32 bytes. +// stack = (t0,t1) are two fp.Elt of fp.Size bytes, and +// (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes. +TEXT ·ladderStepAmd64(SB),NOSPLIT,$192-16 + // Parameters + #define regWork DI + #define regMove SI + #define x1 0*Size(regWork) + #define x2 1*Size(regWork) + #define z2 2*Size(regWork) + #define x3 3*Size(regWork) + #define z3 4*Size(regWork) + // Local variables + #define t0 0*Size(SP) + #define t1 1*Size(SP) + #define b0 2*Size(SP) + #define b1 4*Size(SP) + MOVQ w+0(FP), regWork + MOVQ b+8(FP), regMove + CHECK_BMI2ADX(LLADSTEP, ladderStepLeg, ladderStepBmi2Adx) + #undef regWork + #undef regMove + #undef x1 + #undef x2 + #undef z2 + #undef x3 + #undef z3 + #undef t0 + #undef t1 + #undef b0 + #undef b1 + +// func diffAddAmd64(w *[5]fp255.Elt, b uint) +// diffAddAmd64 calculates a differential point addition using a precomputed point. +// (x1,z1) = (x1,z1)+(mu) using a difference point (x2,z2) +// w = (mu,x1,z1,x2,z2) are five fp.Elt, and +// stack = (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes. +TEXT ·diffAddAmd64(SB),NOSPLIT,$128-16 + // Parameters + #define regWork DI + #define regSwap SI + #define ui 0*Size(regWork) + #define x1 1*Size(regWork) + #define z1 2*Size(regWork) + #define x2 3*Size(regWork) + #define z2 4*Size(regWork) + // Local variables + #define b0 0*Size(SP) + #define b1 2*Size(SP) + MOVQ w+0(FP), regWork + MOVQ b+8(FP), regSwap + cswap(x1,x2,regSwap) + cswap(z1,z2,regSwap) + CHECK_BMI2ADX(LDIFADD, difAddLeg, difAddBmi2Adx) + #undef regWork + #undef regSwap + #undef ui + #undef x1 + #undef z1 + #undef x2 + #undef z2 + #undef b0 + #undef b1 + +// func doubleAmd64(x, z *fp255.Elt) +// doubleAmd64 calculates a point doubling (x1,z1) = 2*(x1,z1). +// stack = (t0,t1) are two fp.Elt of fp.Size bytes, and +// (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes. +TEXT ·doubleAmd64(SB),NOSPLIT,$192-16 + // Parameters + #define x1 0(DI) + #define z1 0(SI) + // Local variables + #define t0 0*Size(SP) + #define t1 1*Size(SP) + #define b0 2*Size(SP) + #define b1 4*Size(SP) + MOVQ x+0(FP), DI + MOVQ z+8(FP), SI + CHECK_BMI2ADX(LDOUB,doubleLeg,doubleBmi2Adx) + #undef x1 + #undef z1 + #undef t0 + #undef t1 + #undef b0 + #undef b1 diff --git a/vendor/github.com/cloudflare/circl/dh/x25519/curve_generic.go b/vendor/github.com/cloudflare/circl/dh/x25519/curve_generic.go new file mode 100644 index 00000000..dae67ea3 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x25519/curve_generic.go @@ -0,0 +1,85 @@ +package x25519 + +import ( + "encoding/binary" + "math/bits" + + fp "github.com/cloudflare/circl/math/fp25519" +) + +func doubleGeneric(x, z *fp.Elt) { + t0, t1 := &fp.Elt{}, &fp.Elt{} + fp.AddSub(x, z) + fp.Sqr(x, x) + fp.Sqr(z, z) + fp.Sub(t0, x, z) + mulA24Generic(t1, t0) + fp.Add(t1, t1, z) + fp.Mul(x, x, z) + fp.Mul(z, t0, t1) +} + +func diffAddGeneric(w *[5]fp.Elt, b uint) { + mu, x1, z1, x2, z2 := &w[0], &w[1], &w[2], &w[3], &w[4] + fp.Cswap(x1, x2, b) + fp.Cswap(z1, z2, b) + fp.AddSub(x1, z1) + fp.Mul(z1, z1, mu) + fp.AddSub(x1, z1) + fp.Sqr(x1, x1) + fp.Sqr(z1, z1) + fp.Mul(x1, x1, z2) + fp.Mul(z1, z1, x2) +} + +func ladderStepGeneric(w *[5]fp.Elt, b uint) { + x1, x2, z2, x3, z3 := &w[0], &w[1], &w[2], &w[3], &w[4] + t0 := &fp.Elt{} + t1 := &fp.Elt{} + fp.AddSub(x2, z2) + fp.AddSub(x3, z3) + fp.Mul(t0, x2, z3) + fp.Mul(t1, x3, z2) + fp.AddSub(t0, t1) + fp.Cmov(x2, x3, b) + fp.Cmov(z2, z3, b) + fp.Sqr(x3, t0) + fp.Sqr(z3, t1) + fp.Mul(z3, x1, z3) + fp.Sqr(x2, x2) + fp.Sqr(z2, z2) + fp.Sub(t0, x2, z2) + mulA24Generic(t1, t0) + fp.Add(t1, t1, z2) + fp.Mul(x2, x2, z2) + fp.Mul(z2, t0, t1) +} + +func mulA24Generic(z, x *fp.Elt) { + const A24 = 121666 + const n = 8 + var xx [4]uint64 + for i := range xx { + xx[i] = binary.LittleEndian.Uint64(x[i*n : (i+1)*n]) + } + + h0, l0 := bits.Mul64(xx[0], A24) + h1, l1 := bits.Mul64(xx[1], A24) + h2, l2 := bits.Mul64(xx[2], A24) + h3, l3 := bits.Mul64(xx[3], A24) + + var c3 uint64 + l1, c0 := bits.Add64(h0, l1, 0) + l2, c1 := bits.Add64(h1, l2, c0) + l3, c2 := bits.Add64(h2, l3, c1) + l4, _ := bits.Add64(h3, 0, c2) + _, l4 = bits.Mul64(l4, 38) + l0, c0 = bits.Add64(l0, l4, 0) + xx[1], c1 = bits.Add64(l1, 0, c0) + xx[2], c2 = bits.Add64(l2, 0, c1) + xx[3], c3 = bits.Add64(l3, 0, c2) + xx[0], _ = bits.Add64(l0, (-c3)&38, 0) + for i := range xx { + binary.LittleEndian.PutUint64(z[i*n:(i+1)*n], xx[i]) + } +} diff --git a/vendor/github.com/cloudflare/circl/dh/x25519/curve_noasm.go b/vendor/github.com/cloudflare/circl/dh/x25519/curve_noasm.go new file mode 100644 index 00000000..07fab97d --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x25519/curve_noasm.go @@ -0,0 +1,11 @@ +//go:build !amd64 || purego +// +build !amd64 purego + +package x25519 + +import fp "github.com/cloudflare/circl/math/fp25519" + +func double(x, z *fp.Elt) { doubleGeneric(x, z) } +func diffAdd(w *[5]fp.Elt, b uint) { diffAddGeneric(w, b) } +func ladderStep(w *[5]fp.Elt, b uint) { ladderStepGeneric(w, b) } +func mulA24(z, x *fp.Elt) { mulA24Generic(z, x) } diff --git a/vendor/github.com/cloudflare/circl/dh/x25519/doc.go b/vendor/github.com/cloudflare/circl/dh/x25519/doc.go new file mode 100644 index 00000000..3ce102d1 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x25519/doc.go @@ -0,0 +1,19 @@ +/* +Package x25519 provides Diffie-Hellman functions as specified in RFC-7748. + +Validation of public keys. + +The Diffie-Hellman function, as described in RFC-7748 [1], works for any +public key. However, if a different protocol requires contributory +behaviour [2,3], then the public keys must be validated against low-order +points [3,4]. To do that, the Shared function performs this validation +internally and returns false when the public key is invalid (i.e., it +is a low-order point). + +References: + - [1] RFC7748 by Langley, Hamburg, Turner (https://rfc-editor.org/rfc/rfc7748.txt) + - [2] Curve25519 by Bernstein (https://cr.yp.to/ecdh.html) + - [3] Bernstein (https://cr.yp.to/ecdh.html#validate) + - [4] Cremers&Jackson (https://eprint.iacr.org/2019/526) +*/ +package x25519 diff --git a/vendor/github.com/cloudflare/circl/dh/x25519/key.go b/vendor/github.com/cloudflare/circl/dh/x25519/key.go new file mode 100644 index 00000000..bbd37ddd --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x25519/key.go @@ -0,0 +1,47 @@ +package x25519 + +import ( + "crypto/subtle" + + fp "github.com/cloudflare/circl/math/fp25519" +) + +// Size is the length in bytes of a X25519 key. +const Size = 32 + +// Key represents a X25519 key. +type Key [Size]byte + +func (k *Key) clamp(in *Key) *Key { + *k = *in + k[0] &= 248 + k[31] = (k[31] & 127) | 64 + return k +} + +// isValidPubKey verifies if the public key is not a low-order point. +func (k *Key) isValidPubKey() bool { + fp.Modp((*fp.Elt)(k)) + isLowOrder := false + for _, P := range lowOrderPoints { + isLowOrder = isLowOrder || subtle.ConstantTimeCompare(P[:], k[:]) != 0 + } + return !isLowOrder +} + +// KeyGen obtains a public key given a secret key. +func KeyGen(public, secret *Key) { + ladderJoye(public.clamp(secret)) +} + +// Shared calculates Alice's shared key from Alice's secret key and Bob's +// public key returning true on success. A failure case happens when the public +// key is a low-order point, thus the shared key is all-zeros and the function +// returns false. +func Shared(shared, secret, public *Key) bool { + validPk := *public + validPk[31] &= (1 << (255 % 8)) - 1 + ok := validPk.isValidPubKey() + ladderMontgomery(shared.clamp(secret), &validPk) + return ok +} diff --git a/vendor/github.com/cloudflare/circl/dh/x25519/table.go b/vendor/github.com/cloudflare/circl/dh/x25519/table.go new file mode 100644 index 00000000..28c8c4ac --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x25519/table.go @@ -0,0 +1,268 @@ +package x25519 + +import "github.com/cloudflare/circl/math/fp25519" + +// tableGenerator contains the set of points: +// +// t[i] = (xi+1)/(xi-1), +// +// where (xi,yi) = 2^iG and G is the generator point +// Size = (256)*(256/8) = 8192 bytes. +var tableGenerator = [256 * fp25519.Size]byte{ + /* (2^ 0)P */ 0xf3, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x5f, + /* (2^ 1)P */ 0x96, 0xfe, 0xaa, 0x16, 0xf4, 0x20, 0x82, 0x6b, 0x34, 0x6a, 0x56, 0x4f, 0x2b, 0xeb, 0xeb, 0x82, 0x0f, 0x95, 0xa5, 0x75, 0xb0, 0xa5, 0xa9, 0xd5, 0xf4, 0x88, 0x24, 0x4b, 0xcf, 0xb2, 0x42, 0x51, + /* (2^ 2)P */ 0x0c, 0x68, 0x69, 0x00, 0x75, 0xbc, 0xae, 0x6a, 0x41, 0x9c, 0xf9, 0xa0, 0x20, 0x78, 0xcf, 0x89, 0xf4, 0xd0, 0x56, 0x3b, 0x18, 0xd9, 0x58, 0x2a, 0xa4, 0x11, 0x60, 0xe3, 0x80, 0xca, 0x5a, 0x4b, + /* (2^ 3)P */ 0x5d, 0x74, 0x29, 0x8c, 0x34, 0x32, 0x91, 0x32, 0xd7, 0x2f, 0x64, 0xe1, 0x16, 0xe6, 0xa2, 0xf4, 0x34, 0xbc, 0x67, 0xff, 0x03, 0xbb, 0x45, 0x1e, 0x4a, 0x9b, 0x2a, 0xf4, 0xd0, 0x12, 0x69, 0x30, + /* (2^ 4)P */ 0x54, 0x71, 0xaf, 0xe6, 0x07, 0x65, 0x88, 0xff, 0x2f, 0xc8, 0xee, 0xdf, 0x13, 0x0e, 0xf5, 0x04, 0xce, 0xb5, 0xba, 0x2a, 0xe8, 0x2f, 0x51, 0xaa, 0x22, 0xf2, 0xd5, 0x68, 0x1a, 0x25, 0x4e, 0x17, + /* (2^ 5)P */ 0x98, 0x88, 0x02, 0x82, 0x0d, 0x70, 0x96, 0xcf, 0xc5, 0x02, 0x2c, 0x0a, 0x37, 0xe3, 0x43, 0x17, 0xaa, 0x6e, 0xe8, 0xb4, 0x98, 0xec, 0x9e, 0x37, 0x2e, 0x48, 0xe0, 0x51, 0x8a, 0x88, 0x59, 0x0c, + /* (2^ 6)P */ 0x89, 0xd1, 0xb5, 0x99, 0xd6, 0xf1, 0xcb, 0xfb, 0x84, 0xdc, 0x9f, 0x8e, 0xd5, 0xf0, 0xae, 0xac, 0x14, 0x76, 0x1f, 0x23, 0x06, 0x0d, 0xc2, 0xc1, 0x72, 0xf9, 0x74, 0xa2, 0x8d, 0x21, 0x38, 0x29, + /* (2^ 7)P */ 0x18, 0x7f, 0x1d, 0xff, 0xbe, 0x49, 0xaf, 0xf6, 0xc2, 0xc9, 0x7a, 0x38, 0x22, 0x1c, 0x54, 0xcc, 0x6b, 0xc5, 0x15, 0x40, 0xef, 0xc9, 0xfc, 0x96, 0xa9, 0x13, 0x09, 0x69, 0x7c, 0x62, 0xc1, 0x69, + /* (2^ 8)P */ 0x0e, 0xdb, 0x33, 0x47, 0x2f, 0xfd, 0x86, 0x7a, 0xe9, 0x7d, 0x08, 0x9e, 0xf2, 0xc4, 0xb8, 0xfd, 0x29, 0xa2, 0xa2, 0x8e, 0x1a, 0x4b, 0x5e, 0x09, 0x79, 0x7a, 0xb3, 0x29, 0xc8, 0xa7, 0xd7, 0x1a, + /* (2^ 9)P */ 0xc0, 0xa0, 0x7e, 0xd1, 0xca, 0x89, 0x2d, 0x34, 0x51, 0x20, 0xed, 0xcc, 0xa6, 0xdd, 0xbe, 0x67, 0x74, 0x2f, 0xb4, 0x2b, 0xbf, 0x31, 0xca, 0x19, 0xbb, 0xac, 0x80, 0x49, 0xc8, 0xb4, 0xf7, 0x3d, + /* (2^ 10)P */ 0x83, 0xd8, 0x0a, 0xc8, 0x4d, 0x44, 0xc6, 0xa8, 0x85, 0xab, 0xe3, 0x66, 0x03, 0x44, 0x1e, 0xb9, 0xd8, 0xf6, 0x64, 0x01, 0xa0, 0xcd, 0x15, 0xc2, 0x68, 0xe6, 0x47, 0xf2, 0x6e, 0x7c, 0x86, 0x3d, + /* (2^ 11)P */ 0x8c, 0x65, 0x3e, 0xcc, 0x2b, 0x58, 0xdd, 0xc7, 0x28, 0x55, 0x0e, 0xee, 0x48, 0x47, 0x2c, 0xfd, 0x71, 0x4f, 0x9f, 0xcc, 0x95, 0x9b, 0xfd, 0xa0, 0xdf, 0x5d, 0x67, 0xb0, 0x71, 0xd8, 0x29, 0x75, + /* (2^ 12)P */ 0x78, 0xbd, 0x3c, 0x2d, 0xb4, 0x68, 0xf5, 0xb8, 0x82, 0xda, 0xf3, 0x91, 0x1b, 0x01, 0x33, 0x12, 0x62, 0x3b, 0x7c, 0x4a, 0xcd, 0x6c, 0xce, 0x2d, 0x03, 0x86, 0x49, 0x9e, 0x8e, 0xfc, 0xe7, 0x75, + /* (2^ 13)P */ 0xec, 0xb6, 0xd0, 0xfc, 0xf1, 0x13, 0x4f, 0x2f, 0x45, 0x7a, 0xff, 0x29, 0x1f, 0xca, 0xa8, 0xf1, 0x9b, 0xe2, 0x81, 0x29, 0xa7, 0xc1, 0x49, 0xc2, 0x6a, 0xb5, 0x83, 0x8c, 0xbb, 0x0d, 0xbe, 0x6e, + /* (2^ 14)P */ 0x22, 0xb2, 0x0b, 0x17, 0x8d, 0xfa, 0x14, 0x71, 0x5f, 0x93, 0x93, 0xbf, 0xd5, 0xdc, 0xa2, 0x65, 0x9a, 0x97, 0x9c, 0xb5, 0x68, 0x1f, 0xc4, 0xbd, 0x89, 0x92, 0xce, 0xa2, 0x79, 0xef, 0x0e, 0x2f, + /* (2^ 15)P */ 0xce, 0x37, 0x3c, 0x08, 0x0c, 0xbf, 0xec, 0x42, 0x22, 0x63, 0x49, 0xec, 0x09, 0xbc, 0x30, 0x29, 0x0d, 0xac, 0xfe, 0x9c, 0xc1, 0xb0, 0x94, 0xf2, 0x80, 0xbb, 0xfa, 0xed, 0x4b, 0xaa, 0x80, 0x37, + /* (2^ 16)P */ 0x29, 0xd9, 0xea, 0x7c, 0x3e, 0x7d, 0xc1, 0x56, 0xc5, 0x22, 0x57, 0x2e, 0xeb, 0x4b, 0xcb, 0xe7, 0x5a, 0xe1, 0xbf, 0x2d, 0x73, 0x31, 0xe9, 0x0c, 0xf8, 0x52, 0x10, 0x62, 0xc7, 0x83, 0xb8, 0x41, + /* (2^ 17)P */ 0x50, 0x53, 0xd2, 0xc3, 0xa0, 0x5c, 0xf7, 0xdb, 0x51, 0xe3, 0xb1, 0x6e, 0x08, 0xbe, 0x36, 0x29, 0x12, 0xb2, 0xa9, 0xb4, 0x3c, 0xe0, 0x36, 0xc9, 0xaa, 0x25, 0x22, 0x32, 0x82, 0xbf, 0x45, 0x1d, + /* (2^ 18)P */ 0xc5, 0x4c, 0x02, 0x6a, 0x03, 0xb1, 0x1a, 0xe8, 0x72, 0x9a, 0x4c, 0x30, 0x1c, 0x20, 0x12, 0xe2, 0xfc, 0xb1, 0x32, 0x68, 0xba, 0x3f, 0xd7, 0xc5, 0x81, 0x95, 0x83, 0x4d, 0x5a, 0xdb, 0xff, 0x20, + /* (2^ 19)P */ 0xad, 0x0f, 0x5d, 0xbe, 0x67, 0xd3, 0x83, 0xa2, 0x75, 0x44, 0x16, 0x8b, 0xca, 0x25, 0x2b, 0x6c, 0x2e, 0xf2, 0xaa, 0x7c, 0x46, 0x35, 0x49, 0x9d, 0x49, 0xff, 0x85, 0xee, 0x8e, 0x40, 0x66, 0x51, + /* (2^ 20)P */ 0x61, 0xe3, 0xb4, 0xfa, 0xa2, 0xba, 0x67, 0x3c, 0xef, 0x5c, 0xf3, 0x7e, 0xc6, 0x33, 0xe4, 0xb3, 0x1c, 0x9b, 0x15, 0x41, 0x92, 0x72, 0x59, 0x52, 0x33, 0xab, 0xb0, 0xd5, 0x92, 0x18, 0x62, 0x6a, + /* (2^ 21)P */ 0xcb, 0xcd, 0x55, 0x75, 0x38, 0x4a, 0xb7, 0x20, 0x3f, 0x92, 0x08, 0x12, 0x0e, 0xa1, 0x2a, 0x53, 0xd1, 0x1d, 0x28, 0x62, 0x77, 0x7b, 0xa1, 0xea, 0xbf, 0x44, 0x5c, 0xf0, 0x43, 0x34, 0xab, 0x61, + /* (2^ 22)P */ 0xf8, 0xde, 0x24, 0x23, 0x42, 0x6c, 0x7a, 0x25, 0x7f, 0xcf, 0xe3, 0x17, 0x10, 0x6c, 0x1c, 0x13, 0x57, 0xa2, 0x30, 0xf6, 0x39, 0x87, 0x75, 0x23, 0x80, 0x85, 0xa7, 0x01, 0x7a, 0x40, 0x5a, 0x29, + /* (2^ 23)P */ 0xd9, 0xa8, 0x5d, 0x6d, 0x24, 0x43, 0xc4, 0xf8, 0x5d, 0xfa, 0x52, 0x0c, 0x45, 0x75, 0xd7, 0x19, 0x3d, 0xf8, 0x1b, 0x73, 0x92, 0xfc, 0xfc, 0x2a, 0x00, 0x47, 0x2b, 0x1b, 0xe8, 0xc8, 0x10, 0x7d, + /* (2^ 24)P */ 0x0b, 0xa2, 0xba, 0x70, 0x1f, 0x27, 0xe0, 0xc8, 0x57, 0x39, 0xa6, 0x7c, 0x86, 0x48, 0x37, 0x99, 0xbb, 0xd4, 0x7e, 0xcb, 0xb3, 0xef, 0x12, 0x54, 0x75, 0x29, 0xe6, 0x73, 0x61, 0xd3, 0x96, 0x31, + /* (2^ 25)P */ 0xfc, 0xdf, 0xc7, 0x41, 0xd1, 0xca, 0x5b, 0xde, 0x48, 0xc8, 0x95, 0xb3, 0xd2, 0x8c, 0xcc, 0x47, 0xcb, 0xf3, 0x1a, 0xe1, 0x42, 0xd9, 0x4c, 0xa3, 0xc2, 0xce, 0x4e, 0xd0, 0xf2, 0xdb, 0x56, 0x02, + /* (2^ 26)P */ 0x7f, 0x66, 0x0e, 0x4b, 0xe9, 0xb7, 0x5a, 0x87, 0x10, 0x0d, 0x85, 0xc0, 0x83, 0xdd, 0xd4, 0xca, 0x9f, 0xc7, 0x72, 0x4e, 0x8f, 0x2e, 0xf1, 0x47, 0x9b, 0xb1, 0x85, 0x8c, 0xbb, 0x87, 0x1a, 0x5f, + /* (2^ 27)P */ 0xb8, 0x51, 0x7f, 0x43, 0xb6, 0xd0, 0xe9, 0x7a, 0x65, 0x90, 0x87, 0x18, 0x55, 0xce, 0xc7, 0x12, 0xee, 0x7a, 0xf7, 0x5c, 0xfe, 0x09, 0xde, 0x2a, 0x27, 0x56, 0x2c, 0x7d, 0x2f, 0x5a, 0xa0, 0x23, + /* (2^ 28)P */ 0x9a, 0x16, 0x7c, 0xf1, 0x28, 0xe1, 0x08, 0x59, 0x2d, 0x85, 0xd0, 0x8a, 0xdd, 0x98, 0x74, 0xf7, 0x64, 0x2f, 0x10, 0xab, 0xce, 0xc4, 0xb4, 0x74, 0x45, 0x98, 0x13, 0x10, 0xdd, 0xba, 0x3a, 0x18, + /* (2^ 29)P */ 0xac, 0xaa, 0x92, 0xaa, 0x8d, 0xba, 0x65, 0xb1, 0x05, 0x67, 0x38, 0x99, 0x95, 0xef, 0xc5, 0xd5, 0xd1, 0x40, 0xfc, 0xf8, 0x0c, 0x8f, 0x2f, 0xbe, 0x14, 0x45, 0x20, 0xee, 0x35, 0xe6, 0x01, 0x27, + /* (2^ 30)P */ 0x14, 0x65, 0x15, 0x20, 0x00, 0xa8, 0x9f, 0x62, 0xce, 0xc1, 0xa8, 0x64, 0x87, 0x86, 0x23, 0xf2, 0x0e, 0x06, 0x3f, 0x0b, 0xff, 0x4f, 0x89, 0x5b, 0xfa, 0xa3, 0x08, 0xf7, 0x4c, 0x94, 0xd9, 0x60, + /* (2^ 31)P */ 0x1f, 0x20, 0x7a, 0x1c, 0x1a, 0x00, 0xea, 0xae, 0x63, 0xce, 0xe2, 0x3e, 0x63, 0x6a, 0xf1, 0xeb, 0xe1, 0x07, 0x7a, 0x4c, 0x59, 0x09, 0x77, 0x6f, 0xcb, 0x08, 0x02, 0x0d, 0x15, 0x58, 0xb9, 0x79, + /* (2^ 32)P */ 0xe7, 0x10, 0xd4, 0x01, 0x53, 0x5e, 0xb5, 0x24, 0x4d, 0xc8, 0xfd, 0xf3, 0xdf, 0x4e, 0xa3, 0xe3, 0xd8, 0x32, 0x40, 0x90, 0xe4, 0x68, 0x87, 0xd8, 0xec, 0xae, 0x3a, 0x7b, 0x42, 0x84, 0x13, 0x13, + /* (2^ 33)P */ 0x14, 0x4f, 0x23, 0x86, 0x12, 0xe5, 0x05, 0x84, 0x29, 0xc5, 0xb4, 0xad, 0x39, 0x47, 0xdc, 0x14, 0xfd, 0x4f, 0x63, 0x50, 0xb2, 0xb5, 0xa2, 0xb8, 0x93, 0xff, 0xa7, 0xd8, 0x4a, 0xa9, 0xe2, 0x2f, + /* (2^ 34)P */ 0xdd, 0xfa, 0x43, 0xe8, 0xef, 0x57, 0x5c, 0xec, 0x18, 0x99, 0xbb, 0xf0, 0x40, 0xce, 0x43, 0x28, 0x05, 0x63, 0x3d, 0xcf, 0xd6, 0x61, 0xb5, 0xa4, 0x7e, 0x77, 0xfb, 0xe8, 0xbd, 0x29, 0x36, 0x74, + /* (2^ 35)P */ 0x8f, 0x73, 0xaf, 0xbb, 0x46, 0xdd, 0x3e, 0x34, 0x51, 0xa6, 0x01, 0xb1, 0x28, 0x18, 0x98, 0xed, 0x7a, 0x79, 0x2c, 0x88, 0x0b, 0x76, 0x01, 0xa4, 0x30, 0x87, 0xc8, 0x8d, 0xe2, 0x23, 0xc2, 0x1f, + /* (2^ 36)P */ 0x0e, 0xba, 0x0f, 0xfc, 0x91, 0x4e, 0x60, 0x48, 0xa4, 0x6f, 0x2c, 0x05, 0x8f, 0xf7, 0x37, 0xb6, 0x9c, 0x23, 0xe9, 0x09, 0x3d, 0xac, 0xcc, 0x91, 0x7c, 0x68, 0x7a, 0x43, 0xd4, 0xee, 0xf7, 0x23, + /* (2^ 37)P */ 0x00, 0xd8, 0x9b, 0x8d, 0x11, 0xb1, 0x73, 0x51, 0xa7, 0xd4, 0x89, 0x31, 0xb6, 0x41, 0xd6, 0x29, 0x86, 0xc5, 0xbb, 0x88, 0x79, 0x17, 0xbf, 0xfd, 0xf5, 0x1d, 0xd8, 0xca, 0x4f, 0x89, 0x59, 0x29, + /* (2^ 38)P */ 0x99, 0xc8, 0xbb, 0xb4, 0xf3, 0x8e, 0xbc, 0xae, 0xb9, 0x92, 0x69, 0xb2, 0x5a, 0x99, 0x48, 0x41, 0xfb, 0x2c, 0xf9, 0x34, 0x01, 0x0b, 0xe2, 0x24, 0xe8, 0xde, 0x05, 0x4a, 0x89, 0x58, 0xd1, 0x40, + /* (2^ 39)P */ 0xf6, 0x76, 0xaf, 0x85, 0x11, 0x0b, 0xb0, 0x46, 0x79, 0x7a, 0x18, 0x73, 0x78, 0xc7, 0xba, 0x26, 0x5f, 0xff, 0x8f, 0xab, 0x95, 0xbf, 0xc0, 0x3d, 0xd7, 0x24, 0x55, 0x94, 0xd8, 0x8b, 0x60, 0x2a, + /* (2^ 40)P */ 0x02, 0x63, 0x44, 0xbd, 0x88, 0x95, 0x44, 0x26, 0x9c, 0x43, 0x88, 0x03, 0x1c, 0xc2, 0x4b, 0x7c, 0xb2, 0x11, 0xbd, 0x83, 0xf3, 0xa4, 0x98, 0x8e, 0xb9, 0x76, 0xd8, 0xc9, 0x7b, 0x8d, 0x21, 0x26, + /* (2^ 41)P */ 0x8a, 0x17, 0x7c, 0x99, 0x42, 0x15, 0x08, 0xe3, 0x6f, 0x60, 0xb6, 0x6f, 0xa8, 0x29, 0x2d, 0x3c, 0x74, 0x93, 0x27, 0xfa, 0x36, 0x77, 0x21, 0x5c, 0xfa, 0xb1, 0xfe, 0x4a, 0x73, 0x05, 0xde, 0x7d, + /* (2^ 42)P */ 0xab, 0x2b, 0xd4, 0x06, 0x39, 0x0e, 0xf1, 0x3b, 0x9c, 0x64, 0x80, 0x19, 0x3e, 0x80, 0xf7, 0xe4, 0x7a, 0xbf, 0x95, 0x95, 0xf8, 0x3b, 0x05, 0xe6, 0x30, 0x55, 0x24, 0xda, 0x38, 0xaf, 0x4f, 0x39, + /* (2^ 43)P */ 0xf4, 0x28, 0x69, 0x89, 0x58, 0xfb, 0x8e, 0x7a, 0x3c, 0x11, 0x6a, 0xcc, 0xe9, 0x78, 0xc7, 0xfb, 0x6f, 0x59, 0xaf, 0x30, 0xe3, 0x0c, 0x67, 0x72, 0xf7, 0x6c, 0x3d, 0x1d, 0xa8, 0x22, 0xf2, 0x48, + /* (2^ 44)P */ 0xa7, 0xca, 0x72, 0x0d, 0x41, 0xce, 0x1f, 0xf0, 0x95, 0x55, 0x3b, 0x21, 0xc7, 0xec, 0x20, 0x5a, 0x83, 0x14, 0xfa, 0xc1, 0x65, 0x11, 0xc2, 0x7b, 0x41, 0xa7, 0xa8, 0x1d, 0xe3, 0x9a, 0xf8, 0x07, + /* (2^ 45)P */ 0xf9, 0x0f, 0x83, 0xc6, 0xb4, 0xc2, 0xd2, 0x05, 0x93, 0x62, 0x31, 0xc6, 0x0f, 0x33, 0x3e, 0xd4, 0x04, 0xa9, 0xd3, 0x96, 0x0a, 0x59, 0xa5, 0xa5, 0xb6, 0x33, 0x53, 0xa6, 0x91, 0xdb, 0x5e, 0x70, + /* (2^ 46)P */ 0xf7, 0xa5, 0xb9, 0x0b, 0x5e, 0xe1, 0x8e, 0x04, 0x5d, 0xaf, 0x0a, 0x9e, 0xca, 0xcf, 0x40, 0x32, 0x0b, 0xa4, 0xc4, 0xed, 0xce, 0x71, 0x4b, 0x8f, 0x6d, 0x4a, 0x54, 0xde, 0xa3, 0x0d, 0x1c, 0x62, + /* (2^ 47)P */ 0x91, 0x40, 0x8c, 0xa0, 0x36, 0x28, 0x87, 0x92, 0x45, 0x14, 0xc9, 0x10, 0xb0, 0x75, 0x83, 0xce, 0x94, 0x63, 0x27, 0x4f, 0x52, 0xeb, 0x72, 0x8a, 0x35, 0x36, 0xc8, 0x7e, 0xfa, 0xfc, 0x67, 0x26, + /* (2^ 48)P */ 0x2a, 0x75, 0xe8, 0x45, 0x33, 0x17, 0x4c, 0x7f, 0xa5, 0x79, 0x70, 0xee, 0xfe, 0x47, 0x1b, 0x06, 0x34, 0xff, 0x86, 0x9f, 0xfa, 0x9a, 0xdd, 0x25, 0x9c, 0xc8, 0x5d, 0x42, 0xf5, 0xce, 0x80, 0x37, + /* (2^ 49)P */ 0xe9, 0xb4, 0x3b, 0x51, 0x5a, 0x03, 0x46, 0x1a, 0xda, 0x5a, 0x57, 0xac, 0x79, 0xf3, 0x1e, 0x3e, 0x50, 0x4b, 0xa2, 0x5f, 0x1c, 0x5f, 0x8c, 0xc7, 0x22, 0x9f, 0xfd, 0x34, 0x76, 0x96, 0x1a, 0x32, + /* (2^ 50)P */ 0xfa, 0x27, 0x6e, 0x82, 0xb8, 0x07, 0x67, 0x94, 0xd0, 0x6f, 0x50, 0x4c, 0xd6, 0x84, 0xca, 0x3d, 0x36, 0x14, 0xe9, 0x75, 0x80, 0x21, 0x89, 0xc1, 0x84, 0x84, 0x3b, 0x9b, 0x16, 0x84, 0x92, 0x6d, + /* (2^ 51)P */ 0xdf, 0x2d, 0x3f, 0x38, 0x40, 0xe8, 0x67, 0x3a, 0x75, 0x9b, 0x4f, 0x0c, 0xa3, 0xc9, 0xee, 0x33, 0x47, 0xef, 0x83, 0xa7, 0x6f, 0xc8, 0xc7, 0x3e, 0xc4, 0xfb, 0xc9, 0xba, 0x9f, 0x44, 0xec, 0x26, + /* (2^ 52)P */ 0x7d, 0x9e, 0x9b, 0xa0, 0xcb, 0x38, 0x0f, 0x5c, 0x8c, 0x47, 0xa3, 0x62, 0xc7, 0x8c, 0x16, 0x81, 0x1c, 0x12, 0xfc, 0x06, 0xd3, 0xb0, 0x23, 0x3e, 0xdd, 0xdc, 0xef, 0xa5, 0xa0, 0x8a, 0x23, 0x5a, + /* (2^ 53)P */ 0xff, 0x43, 0xea, 0xc4, 0x21, 0x61, 0xa2, 0x1b, 0xb5, 0x32, 0x88, 0x7c, 0x7f, 0xc7, 0xf8, 0x36, 0x9a, 0xf9, 0xdc, 0x0a, 0x0b, 0xea, 0xfb, 0x88, 0xf9, 0xeb, 0x5b, 0xc2, 0x8e, 0x93, 0xa9, 0x5c, + /* (2^ 54)P */ 0xa0, 0xcd, 0xfc, 0x51, 0x5e, 0x6a, 0x43, 0xd5, 0x3b, 0x89, 0xcd, 0xc2, 0x97, 0x47, 0xbc, 0x1d, 0x08, 0x4a, 0x22, 0xd3, 0x65, 0x6a, 0x34, 0x19, 0x66, 0xf4, 0x9a, 0x9b, 0xe4, 0x34, 0x50, 0x0f, + /* (2^ 55)P */ 0x6e, 0xb9, 0xe0, 0xa1, 0x67, 0x39, 0x3c, 0xf2, 0x88, 0x4d, 0x7a, 0x86, 0xfa, 0x08, 0x8b, 0xe5, 0x79, 0x16, 0x34, 0xa7, 0xc6, 0xab, 0x2f, 0xfb, 0x46, 0x69, 0x02, 0xb6, 0x1e, 0x38, 0x75, 0x2a, + /* (2^ 56)P */ 0xac, 0x20, 0x94, 0xc1, 0xe4, 0x3b, 0x0a, 0xc8, 0xdc, 0xb6, 0xf2, 0x81, 0xc6, 0xf6, 0xb1, 0x66, 0x88, 0x33, 0xe9, 0x61, 0x67, 0x03, 0xf7, 0x7c, 0xc4, 0xa4, 0x60, 0xa6, 0xd8, 0xbb, 0xab, 0x25, + /* (2^ 57)P */ 0x98, 0x51, 0xfd, 0x14, 0xba, 0x12, 0xea, 0x91, 0xa9, 0xff, 0x3c, 0x4a, 0xfc, 0x50, 0x49, 0x68, 0x28, 0xad, 0xf5, 0x30, 0x21, 0x84, 0x26, 0xf8, 0x41, 0xa4, 0x01, 0x53, 0xf7, 0x88, 0xa9, 0x3e, + /* (2^ 58)P */ 0x6f, 0x8c, 0x5f, 0x69, 0x9a, 0x10, 0x78, 0xc9, 0xf3, 0xc3, 0x30, 0x05, 0x4a, 0xeb, 0x46, 0x17, 0x95, 0x99, 0x45, 0xb4, 0x77, 0x6d, 0x4d, 0x44, 0xc7, 0x5c, 0x4e, 0x05, 0x8c, 0x2b, 0x95, 0x75, + /* (2^ 59)P */ 0xaa, 0xd6, 0xf4, 0x15, 0x79, 0x3f, 0x70, 0xa3, 0xd8, 0x47, 0x26, 0x2f, 0x20, 0x46, 0xc3, 0x66, 0x4b, 0x64, 0x1d, 0x81, 0xdf, 0x69, 0x14, 0xd0, 0x1f, 0xd7, 0xa5, 0x81, 0x7d, 0xa4, 0xfe, 0x77, + /* (2^ 60)P */ 0x81, 0xa3, 0x7c, 0xf5, 0x9e, 0x52, 0xe9, 0xc5, 0x1a, 0x88, 0x2f, 0xce, 0xb9, 0xb4, 0xee, 0x6e, 0xd6, 0x9b, 0x00, 0xe8, 0x28, 0x1a, 0xe9, 0xb6, 0xec, 0x3f, 0xfc, 0x9a, 0x3e, 0xbe, 0x80, 0x4b, + /* (2^ 61)P */ 0xc5, 0xd2, 0xae, 0x26, 0xc5, 0x73, 0x37, 0x7e, 0x9d, 0xa4, 0xc9, 0x53, 0xb4, 0xfc, 0x4a, 0x1b, 0x4d, 0xb2, 0xff, 0xba, 0xd7, 0xbd, 0x20, 0xa9, 0x0e, 0x40, 0x2d, 0x12, 0x9f, 0x69, 0x54, 0x7c, + /* (2^ 62)P */ 0xc8, 0x4b, 0xa9, 0x4f, 0xe1, 0xc8, 0x46, 0xef, 0x5e, 0xed, 0x52, 0x29, 0xce, 0x74, 0xb0, 0xe0, 0xd5, 0x85, 0xd8, 0xdb, 0xe1, 0x50, 0xa4, 0xbe, 0x2c, 0x71, 0x0f, 0x32, 0x49, 0x86, 0xb6, 0x61, + /* (2^ 63)P */ 0xd1, 0xbd, 0xcc, 0x09, 0x73, 0x5f, 0x48, 0x8a, 0x2d, 0x1a, 0x4d, 0x7d, 0x0d, 0x32, 0x06, 0xbd, 0xf4, 0xbe, 0x2d, 0x32, 0x73, 0x29, 0x23, 0x25, 0x70, 0xf7, 0x17, 0x8c, 0x75, 0xc4, 0x5d, 0x44, + /* (2^ 64)P */ 0x3c, 0x93, 0xc8, 0x7c, 0x17, 0x34, 0x04, 0xdb, 0x9f, 0x05, 0xea, 0x75, 0x21, 0xe8, 0x6f, 0xed, 0x34, 0xdb, 0x53, 0xc0, 0xfd, 0xbe, 0xfe, 0x1e, 0x99, 0xaf, 0x5d, 0xc6, 0x67, 0xe8, 0xdb, 0x4a, + /* (2^ 65)P */ 0xdf, 0x09, 0x06, 0xa9, 0xa2, 0x71, 0xcd, 0x3a, 0x50, 0x40, 0xd0, 0x6d, 0x85, 0x91, 0xe9, 0xe5, 0x3c, 0xc2, 0x57, 0x81, 0x68, 0x9b, 0xc6, 0x1e, 0x4d, 0xfe, 0x5c, 0x88, 0xf6, 0x27, 0x74, 0x69, + /* (2^ 66)P */ 0x51, 0xa8, 0xe1, 0x65, 0x9b, 0x7b, 0xbe, 0xd7, 0xdd, 0x36, 0xc5, 0x22, 0xd5, 0x28, 0x3d, 0xa0, 0x45, 0xb6, 0xd2, 0x8f, 0x65, 0x9d, 0x39, 0x28, 0xe1, 0x41, 0x26, 0x7c, 0xe1, 0xb7, 0xe5, 0x49, + /* (2^ 67)P */ 0xa4, 0x57, 0x04, 0x70, 0x98, 0x3a, 0x8c, 0x6f, 0x78, 0x67, 0xbb, 0x5e, 0xa2, 0xf0, 0x78, 0x50, 0x0f, 0x96, 0x82, 0xc3, 0xcb, 0x3c, 0x3c, 0xd1, 0xb1, 0x84, 0xdf, 0xa7, 0x58, 0x32, 0x00, 0x2e, + /* (2^ 68)P */ 0x1c, 0x6a, 0x29, 0xe6, 0x9b, 0xf3, 0xd1, 0x8a, 0xb2, 0xbf, 0x5f, 0x2a, 0x65, 0xaa, 0xee, 0xc1, 0xcb, 0xf3, 0x26, 0xfd, 0x73, 0x06, 0xee, 0x33, 0xcc, 0x2c, 0x9d, 0xa6, 0x73, 0x61, 0x25, 0x59, + /* (2^ 69)P */ 0x41, 0xfc, 0x18, 0x4e, 0xaa, 0x07, 0xea, 0x41, 0x1e, 0xa5, 0x87, 0x7c, 0x52, 0x19, 0xfc, 0xd9, 0x6f, 0xca, 0x31, 0x58, 0x80, 0xcb, 0xaa, 0xbd, 0x4f, 0x69, 0x16, 0xc9, 0x2d, 0x65, 0x5b, 0x44, + /* (2^ 70)P */ 0x15, 0x23, 0x17, 0xf2, 0xa7, 0xa3, 0x92, 0xce, 0x64, 0x99, 0x1b, 0xe1, 0x2d, 0x28, 0xdc, 0x1e, 0x4a, 0x31, 0x4c, 0xe0, 0xaf, 0x3a, 0x82, 0xa1, 0x86, 0xf5, 0x7c, 0x43, 0x94, 0x2d, 0x0a, 0x79, + /* (2^ 71)P */ 0x09, 0xe0, 0xf6, 0x93, 0xfb, 0x47, 0xc4, 0x71, 0x76, 0x52, 0x84, 0x22, 0x67, 0xa5, 0x22, 0x89, 0x69, 0x51, 0x4f, 0x20, 0x3b, 0x90, 0x70, 0xbf, 0xfe, 0x19, 0xa3, 0x1b, 0x89, 0x89, 0x7a, 0x2f, + /* (2^ 72)P */ 0x0c, 0x14, 0xe2, 0x77, 0xb5, 0x8e, 0xa0, 0x02, 0xf4, 0xdc, 0x7b, 0x42, 0xd4, 0x4e, 0x9a, 0xed, 0xd1, 0x3c, 0x32, 0xe4, 0x44, 0xec, 0x53, 0x52, 0x5b, 0x35, 0xe9, 0x14, 0x3c, 0x36, 0x88, 0x3e, + /* (2^ 73)P */ 0x8c, 0x0b, 0x11, 0x77, 0x42, 0xc1, 0x66, 0xaa, 0x90, 0x33, 0xa2, 0x10, 0x16, 0x39, 0xe0, 0x1a, 0xa2, 0xc2, 0x3f, 0xc9, 0x12, 0xbd, 0x30, 0x20, 0xab, 0xc7, 0x55, 0x95, 0x57, 0x41, 0xe1, 0x3e, + /* (2^ 74)P */ 0x41, 0x7d, 0x6e, 0x6d, 0x3a, 0xde, 0x14, 0x92, 0xfe, 0x7e, 0xf1, 0x07, 0x86, 0xd8, 0xcd, 0x3c, 0x17, 0x12, 0xe1, 0xf8, 0x88, 0x12, 0x4f, 0x67, 0xd0, 0x93, 0x9f, 0x32, 0x0f, 0x25, 0x82, 0x56, + /* (2^ 75)P */ 0x6e, 0x39, 0x2e, 0x6d, 0x13, 0x0b, 0xf0, 0x6c, 0xbf, 0xde, 0x14, 0x10, 0x6f, 0xf8, 0x4c, 0x6e, 0x83, 0x4e, 0xcc, 0xbf, 0xb5, 0xb1, 0x30, 0x59, 0xb6, 0x16, 0xba, 0x8a, 0xb4, 0x69, 0x70, 0x04, + /* (2^ 76)P */ 0x93, 0x07, 0xb2, 0x69, 0xab, 0xe4, 0x4c, 0x0d, 0x9e, 0xfb, 0xd0, 0x97, 0x1a, 0xb9, 0x4d, 0xb2, 0x1d, 0xd0, 0x00, 0x4e, 0xf5, 0x50, 0xfa, 0xcd, 0xb5, 0xdd, 0x8b, 0x36, 0x85, 0x10, 0x1b, 0x22, + /* (2^ 77)P */ 0xd2, 0xd8, 0xe3, 0xb1, 0x68, 0x94, 0xe5, 0xe7, 0x93, 0x2f, 0x12, 0xbd, 0x63, 0x65, 0xc5, 0x53, 0x09, 0x3f, 0x66, 0xe0, 0x03, 0xa9, 0xe8, 0xee, 0x42, 0x3d, 0xbe, 0xcb, 0x62, 0xa6, 0xef, 0x61, + /* (2^ 78)P */ 0x2a, 0xab, 0x6e, 0xde, 0xdd, 0xdd, 0xf8, 0x2c, 0x31, 0xf2, 0x35, 0x14, 0xd5, 0x0a, 0xf8, 0x9b, 0x73, 0x49, 0xf0, 0xc9, 0xce, 0xda, 0xea, 0x5d, 0x27, 0x9b, 0xd2, 0x41, 0x5d, 0x5b, 0x27, 0x29, + /* (2^ 79)P */ 0x4f, 0xf1, 0xeb, 0x95, 0x08, 0x0f, 0xde, 0xcf, 0xa7, 0x05, 0x49, 0x05, 0x6b, 0xb9, 0xaa, 0xb9, 0xfd, 0x20, 0xc4, 0xa1, 0xd9, 0x0d, 0xe8, 0xca, 0xc7, 0xbb, 0x73, 0x16, 0x2f, 0xbf, 0x63, 0x0a, + /* (2^ 80)P */ 0x8c, 0xbc, 0x8f, 0x95, 0x11, 0x6e, 0x2f, 0x09, 0xad, 0x2f, 0x82, 0x04, 0xe8, 0x81, 0x2a, 0x67, 0x17, 0x25, 0xd5, 0x60, 0x15, 0x35, 0xc8, 0xca, 0xf8, 0x92, 0xf1, 0xc8, 0x22, 0x77, 0x3f, 0x6f, + /* (2^ 81)P */ 0xb7, 0x94, 0xe8, 0xc2, 0xcc, 0x90, 0xba, 0xf8, 0x0d, 0x9f, 0xff, 0x38, 0xa4, 0x57, 0x75, 0x2c, 0x59, 0x23, 0xe5, 0x5a, 0x85, 0x1d, 0x4d, 0x89, 0x69, 0x3d, 0x74, 0x7b, 0x15, 0x22, 0xe1, 0x68, + /* (2^ 82)P */ 0xf3, 0x19, 0xb9, 0xcf, 0x70, 0x55, 0x7e, 0xd8, 0xb9, 0x8d, 0x79, 0x95, 0xcd, 0xde, 0x2c, 0x3f, 0xce, 0xa2, 0xc0, 0x10, 0x47, 0x15, 0x21, 0x21, 0xb2, 0xc5, 0x6d, 0x24, 0x15, 0xa1, 0x66, 0x3c, + /* (2^ 83)P */ 0x72, 0xcb, 0x4e, 0x29, 0x62, 0xc5, 0xed, 0xcb, 0x16, 0x0b, 0x28, 0x6a, 0xc3, 0x43, 0x71, 0xba, 0x67, 0x8b, 0x07, 0xd4, 0xef, 0xc2, 0x10, 0x96, 0x1e, 0x4b, 0x6a, 0x94, 0x5d, 0x73, 0x44, 0x61, + /* (2^ 84)P */ 0x50, 0x33, 0x5b, 0xd7, 0x1e, 0x11, 0x6f, 0x53, 0x1b, 0xd8, 0x41, 0x20, 0x8c, 0xdb, 0x11, 0x02, 0x3c, 0x41, 0x10, 0x0e, 0x00, 0xb1, 0x3c, 0xf9, 0x76, 0x88, 0x9e, 0x03, 0x3c, 0xfd, 0x9d, 0x14, + /* (2^ 85)P */ 0x5b, 0x15, 0x63, 0x6b, 0xe4, 0xdd, 0x79, 0xd4, 0x76, 0x79, 0x83, 0x3c, 0xe9, 0x15, 0x6e, 0xb6, 0x38, 0xe0, 0x13, 0x1f, 0x3b, 0xe4, 0xfd, 0xda, 0x35, 0x0b, 0x4b, 0x2e, 0x1a, 0xda, 0xaf, 0x5f, + /* (2^ 86)P */ 0x81, 0x75, 0x19, 0x17, 0xdf, 0xbb, 0x00, 0x36, 0xc2, 0xd2, 0x3c, 0xbe, 0x0b, 0x05, 0x72, 0x39, 0x86, 0xbe, 0xd5, 0xbd, 0x6d, 0x90, 0x38, 0x59, 0x0f, 0x86, 0x9b, 0x3f, 0xe4, 0xe5, 0xfc, 0x34, + /* (2^ 87)P */ 0x02, 0x4d, 0xd1, 0x42, 0xcd, 0xa4, 0xa8, 0x75, 0x65, 0xdf, 0x41, 0x34, 0xc5, 0xab, 0x8d, 0x82, 0xd3, 0x31, 0xe1, 0xd2, 0xed, 0xab, 0xdc, 0x33, 0x5f, 0xd2, 0x14, 0xb8, 0x6f, 0xd7, 0xba, 0x3e, + /* (2^ 88)P */ 0x0f, 0xe1, 0x70, 0x6f, 0x56, 0x6f, 0x90, 0xd4, 0x5a, 0x0f, 0x69, 0x51, 0xaa, 0xf7, 0x12, 0x5d, 0xf2, 0xfc, 0xce, 0x76, 0x6e, 0xb1, 0xad, 0x45, 0x99, 0x29, 0x23, 0xad, 0xae, 0x68, 0xf7, 0x01, + /* (2^ 89)P */ 0xbd, 0xfe, 0x48, 0x62, 0x7b, 0xc7, 0x6c, 0x2b, 0xfd, 0xaf, 0x3a, 0xec, 0x28, 0x06, 0xd3, 0x3c, 0x6a, 0x48, 0xef, 0xd4, 0x80, 0x0b, 0x1c, 0xce, 0x23, 0x6c, 0xf6, 0xa6, 0x2e, 0xff, 0x3b, 0x4c, + /* (2^ 90)P */ 0x5f, 0xeb, 0xea, 0x4a, 0x09, 0xc4, 0x2e, 0x3f, 0xa7, 0x2c, 0x37, 0x6e, 0x28, 0x9b, 0xb1, 0x61, 0x1d, 0x70, 0x2a, 0xde, 0x66, 0xa9, 0xef, 0x5e, 0xef, 0xe3, 0x55, 0xde, 0x65, 0x05, 0xb2, 0x23, + /* (2^ 91)P */ 0x57, 0x85, 0xd5, 0x79, 0x52, 0xca, 0x01, 0xe3, 0x4f, 0x87, 0xc2, 0x27, 0xce, 0xd4, 0xb2, 0x07, 0x67, 0x1d, 0xcf, 0x9d, 0x8a, 0xcd, 0x32, 0xa5, 0x56, 0xff, 0x2b, 0x3f, 0xe2, 0xfe, 0x52, 0x2a, + /* (2^ 92)P */ 0x3d, 0x66, 0xd8, 0x7c, 0xb3, 0xef, 0x24, 0x86, 0x94, 0x75, 0xbd, 0xff, 0x20, 0xac, 0xc7, 0xbb, 0x45, 0x74, 0xd3, 0x82, 0x9c, 0x5e, 0xb8, 0x57, 0x66, 0xec, 0xa6, 0x86, 0xcb, 0x52, 0x30, 0x7b, + /* (2^ 93)P */ 0x1e, 0xe9, 0x25, 0x25, 0xad, 0xf0, 0x82, 0x34, 0xa0, 0xdc, 0x8e, 0xd2, 0x43, 0x80, 0xb6, 0x2c, 0x3a, 0x00, 0x1b, 0x2e, 0x05, 0x6d, 0x4f, 0xaf, 0x0a, 0x1b, 0x78, 0x29, 0x25, 0x8c, 0x5f, 0x18, + /* (2^ 94)P */ 0xd6, 0xe0, 0x0c, 0xd8, 0x5b, 0xde, 0x41, 0xaa, 0xd6, 0xe9, 0x53, 0x68, 0x41, 0xb2, 0x07, 0x94, 0x3a, 0x4c, 0x7f, 0x35, 0x6e, 0xc3, 0x3e, 0x56, 0xce, 0x7b, 0x29, 0x0e, 0xdd, 0xb8, 0xc4, 0x4c, + /* (2^ 95)P */ 0x0e, 0x73, 0xb8, 0xff, 0x52, 0x1a, 0xfc, 0xa2, 0x37, 0x8e, 0x05, 0x67, 0x6e, 0xf1, 0x11, 0x18, 0xe1, 0x4e, 0xdf, 0xcd, 0x66, 0xa3, 0xf9, 0x10, 0x99, 0xf0, 0xb9, 0xa0, 0xc4, 0xa0, 0xf4, 0x72, + /* (2^ 96)P */ 0xa7, 0x4e, 0x3f, 0x66, 0x6f, 0xc0, 0x16, 0x8c, 0xba, 0x0f, 0x97, 0x4e, 0xf7, 0x3a, 0x3b, 0x69, 0x45, 0xc3, 0x9e, 0xd6, 0xf1, 0xe7, 0x02, 0x21, 0x89, 0x80, 0x8a, 0x96, 0xbc, 0x3c, 0xa5, 0x0b, + /* (2^ 97)P */ 0x37, 0x55, 0xa1, 0xfe, 0xc7, 0x9d, 0x3d, 0xca, 0x93, 0x64, 0x53, 0x51, 0xbb, 0x24, 0x68, 0x4c, 0xb1, 0x06, 0x40, 0x84, 0x14, 0x63, 0x88, 0xb9, 0x60, 0xcc, 0x54, 0xb4, 0x2a, 0xa7, 0xd2, 0x40, + /* (2^ 98)P */ 0x75, 0x09, 0x57, 0x12, 0xb7, 0xa1, 0x36, 0x59, 0x57, 0xa6, 0xbd, 0xde, 0x48, 0xd6, 0xb9, 0x91, 0xea, 0x30, 0x43, 0xb6, 0x4b, 0x09, 0x44, 0x33, 0xd0, 0x51, 0xee, 0x12, 0x0d, 0xa1, 0x6b, 0x00, + /* (2^ 99)P */ 0x58, 0x5d, 0xde, 0xf5, 0x68, 0x84, 0x22, 0x19, 0xb0, 0x05, 0xcc, 0x38, 0x4c, 0x2f, 0xb1, 0x0e, 0x90, 0x19, 0x60, 0xd5, 0x9d, 0x9f, 0x03, 0xa1, 0x0b, 0x0e, 0xff, 0x4f, 0xce, 0xd4, 0x02, 0x45, + /* (2^100)P */ 0x89, 0xc1, 0x37, 0x68, 0x10, 0x54, 0x20, 0xeb, 0x3c, 0xb9, 0xd3, 0x6d, 0x4c, 0x54, 0xf6, 0xd0, 0x4f, 0xd7, 0x16, 0xc4, 0x64, 0x70, 0x72, 0x40, 0xf0, 0x2e, 0x50, 0x4b, 0x11, 0xc6, 0x15, 0x6e, + /* (2^101)P */ 0x6b, 0xa7, 0xb1, 0xcf, 0x98, 0xa3, 0xf2, 0x4d, 0xb1, 0xf6, 0xf2, 0x19, 0x74, 0x6c, 0x25, 0x11, 0x43, 0x60, 0x6e, 0x06, 0x62, 0x79, 0x49, 0x4a, 0x44, 0x5b, 0x35, 0x41, 0xab, 0x3a, 0x5b, 0x70, + /* (2^102)P */ 0xd8, 0xb1, 0x97, 0xd7, 0x36, 0xf5, 0x5e, 0x36, 0xdb, 0xf0, 0xdd, 0x22, 0xd6, 0x6b, 0x07, 0x00, 0x88, 0x5a, 0x57, 0xe0, 0xb0, 0x33, 0xbf, 0x3b, 0x4d, 0xca, 0xe4, 0xc8, 0x05, 0xaa, 0x77, 0x37, + /* (2^103)P */ 0x5f, 0xdb, 0x78, 0x55, 0xc8, 0x45, 0x27, 0x39, 0xe2, 0x5a, 0xae, 0xdb, 0x49, 0x41, 0xda, 0x6f, 0x67, 0x98, 0xdc, 0x8a, 0x0b, 0xb0, 0xf0, 0xb1, 0xa3, 0x1d, 0x6f, 0xd3, 0x37, 0x34, 0x96, 0x09, + /* (2^104)P */ 0x53, 0x38, 0xdc, 0xa5, 0x90, 0x4e, 0x82, 0x7e, 0xbd, 0x5c, 0x13, 0x1f, 0x64, 0xf6, 0xb5, 0xcc, 0xcc, 0x8f, 0xce, 0x87, 0x6c, 0xd8, 0x36, 0x67, 0x9f, 0x24, 0x04, 0x66, 0xe2, 0x3c, 0x5f, 0x62, + /* (2^105)P */ 0x3f, 0xf6, 0x02, 0x95, 0x05, 0xc8, 0x8a, 0xaf, 0x69, 0x14, 0x35, 0x2e, 0x0a, 0xe7, 0x05, 0x0c, 0x05, 0x63, 0x4b, 0x76, 0x9c, 0x2e, 0x29, 0x35, 0xc3, 0x3a, 0xe2, 0xc7, 0x60, 0x43, 0x39, 0x1a, + /* (2^106)P */ 0x64, 0x32, 0x18, 0x51, 0x32, 0xd5, 0xc6, 0xd5, 0x4f, 0xb7, 0xc2, 0x43, 0xbd, 0x5a, 0x06, 0x62, 0x9b, 0x3f, 0x97, 0x3b, 0xd0, 0xf5, 0xfb, 0xb5, 0x5e, 0x6e, 0x20, 0x61, 0x36, 0xda, 0xa3, 0x13, + /* (2^107)P */ 0xe5, 0x94, 0x5d, 0x72, 0x37, 0x58, 0xbd, 0xc6, 0xc5, 0x16, 0x50, 0x20, 0x12, 0x09, 0xe3, 0x18, 0x68, 0x3c, 0x03, 0x70, 0x15, 0xce, 0x88, 0x20, 0x87, 0x79, 0x83, 0x5c, 0x49, 0x1f, 0xba, 0x7f, + /* (2^108)P */ 0x9d, 0x07, 0xf9, 0xf2, 0x23, 0x74, 0x8c, 0x5a, 0xc5, 0x3f, 0x02, 0x34, 0x7b, 0x15, 0x35, 0x17, 0x51, 0xb3, 0xfa, 0xd2, 0x9a, 0xb4, 0xf9, 0xe4, 0x3c, 0xe3, 0x78, 0xc8, 0x72, 0xff, 0x91, 0x66, + /* (2^109)P */ 0x3e, 0xff, 0x5e, 0xdc, 0xde, 0x2a, 0x2c, 0x12, 0xf4, 0x6c, 0x95, 0xd8, 0xf1, 0x4b, 0xdd, 0xf8, 0xda, 0x5b, 0x9e, 0x9e, 0x5d, 0x20, 0x86, 0xeb, 0x43, 0xc7, 0x75, 0xd9, 0xb9, 0x92, 0x9b, 0x04, + /* (2^110)P */ 0x5a, 0xc0, 0xf6, 0xb0, 0x30, 0x97, 0x37, 0xa5, 0x53, 0xa5, 0xf3, 0xc6, 0xac, 0xff, 0xa0, 0x72, 0x6d, 0xcd, 0x0d, 0xb2, 0x34, 0x2c, 0x03, 0xb0, 0x4a, 0x16, 0xd5, 0x88, 0xbc, 0x9d, 0x0e, 0x47, + /* (2^111)P */ 0x47, 0xc0, 0x37, 0xa2, 0x0c, 0xf1, 0x9c, 0xb1, 0xa2, 0x81, 0x6c, 0x1f, 0x71, 0x66, 0x54, 0xb6, 0x43, 0x0b, 0xd8, 0x6d, 0xd1, 0x1b, 0x32, 0xb3, 0x8e, 0xbe, 0x5f, 0x0c, 0x60, 0x4f, 0xc1, 0x48, + /* (2^112)P */ 0x03, 0xc8, 0xa6, 0x4a, 0x26, 0x1c, 0x45, 0x66, 0xa6, 0x7d, 0xfa, 0xa4, 0x04, 0x39, 0x6e, 0xb6, 0x95, 0x83, 0x12, 0xb3, 0xb0, 0x19, 0x5f, 0xd4, 0x10, 0xbc, 0xc9, 0xc3, 0x27, 0x26, 0x60, 0x31, + /* (2^113)P */ 0x0d, 0xe1, 0xe4, 0x32, 0x48, 0xdc, 0x20, 0x31, 0xf7, 0x17, 0xc7, 0x56, 0x67, 0xc4, 0x20, 0xeb, 0x94, 0x02, 0x28, 0x67, 0x3f, 0x2e, 0xf5, 0x00, 0x09, 0xc5, 0x30, 0x47, 0xc1, 0x4f, 0x6d, 0x56, + /* (2^114)P */ 0x06, 0x72, 0x83, 0xfd, 0x40, 0x5d, 0x3a, 0x7e, 0x7a, 0x54, 0x59, 0x71, 0xdc, 0x26, 0xe9, 0xc1, 0x95, 0x60, 0x8d, 0xa6, 0xfb, 0x30, 0x67, 0x21, 0xa7, 0xce, 0x69, 0x3f, 0x84, 0xc3, 0xe8, 0x22, + /* (2^115)P */ 0x2b, 0x4b, 0x0e, 0x93, 0xe8, 0x74, 0xd0, 0x33, 0x16, 0x58, 0xd1, 0x84, 0x0e, 0x35, 0xe4, 0xb6, 0x65, 0x23, 0xba, 0xd6, 0x6a, 0xc2, 0x34, 0x55, 0xf3, 0xf3, 0xf1, 0x89, 0x2f, 0xc1, 0x73, 0x77, + /* (2^116)P */ 0xaa, 0x62, 0x79, 0xa5, 0x4d, 0x40, 0xba, 0x8c, 0x56, 0xce, 0x99, 0x19, 0xa8, 0x97, 0x98, 0x5b, 0xfc, 0x92, 0x16, 0x12, 0x2f, 0x86, 0x8e, 0x50, 0x91, 0xc2, 0x93, 0xa0, 0x7f, 0x90, 0x81, 0x3a, + /* (2^117)P */ 0x10, 0xa5, 0x25, 0x47, 0xff, 0xd0, 0xde, 0x0d, 0x03, 0xc5, 0x3f, 0x67, 0x10, 0xcc, 0xd8, 0x10, 0x89, 0x4e, 0x1f, 0x9f, 0x1c, 0x15, 0x9d, 0x5b, 0x4c, 0xa4, 0x09, 0xcb, 0xd5, 0xc1, 0xa5, 0x32, + /* (2^118)P */ 0xfb, 0x41, 0x05, 0xb9, 0x42, 0xa4, 0x0a, 0x1e, 0xdb, 0x85, 0xb4, 0xc1, 0x7c, 0xeb, 0x85, 0x5f, 0xe5, 0xf2, 0x9d, 0x8a, 0xce, 0x95, 0xe5, 0xbe, 0x36, 0x22, 0x42, 0x22, 0xc7, 0x96, 0xe4, 0x25, + /* (2^119)P */ 0xb9, 0xe5, 0x0f, 0xcd, 0x46, 0x3c, 0xdf, 0x5e, 0x88, 0x33, 0xa4, 0xd2, 0x7e, 0x5a, 0xe7, 0x34, 0x52, 0xe3, 0x61, 0xd7, 0x11, 0xde, 0x88, 0xe4, 0x5c, 0x54, 0x85, 0xa0, 0x01, 0x8a, 0x87, 0x0e, + /* (2^120)P */ 0x04, 0xbb, 0x21, 0xe0, 0x77, 0x3c, 0x49, 0xba, 0x9a, 0x89, 0xdf, 0xc7, 0x43, 0x18, 0x4d, 0x2b, 0x67, 0x0d, 0xe8, 0x7a, 0x48, 0x7a, 0xa3, 0x9e, 0x94, 0x17, 0xe4, 0x11, 0x80, 0x95, 0xa9, 0x67, + /* (2^121)P */ 0x65, 0xb0, 0x97, 0x66, 0x1a, 0x05, 0x58, 0x4b, 0xd4, 0xa6, 0x6b, 0x8d, 0x7d, 0x3f, 0xe3, 0x47, 0xc1, 0x46, 0xca, 0x83, 0xd4, 0xa8, 0x4d, 0xbb, 0x0d, 0xdb, 0xc2, 0x81, 0xa1, 0xca, 0xbe, 0x68, + /* (2^122)P */ 0xa5, 0x9a, 0x98, 0x0b, 0xe9, 0x80, 0x89, 0x8d, 0x9b, 0xc9, 0x93, 0x2c, 0x4a, 0xb1, 0x5e, 0xf9, 0xa2, 0x73, 0x6e, 0x79, 0xc4, 0xc7, 0xc6, 0x51, 0x69, 0xb5, 0xef, 0xb5, 0x63, 0x83, 0x22, 0x6e, + /* (2^123)P */ 0xc8, 0x24, 0xd6, 0x2d, 0xb0, 0xc0, 0xbb, 0xc6, 0xee, 0x70, 0x81, 0xec, 0x7d, 0xb4, 0x7e, 0x77, 0xa9, 0xaf, 0xcf, 0x04, 0xa0, 0x15, 0xde, 0x3c, 0x9b, 0xbf, 0x60, 0x71, 0x08, 0xbc, 0xc6, 0x1d, + /* (2^124)P */ 0x02, 0x40, 0xc3, 0xee, 0x43, 0xe0, 0x07, 0x2e, 0x7f, 0xdc, 0x68, 0x7a, 0x67, 0xfc, 0xe9, 0x18, 0x9a, 0x5b, 0xd1, 0x8b, 0x18, 0x03, 0xda, 0xd8, 0x53, 0x82, 0x56, 0x00, 0xbb, 0xc3, 0xfb, 0x48, + /* (2^125)P */ 0xe1, 0x4c, 0x65, 0xfb, 0x4c, 0x7d, 0x54, 0x57, 0xad, 0xe2, 0x58, 0xa0, 0x82, 0x5b, 0x56, 0xd3, 0x78, 0x44, 0x15, 0xbf, 0x0b, 0xaf, 0x3e, 0xf6, 0x18, 0xbb, 0xdf, 0x14, 0xf1, 0x1e, 0x53, 0x47, + /* (2^126)P */ 0x87, 0xc5, 0x78, 0x42, 0x0a, 0x63, 0xec, 0xe1, 0xf3, 0x83, 0x8e, 0xca, 0x46, 0xd5, 0x07, 0x55, 0x2b, 0x0c, 0xdc, 0x3a, 0xc6, 0x35, 0xe1, 0x85, 0x4e, 0x84, 0x82, 0x56, 0xa8, 0xef, 0xa7, 0x0a, + /* (2^127)P */ 0x15, 0xf6, 0xe1, 0xb3, 0xa8, 0x1b, 0x69, 0x72, 0xfa, 0x3f, 0xbe, 0x1f, 0x70, 0xe9, 0xb4, 0x32, 0x68, 0x78, 0xbb, 0x39, 0x2e, 0xd9, 0xb6, 0x97, 0xe8, 0x39, 0x2e, 0xa0, 0xde, 0x53, 0xfe, 0x2c, + /* (2^128)P */ 0xb0, 0x52, 0xcd, 0x85, 0xcd, 0x92, 0x73, 0x68, 0x31, 0x98, 0xe2, 0x10, 0xc9, 0x66, 0xff, 0x27, 0x06, 0x2d, 0x83, 0xa9, 0x56, 0x45, 0x13, 0x97, 0xa0, 0xf8, 0x84, 0x0a, 0x36, 0xb0, 0x9b, 0x26, + /* (2^129)P */ 0x5c, 0xf8, 0x43, 0x76, 0x45, 0x55, 0x6e, 0x70, 0x1b, 0x7d, 0x59, 0x9b, 0x8c, 0xa4, 0x34, 0x37, 0x72, 0xa4, 0xef, 0xc6, 0xe8, 0x91, 0xee, 0x7a, 0xe0, 0xd9, 0xa9, 0x98, 0xc1, 0xab, 0xd6, 0x5c, + /* (2^130)P */ 0x1a, 0xe4, 0x3c, 0xcb, 0x06, 0xde, 0x04, 0x0e, 0x38, 0xe1, 0x02, 0x34, 0x89, 0xeb, 0xc6, 0xd8, 0x72, 0x37, 0x6e, 0x68, 0xbb, 0x59, 0x46, 0x90, 0xc8, 0xa8, 0x6b, 0x74, 0x71, 0xc3, 0x15, 0x72, + /* (2^131)P */ 0xd9, 0xa2, 0xe4, 0xea, 0x7e, 0xa9, 0x12, 0xfd, 0xc5, 0xf2, 0x94, 0x63, 0x51, 0xb7, 0x14, 0x95, 0x94, 0xf2, 0x08, 0x92, 0x80, 0xd5, 0x6f, 0x26, 0xb9, 0x26, 0x9a, 0x61, 0x85, 0x70, 0x84, 0x5c, + /* (2^132)P */ 0xea, 0x94, 0xd6, 0xfe, 0x10, 0x54, 0x98, 0x52, 0x54, 0xd2, 0x2e, 0x4a, 0x93, 0x5b, 0x90, 0x3c, 0x67, 0xe4, 0x3b, 0x2d, 0x69, 0x47, 0xbb, 0x10, 0xe1, 0xe9, 0xe5, 0x69, 0x2d, 0x3d, 0x3b, 0x06, + /* (2^133)P */ 0xeb, 0x7d, 0xa5, 0xdd, 0xee, 0x26, 0x27, 0x47, 0x91, 0x18, 0xf4, 0x10, 0xae, 0xc4, 0xb6, 0xef, 0x14, 0x76, 0x30, 0x7b, 0x91, 0x41, 0x16, 0x2b, 0x7c, 0x5b, 0xf4, 0xc4, 0x4f, 0x55, 0x7c, 0x11, + /* (2^134)P */ 0x12, 0x88, 0x9d, 0x8f, 0x11, 0xf3, 0x7c, 0xc0, 0x39, 0x79, 0x01, 0x50, 0x20, 0xd8, 0xdb, 0x01, 0x27, 0x28, 0x1b, 0x17, 0xf4, 0x03, 0xe8, 0xd7, 0xea, 0x25, 0xd2, 0x87, 0x74, 0xe8, 0x15, 0x10, + /* (2^135)P */ 0x4d, 0xcc, 0x3a, 0xd2, 0xfe, 0xe3, 0x8d, 0xc5, 0x2d, 0xbe, 0xa7, 0x94, 0xc2, 0x91, 0xdb, 0x50, 0x57, 0xf4, 0x9c, 0x1c, 0x3d, 0xd4, 0x94, 0x0b, 0x4a, 0x52, 0x37, 0x6e, 0xfa, 0x40, 0x16, 0x6b, + /* (2^136)P */ 0x09, 0x0d, 0xda, 0x5f, 0x6c, 0x34, 0x2f, 0x69, 0x51, 0x31, 0x4d, 0xfa, 0x59, 0x1c, 0x0b, 0x20, 0x96, 0xa2, 0x77, 0x07, 0x76, 0x6f, 0xc4, 0xb8, 0xcf, 0xfb, 0xfd, 0x3f, 0x5f, 0x39, 0x38, 0x4b, + /* (2^137)P */ 0x71, 0xd6, 0x54, 0xbe, 0x00, 0x5e, 0xd2, 0x18, 0xa6, 0xab, 0xc8, 0xbe, 0x82, 0x05, 0xd5, 0x60, 0x82, 0xb9, 0x78, 0x3b, 0x26, 0x8f, 0xad, 0x87, 0x32, 0x04, 0xda, 0x9c, 0x4e, 0xf6, 0xfd, 0x50, + /* (2^138)P */ 0xf0, 0xdc, 0x78, 0xc5, 0xaa, 0x67, 0xf5, 0x90, 0x3b, 0x13, 0xa3, 0xf2, 0x0e, 0x9b, 0x1e, 0xef, 0x71, 0xde, 0xd9, 0x42, 0x92, 0xba, 0xeb, 0x0e, 0xc7, 0x01, 0x31, 0xf0, 0x9b, 0x3c, 0x47, 0x15, + /* (2^139)P */ 0x95, 0x80, 0xb7, 0x56, 0xae, 0xe8, 0x77, 0x7c, 0x8e, 0x07, 0x6f, 0x6e, 0x66, 0xe7, 0x78, 0xb6, 0x1f, 0xba, 0x48, 0x53, 0x61, 0xb9, 0xa0, 0x2d, 0x0b, 0x3f, 0x73, 0xff, 0xc1, 0x31, 0xf9, 0x7c, + /* (2^140)P */ 0x6c, 0x36, 0x0a, 0x0a, 0xf5, 0x57, 0xb3, 0x26, 0x32, 0xd7, 0x87, 0x2b, 0xf4, 0x8c, 0x70, 0xe9, 0xc0, 0xb2, 0x1c, 0xf9, 0xa5, 0xee, 0x3a, 0xc1, 0x4c, 0xbb, 0x43, 0x11, 0x99, 0x0c, 0xd9, 0x35, + /* (2^141)P */ 0xdc, 0xd9, 0xa0, 0xa9, 0x04, 0xc4, 0xc1, 0x47, 0x51, 0xd2, 0x72, 0x19, 0x45, 0x58, 0x9e, 0x65, 0x31, 0x8c, 0xb3, 0x73, 0xc4, 0xa8, 0x75, 0x38, 0x24, 0x1f, 0x56, 0x79, 0xd3, 0x9e, 0xbd, 0x1f, + /* (2^142)P */ 0x8d, 0xc2, 0x1e, 0xd4, 0x6f, 0xbc, 0xfa, 0x11, 0xca, 0x2d, 0x2a, 0xcd, 0xe3, 0xdf, 0xf8, 0x7e, 0x95, 0x45, 0x40, 0x8c, 0x5d, 0x3b, 0xe7, 0x72, 0x27, 0x2f, 0xb7, 0x54, 0x49, 0xfa, 0x35, 0x61, + /* (2^143)P */ 0x9c, 0xb6, 0x24, 0xde, 0xa2, 0x32, 0xfc, 0xcc, 0x88, 0x5d, 0x09, 0x1f, 0x8c, 0x69, 0x55, 0x3f, 0x29, 0xf9, 0xc3, 0x5a, 0xed, 0x50, 0x33, 0xbe, 0xeb, 0x7e, 0x47, 0xca, 0x06, 0xf8, 0x9b, 0x5e, + /* (2^144)P */ 0x68, 0x9f, 0x30, 0x3c, 0xb6, 0x8f, 0xce, 0xe9, 0xf4, 0xf9, 0xe1, 0x65, 0x35, 0xf6, 0x76, 0x53, 0xf1, 0x93, 0x63, 0x5a, 0xb3, 0xcf, 0xaf, 0xd1, 0x06, 0x35, 0x62, 0xe5, 0xed, 0xa1, 0x32, 0x66, + /* (2^145)P */ 0x4c, 0xed, 0x2d, 0x0c, 0x39, 0x6c, 0x7d, 0x0b, 0x1f, 0xcb, 0x04, 0xdf, 0x81, 0x32, 0xcb, 0x56, 0xc7, 0xc3, 0xec, 0x49, 0x12, 0x5a, 0x30, 0x66, 0x2a, 0xa7, 0x8c, 0xa3, 0x60, 0x8b, 0x58, 0x5d, + /* (2^146)P */ 0x2d, 0xf4, 0xe5, 0xe8, 0x78, 0xbf, 0xec, 0xa6, 0xec, 0x3e, 0x8a, 0x3c, 0x4b, 0xb4, 0xee, 0x86, 0x04, 0x16, 0xd2, 0xfb, 0x48, 0x9c, 0x21, 0xec, 0x31, 0x67, 0xc3, 0x17, 0xf5, 0x1a, 0xaf, 0x1a, + /* (2^147)P */ 0xe7, 0xbd, 0x69, 0x67, 0x83, 0xa2, 0x06, 0xc3, 0xdb, 0x2a, 0x1e, 0x2b, 0x62, 0x80, 0x82, 0x20, 0xa6, 0x94, 0xff, 0xfb, 0x1f, 0xf5, 0x27, 0x80, 0x6b, 0xf2, 0x24, 0x11, 0xce, 0xa1, 0xcf, 0x76, + /* (2^148)P */ 0xb6, 0xab, 0x22, 0x24, 0x56, 0x00, 0xeb, 0x18, 0xc3, 0x29, 0x8c, 0x8f, 0xd5, 0xc4, 0x77, 0xf3, 0x1a, 0x56, 0x31, 0xf5, 0x07, 0xc2, 0xbb, 0x4d, 0x27, 0x8a, 0x12, 0x82, 0xf0, 0xb7, 0x53, 0x02, + /* (2^149)P */ 0xe0, 0x17, 0x2c, 0xb6, 0x1c, 0x09, 0x1f, 0x3d, 0xa9, 0x28, 0x46, 0xd6, 0xab, 0xe1, 0x60, 0x48, 0x53, 0x42, 0x9d, 0x30, 0x36, 0x74, 0xd1, 0x52, 0x76, 0xe5, 0xfa, 0x3e, 0xe1, 0x97, 0x6f, 0x35, + /* (2^150)P */ 0x5b, 0x53, 0x50, 0xa1, 0x1a, 0xe1, 0x51, 0xd3, 0xcc, 0x78, 0xd8, 0x1d, 0xbb, 0x45, 0x6b, 0x3e, 0x98, 0x2c, 0xd9, 0xbe, 0x28, 0x61, 0x77, 0x0c, 0xb8, 0x85, 0x28, 0x03, 0x93, 0xae, 0x34, 0x1d, + /* (2^151)P */ 0xc3, 0xa4, 0x5b, 0xa8, 0x8c, 0x48, 0xa0, 0x4b, 0xce, 0xe6, 0x9c, 0x3c, 0xc3, 0x48, 0x53, 0x98, 0x70, 0xa7, 0xbd, 0x97, 0x6f, 0x4c, 0x12, 0x66, 0x4a, 0x12, 0x54, 0x06, 0x29, 0xa0, 0x81, 0x0f, + /* (2^152)P */ 0xfd, 0x86, 0x9b, 0x56, 0xa6, 0x9c, 0xd0, 0x9e, 0x2d, 0x9a, 0xaf, 0x18, 0xfd, 0x09, 0x10, 0x81, 0x0a, 0xc2, 0xd8, 0x93, 0x3f, 0xd0, 0x08, 0xff, 0x6b, 0xf2, 0xae, 0x9f, 0x19, 0x48, 0xa1, 0x52, + /* (2^153)P */ 0x73, 0x1b, 0x8d, 0x2d, 0xdc, 0xf9, 0x03, 0x3e, 0x70, 0x1a, 0x96, 0x73, 0x18, 0x80, 0x05, 0x42, 0x70, 0x59, 0xa3, 0x41, 0xf0, 0x87, 0xd9, 0xc0, 0x49, 0xd5, 0xc0, 0xa1, 0x15, 0x1f, 0xaa, 0x07, + /* (2^154)P */ 0x24, 0x72, 0xd2, 0x8c, 0xe0, 0x6c, 0xd4, 0xdf, 0x39, 0x42, 0x4e, 0x93, 0x4f, 0x02, 0x0a, 0x6d, 0x59, 0x7b, 0x89, 0x99, 0x63, 0x7a, 0x8a, 0x80, 0xa2, 0x95, 0x3d, 0xe1, 0xe9, 0x56, 0x45, 0x0a, + /* (2^155)P */ 0x45, 0x30, 0xc1, 0xe9, 0x1f, 0x99, 0x1a, 0xd2, 0xb8, 0x51, 0x77, 0xfe, 0x48, 0x85, 0x0e, 0x9b, 0x35, 0x00, 0xf3, 0x4b, 0xcb, 0x43, 0xa6, 0x5d, 0x21, 0xf7, 0x40, 0x39, 0xd6, 0x28, 0xdb, 0x77, + /* (2^156)P */ 0x11, 0x90, 0xdc, 0x4a, 0x61, 0xeb, 0x5e, 0xfc, 0xeb, 0x11, 0xc4, 0xe8, 0x9a, 0x41, 0x29, 0x52, 0x74, 0xcf, 0x1d, 0x7d, 0x78, 0xe7, 0xc3, 0x9e, 0xb5, 0x4c, 0x6e, 0x21, 0x3e, 0x05, 0x0d, 0x34, + /* (2^157)P */ 0xb4, 0xf2, 0x8d, 0xb4, 0x39, 0xaf, 0xc7, 0xca, 0x94, 0x0a, 0xa1, 0x71, 0x28, 0xec, 0xfa, 0xc0, 0xed, 0x75, 0xa5, 0x5c, 0x24, 0x69, 0x0a, 0x14, 0x4c, 0x3a, 0x27, 0x34, 0x71, 0xc3, 0xf1, 0x0c, + /* (2^158)P */ 0xa5, 0xb8, 0x24, 0xc2, 0x6a, 0x30, 0xee, 0xc8, 0xb0, 0x30, 0x49, 0xcb, 0x7c, 0xee, 0xea, 0x57, 0x4f, 0xe7, 0xcb, 0xaa, 0xbd, 0x06, 0xe8, 0xa1, 0x7d, 0x65, 0xeb, 0x2e, 0x74, 0x62, 0x9a, 0x7d, + /* (2^159)P */ 0x30, 0x48, 0x6c, 0x54, 0xef, 0xb6, 0xb6, 0x9e, 0x2e, 0x6e, 0xb3, 0xdd, 0x1f, 0xca, 0x5c, 0x88, 0x05, 0x71, 0x0d, 0xef, 0x83, 0xf3, 0xb9, 0xe6, 0x12, 0x04, 0x2e, 0x9d, 0xef, 0x4f, 0x65, 0x58, + /* (2^160)P */ 0x26, 0x8e, 0x0e, 0xbe, 0xff, 0xc4, 0x05, 0xa9, 0x6e, 0x81, 0x31, 0x9b, 0xdf, 0xe5, 0x2d, 0x94, 0xe1, 0x88, 0x2e, 0x80, 0x3f, 0x72, 0x7d, 0x49, 0x8d, 0x40, 0x2f, 0x60, 0xea, 0x4d, 0x68, 0x30, + /* (2^161)P */ 0x34, 0xcb, 0xe6, 0xa3, 0x78, 0xa2, 0xe5, 0x21, 0xc4, 0x1d, 0x15, 0x5b, 0x6f, 0x6e, 0xfb, 0xae, 0x15, 0xca, 0x77, 0x9d, 0x04, 0x8e, 0x0b, 0xb3, 0x81, 0x89, 0xb9, 0x53, 0xcf, 0xc9, 0xc3, 0x28, + /* (2^162)P */ 0x2a, 0xdd, 0x6c, 0x55, 0x21, 0xb7, 0x7f, 0x28, 0x74, 0x22, 0x02, 0x97, 0xa8, 0x7c, 0x31, 0x0d, 0x58, 0x32, 0x54, 0x3a, 0x42, 0xc7, 0x68, 0x74, 0x2f, 0x64, 0xb5, 0x4e, 0x46, 0x11, 0x7f, 0x4a, + /* (2^163)P */ 0xa6, 0x3a, 0x19, 0x4d, 0x77, 0xa4, 0x37, 0xa2, 0xa1, 0x29, 0x21, 0xa9, 0x6e, 0x98, 0x65, 0xd8, 0x88, 0x1a, 0x7c, 0xf8, 0xec, 0x15, 0xc5, 0x24, 0xeb, 0xf5, 0x39, 0x5f, 0x57, 0x03, 0x40, 0x60, + /* (2^164)P */ 0x27, 0x9b, 0x0a, 0x57, 0x89, 0xf1, 0xb9, 0x47, 0x78, 0x4b, 0x5e, 0x46, 0xde, 0xce, 0x98, 0x2b, 0x20, 0x5c, 0xb8, 0xdb, 0x51, 0xf5, 0x6d, 0x02, 0x01, 0x19, 0xe2, 0x47, 0x10, 0xd9, 0xfc, 0x74, + /* (2^165)P */ 0xa3, 0xbf, 0xc1, 0x23, 0x0a, 0xa9, 0xe2, 0x13, 0xf6, 0x19, 0x85, 0x47, 0x4e, 0x07, 0xb0, 0x0c, 0x44, 0xcf, 0xf6, 0x3a, 0xbe, 0xcb, 0xf1, 0x5f, 0xbe, 0x2d, 0x81, 0xbe, 0x38, 0x54, 0xfe, 0x67, + /* (2^166)P */ 0xb0, 0x05, 0x0f, 0xa4, 0x4f, 0xf6, 0x3c, 0xd1, 0x87, 0x37, 0x28, 0x32, 0x2f, 0xfb, 0x4d, 0x05, 0xea, 0x2a, 0x0d, 0x7f, 0x5b, 0x91, 0x73, 0x41, 0x4e, 0x0d, 0x61, 0x1f, 0x4f, 0x14, 0x2f, 0x48, + /* (2^167)P */ 0x34, 0x82, 0x7f, 0xb4, 0x01, 0x02, 0x21, 0xf6, 0x90, 0xb9, 0x70, 0x9e, 0x92, 0xe1, 0x0a, 0x5d, 0x7c, 0x56, 0x49, 0xb0, 0x55, 0xf4, 0xd7, 0xdc, 0x01, 0x6f, 0x91, 0xf0, 0xf1, 0xd0, 0x93, 0x7e, + /* (2^168)P */ 0xfa, 0xb4, 0x7d, 0x8a, 0xf1, 0xcb, 0x79, 0xdd, 0x2f, 0xc6, 0x74, 0x6f, 0xbf, 0x91, 0x83, 0xbe, 0xbd, 0x91, 0x82, 0x4b, 0xd1, 0x45, 0x71, 0x02, 0x05, 0x17, 0xbf, 0x2c, 0xea, 0x73, 0x5a, 0x58, + /* (2^169)P */ 0xb2, 0x0d, 0x8a, 0x92, 0x3e, 0xa0, 0x5c, 0x48, 0xe7, 0x57, 0x28, 0x74, 0xa5, 0x01, 0xfc, 0x10, 0xa7, 0x51, 0xd5, 0xd6, 0xdb, 0x2e, 0x48, 0x2f, 0x8a, 0xdb, 0x8f, 0x04, 0xb5, 0x33, 0x04, 0x0f, + /* (2^170)P */ 0x47, 0x62, 0xdc, 0xd7, 0x8d, 0x2e, 0xda, 0x60, 0x9a, 0x81, 0xd4, 0x8c, 0xd3, 0xc9, 0xb4, 0x88, 0x97, 0x66, 0xf6, 0x01, 0xc0, 0x3a, 0x03, 0x13, 0x75, 0x7d, 0x36, 0x3b, 0xfe, 0x24, 0x3b, 0x27, + /* (2^171)P */ 0xd4, 0xb9, 0xb3, 0x31, 0x6a, 0xf6, 0xe8, 0xc6, 0xd5, 0x49, 0xdf, 0x94, 0xa4, 0x14, 0x15, 0x28, 0xa7, 0x3d, 0xb2, 0xc8, 0xdf, 0x6f, 0x72, 0xd1, 0x48, 0xe5, 0xde, 0x03, 0xd1, 0xe7, 0x3a, 0x4b, + /* (2^172)P */ 0x7e, 0x9d, 0x4b, 0xce, 0x19, 0x6e, 0x25, 0xc6, 0x1c, 0xc6, 0xe3, 0x86, 0xf1, 0x5c, 0x5c, 0xff, 0x45, 0xc1, 0x8e, 0x4b, 0xa3, 0x3c, 0xc6, 0xac, 0x74, 0x65, 0xe6, 0xfe, 0x88, 0x18, 0x62, 0x74, + /* (2^173)P */ 0x1e, 0x0a, 0x29, 0x45, 0x96, 0x40, 0x6f, 0x95, 0x2e, 0x96, 0x3a, 0x26, 0xe3, 0xf8, 0x0b, 0xef, 0x7b, 0x64, 0xc2, 0x5e, 0xeb, 0x50, 0x6a, 0xed, 0x02, 0x75, 0xca, 0x9d, 0x3a, 0x28, 0x94, 0x06, + /* (2^174)P */ 0xd1, 0xdc, 0xa2, 0x43, 0x36, 0x96, 0x9b, 0x76, 0x53, 0x53, 0xfc, 0x09, 0xea, 0xc8, 0xb7, 0x42, 0xab, 0x7e, 0x39, 0x13, 0xee, 0x2a, 0x00, 0x4f, 0x3a, 0xd6, 0xb7, 0x19, 0x2c, 0x5e, 0x00, 0x63, + /* (2^175)P */ 0xea, 0x3b, 0x02, 0x63, 0xda, 0x36, 0x67, 0xca, 0xb7, 0x99, 0x2a, 0xb1, 0x6d, 0x7f, 0x6c, 0x96, 0xe1, 0xc5, 0x37, 0xc5, 0x90, 0x93, 0xe0, 0xac, 0xee, 0x89, 0xaa, 0xa1, 0x63, 0x60, 0x69, 0x0b, + /* (2^176)P */ 0xe5, 0x56, 0x8c, 0x28, 0x97, 0x3e, 0xb0, 0xeb, 0xe8, 0x8b, 0x8c, 0x93, 0x9f, 0x9f, 0x2a, 0x43, 0x71, 0x7f, 0x71, 0x5b, 0x3d, 0xa9, 0xa5, 0xa6, 0x97, 0x9d, 0x8f, 0xe1, 0xc3, 0xb4, 0x5f, 0x1a, + /* (2^177)P */ 0xce, 0xcd, 0x60, 0x1c, 0xad, 0xe7, 0x94, 0x1c, 0xa0, 0xc4, 0x02, 0xfc, 0x43, 0x2a, 0x20, 0xee, 0x20, 0x6a, 0xc4, 0x67, 0xd8, 0xe4, 0xaf, 0x8d, 0x58, 0x7b, 0xc2, 0x8a, 0x3c, 0x26, 0x10, 0x0a, + /* (2^178)P */ 0x4a, 0x2a, 0x43, 0xe4, 0xdf, 0xa9, 0xde, 0xd0, 0xc5, 0x77, 0x92, 0xbe, 0x7b, 0xf8, 0x6a, 0x85, 0x1a, 0xc7, 0x12, 0xc2, 0xac, 0x72, 0x84, 0xce, 0x91, 0x1e, 0xbb, 0x9b, 0x6d, 0x1b, 0x15, 0x6f, + /* (2^179)P */ 0x6a, 0xd5, 0xee, 0x7c, 0x52, 0x6c, 0x77, 0x26, 0xec, 0xfa, 0xf8, 0xfb, 0xb7, 0x1c, 0x21, 0x7d, 0xcc, 0x09, 0x46, 0xfd, 0xa6, 0x66, 0xae, 0x37, 0x42, 0x0c, 0x77, 0xd2, 0x02, 0xb7, 0x81, 0x1f, + /* (2^180)P */ 0x92, 0x83, 0xc5, 0xea, 0x57, 0xb0, 0xb0, 0x2f, 0x9d, 0x4e, 0x74, 0x29, 0xfe, 0x89, 0xdd, 0xe1, 0xf8, 0xb4, 0xbe, 0x17, 0xeb, 0xf8, 0x64, 0xc9, 0x1e, 0xd4, 0xa2, 0xc9, 0x73, 0x10, 0x57, 0x29, + /* (2^181)P */ 0x54, 0xe2, 0xc0, 0x81, 0x89, 0xa1, 0x48, 0xa9, 0x30, 0x28, 0xb2, 0x65, 0x9b, 0x36, 0xf6, 0x2d, 0xc6, 0xd3, 0xcf, 0x5f, 0xd7, 0xb2, 0x3e, 0xa3, 0x1f, 0xa0, 0x99, 0x41, 0xec, 0xd6, 0x8c, 0x07, + /* (2^182)P */ 0x2f, 0x0d, 0x90, 0xad, 0x41, 0x4a, 0x58, 0x4a, 0x52, 0x4c, 0xc7, 0xe2, 0x78, 0x2b, 0x14, 0x32, 0x78, 0xc9, 0x31, 0x84, 0x33, 0xe8, 0xc4, 0x68, 0xc2, 0x9f, 0x68, 0x08, 0x90, 0xea, 0x69, 0x7f, + /* (2^183)P */ 0x65, 0x82, 0xa3, 0x46, 0x1e, 0xc8, 0xf2, 0x52, 0xfd, 0x32, 0xa8, 0x04, 0x2d, 0x07, 0x78, 0xfd, 0x94, 0x9e, 0x35, 0x25, 0xfa, 0xd5, 0xd7, 0x8c, 0xd2, 0x29, 0xcc, 0x54, 0x74, 0x1b, 0xe7, 0x4d, + /* (2^184)P */ 0xc9, 0x6a, 0xda, 0x1e, 0xad, 0x60, 0xeb, 0x42, 0x3a, 0x9c, 0xc0, 0xdb, 0xdf, 0x37, 0xad, 0x0a, 0x91, 0xc1, 0x3c, 0xe3, 0x71, 0x4b, 0x00, 0x81, 0x3c, 0x80, 0x22, 0x51, 0x34, 0xbe, 0xe6, 0x44, + /* (2^185)P */ 0xdb, 0x20, 0x19, 0xba, 0x88, 0x83, 0xfe, 0x03, 0x08, 0xb0, 0x0d, 0x15, 0x32, 0x7c, 0xd5, 0xf5, 0x29, 0x0c, 0xf6, 0x1a, 0x28, 0xc4, 0xc8, 0x49, 0xee, 0x1a, 0x70, 0xde, 0x18, 0xb5, 0xed, 0x21, + /* (2^186)P */ 0x99, 0xdc, 0x06, 0x8f, 0x41, 0x3e, 0xb6, 0x7f, 0xb8, 0xd7, 0x66, 0xc1, 0x99, 0x0d, 0x46, 0xa4, 0x83, 0x0a, 0x52, 0xce, 0x48, 0x52, 0xdd, 0x24, 0x58, 0x83, 0x92, 0x2b, 0x71, 0xad, 0xc3, 0x5e, + /* (2^187)P */ 0x0f, 0x93, 0x17, 0xbd, 0x5f, 0x2a, 0x02, 0x15, 0xe3, 0x70, 0x25, 0xd8, 0x77, 0x4a, 0xf6, 0xa4, 0x12, 0x37, 0x78, 0x15, 0x69, 0x8d, 0xbc, 0x12, 0xbb, 0x0a, 0x62, 0xfc, 0xc0, 0x94, 0x81, 0x49, + /* (2^188)P */ 0x82, 0x6c, 0x68, 0x55, 0xd2, 0xd9, 0xa2, 0x38, 0xf0, 0x21, 0x3e, 0x19, 0xd9, 0x6b, 0x5c, 0x78, 0x84, 0x54, 0x4a, 0xb2, 0x1a, 0xc8, 0xd5, 0xe4, 0x89, 0x09, 0xe2, 0xb2, 0x60, 0x78, 0x30, 0x56, + /* (2^189)P */ 0xc4, 0x74, 0x4d, 0x8b, 0xf7, 0x55, 0x9d, 0x42, 0x31, 0x01, 0x35, 0x43, 0x46, 0x83, 0xf1, 0x22, 0xff, 0x1f, 0xc7, 0x98, 0x45, 0xc2, 0x60, 0x1e, 0xef, 0x83, 0x99, 0x97, 0x14, 0xf0, 0xf2, 0x59, + /* (2^190)P */ 0x44, 0x4a, 0x49, 0xeb, 0x56, 0x7d, 0xa4, 0x46, 0x8e, 0xa1, 0x36, 0xd6, 0x54, 0xa8, 0x22, 0x3e, 0x3b, 0x1c, 0x49, 0x74, 0x52, 0xe1, 0x46, 0xb3, 0xe7, 0xcd, 0x90, 0x53, 0x4e, 0xfd, 0xea, 0x2c, + /* (2^191)P */ 0x75, 0x66, 0x0d, 0xbe, 0x38, 0x85, 0x8a, 0xba, 0x23, 0x8e, 0x81, 0x50, 0xbb, 0x74, 0x90, 0x4b, 0xc3, 0x04, 0xd3, 0x85, 0x90, 0xb8, 0xda, 0xcb, 0xc4, 0x92, 0x61, 0xe5, 0xe0, 0x4f, 0xa2, 0x61, + /* (2^192)P */ 0xcb, 0x5b, 0x52, 0xdb, 0xe6, 0x15, 0x76, 0xcb, 0xca, 0xe4, 0x67, 0xa5, 0x35, 0x8c, 0x7d, 0xdd, 0x69, 0xdd, 0xfc, 0xca, 0x3a, 0x15, 0xb4, 0xe6, 0x66, 0x97, 0x3c, 0x7f, 0x09, 0x8e, 0x66, 0x2d, + /* (2^193)P */ 0xf0, 0x5e, 0xe5, 0x5c, 0x26, 0x7e, 0x7e, 0xa5, 0x67, 0xb9, 0xd4, 0x7c, 0x52, 0x4e, 0x9f, 0x5d, 0xe5, 0xd1, 0x2f, 0x49, 0x06, 0x36, 0xc8, 0xfb, 0xae, 0xf7, 0xc3, 0xb7, 0xbe, 0x52, 0x0d, 0x09, + /* (2^194)P */ 0x7c, 0x4d, 0x7b, 0x1e, 0x5a, 0x51, 0xb9, 0x09, 0xc0, 0x44, 0xda, 0x99, 0x25, 0x6a, 0x26, 0x1f, 0x04, 0x55, 0xc5, 0xe2, 0x48, 0x95, 0xc4, 0xa1, 0xcc, 0x15, 0x6f, 0x12, 0x87, 0x42, 0xf0, 0x7e, + /* (2^195)P */ 0x15, 0xef, 0x30, 0xbd, 0x9d, 0x65, 0xd1, 0xfe, 0x7b, 0x27, 0xe0, 0xc4, 0xee, 0xb9, 0x4a, 0x8b, 0x91, 0x32, 0xdf, 0xa5, 0x36, 0x62, 0x4d, 0x88, 0x88, 0xf7, 0x5c, 0xbf, 0xa6, 0x6e, 0xd9, 0x1f, + /* (2^196)P */ 0x9a, 0x0d, 0x19, 0x1f, 0x98, 0x61, 0xa1, 0x42, 0xc1, 0x52, 0x60, 0x7e, 0x50, 0x49, 0xd8, 0x61, 0xd5, 0x2c, 0x5a, 0x28, 0xbf, 0x13, 0xe1, 0x9f, 0xd8, 0x85, 0xad, 0xdb, 0x76, 0xd6, 0x22, 0x7c, + /* (2^197)P */ 0x7d, 0xd2, 0xfb, 0x2b, 0xed, 0x70, 0xe7, 0x82, 0xa5, 0xf5, 0x96, 0xe9, 0xec, 0xb2, 0x05, 0x4c, 0x50, 0x01, 0x90, 0xb0, 0xc2, 0xa9, 0x40, 0xcd, 0x64, 0xbf, 0xd9, 0x13, 0x92, 0x31, 0x95, 0x58, + /* (2^198)P */ 0x08, 0x2e, 0xea, 0x3f, 0x70, 0x5d, 0xcc, 0xe7, 0x8c, 0x18, 0xe2, 0x58, 0x12, 0x49, 0x0c, 0xb5, 0xf0, 0x5b, 0x20, 0x48, 0xaa, 0x0b, 0xe3, 0xcc, 0x62, 0x2d, 0xa3, 0xcf, 0x9c, 0x65, 0x7c, 0x53, + /* (2^199)P */ 0x88, 0xc0, 0xcf, 0x98, 0x3a, 0x62, 0xb6, 0x37, 0xa4, 0xac, 0xd6, 0xa4, 0x1f, 0xed, 0x9b, 0xfe, 0xb0, 0xd1, 0xa8, 0x56, 0x8e, 0x9b, 0xd2, 0x04, 0x75, 0x95, 0x51, 0x0b, 0xc4, 0x71, 0x5f, 0x72, + /* (2^200)P */ 0xe6, 0x9c, 0x33, 0xd0, 0x9c, 0xf8, 0xc7, 0x28, 0x8b, 0xc1, 0xdd, 0x69, 0x44, 0xb1, 0x67, 0x83, 0x2c, 0x65, 0xa1, 0xa6, 0x83, 0xda, 0x3a, 0x88, 0x17, 0x6c, 0x4d, 0x03, 0x74, 0x19, 0x5f, 0x58, + /* (2^201)P */ 0x88, 0x91, 0xb1, 0xf1, 0x66, 0xb2, 0xcf, 0x89, 0x17, 0x52, 0xc3, 0xe7, 0x63, 0x48, 0x3b, 0xe6, 0x6a, 0x52, 0xc0, 0xb4, 0xa6, 0x9d, 0x8c, 0xd8, 0x35, 0x46, 0x95, 0xf0, 0x9d, 0x5c, 0x03, 0x3e, + /* (2^202)P */ 0x9d, 0xde, 0x45, 0xfb, 0x12, 0x54, 0x9d, 0xdd, 0x0d, 0xf4, 0xcf, 0xe4, 0x32, 0x45, 0x68, 0xdd, 0x1c, 0x67, 0x1d, 0x15, 0x9b, 0x99, 0x5c, 0x4b, 0x90, 0xf6, 0xe7, 0x11, 0xc8, 0x2c, 0x8c, 0x2d, + /* (2^203)P */ 0x40, 0x5d, 0x05, 0x90, 0x1d, 0xbe, 0x54, 0x7f, 0x40, 0xaf, 0x4a, 0x46, 0xdf, 0xc5, 0x64, 0xa4, 0xbe, 0x17, 0xe9, 0xf0, 0x24, 0x96, 0x97, 0x33, 0x30, 0x6b, 0x35, 0x27, 0xc5, 0x8d, 0x01, 0x2c, + /* (2^204)P */ 0xd4, 0xb3, 0x30, 0xe3, 0x24, 0x50, 0x41, 0xa5, 0xd3, 0x52, 0x16, 0x69, 0x96, 0x3d, 0xff, 0x73, 0xf1, 0x59, 0x9b, 0xef, 0xc4, 0x42, 0xec, 0x94, 0x5a, 0x8e, 0xd0, 0x18, 0x16, 0x20, 0x47, 0x07, + /* (2^205)P */ 0x53, 0x1c, 0x41, 0xca, 0x8a, 0xa4, 0x6c, 0x4d, 0x19, 0x61, 0xa6, 0xcf, 0x2f, 0x5f, 0x41, 0x66, 0xff, 0x27, 0xe2, 0x51, 0x00, 0xd4, 0x4d, 0x9c, 0xeb, 0xf7, 0x02, 0x9a, 0xc0, 0x0b, 0x81, 0x59, + /* (2^206)P */ 0x1d, 0x10, 0xdc, 0xb3, 0x71, 0xb1, 0x7e, 0x2a, 0x8e, 0xf6, 0xfe, 0x9f, 0xb9, 0x5a, 0x1c, 0x44, 0xea, 0x59, 0xb3, 0x93, 0x9b, 0x5c, 0x02, 0x32, 0x2f, 0x11, 0x9d, 0x1e, 0xa7, 0xe0, 0x8c, 0x5e, + /* (2^207)P */ 0xfd, 0x03, 0x95, 0x42, 0x92, 0xcb, 0xcc, 0xbf, 0x55, 0x5d, 0x09, 0x2f, 0x75, 0xba, 0x71, 0xd2, 0x1e, 0x09, 0x2d, 0x97, 0x5e, 0xad, 0x5e, 0x34, 0xba, 0x03, 0x31, 0xa8, 0x11, 0xdf, 0xc8, 0x18, + /* (2^208)P */ 0x4c, 0x0f, 0xed, 0x9a, 0x9a, 0x94, 0xcd, 0x90, 0x7e, 0xe3, 0x60, 0x66, 0xcb, 0xf4, 0xd1, 0xc5, 0x0b, 0x2e, 0xc5, 0x56, 0x2d, 0xc5, 0xca, 0xb8, 0x0d, 0x8e, 0x80, 0xc5, 0x00, 0xe4, 0x42, 0x6e, + /* (2^209)P */ 0x23, 0xfd, 0xae, 0xee, 0x66, 0x69, 0xb4, 0xa3, 0xca, 0xcd, 0x9e, 0xe3, 0x0b, 0x1f, 0x4f, 0x0c, 0x1d, 0xa5, 0x83, 0xd6, 0xc9, 0xc8, 0x9d, 0x18, 0x1b, 0x35, 0x09, 0x4c, 0x05, 0x7f, 0xf2, 0x51, + /* (2^210)P */ 0x82, 0x06, 0x32, 0x2a, 0xcd, 0x7c, 0x48, 0x4c, 0x96, 0x1c, 0xdf, 0xb3, 0x5b, 0xa9, 0x7e, 0x58, 0xe8, 0xb8, 0x5c, 0x55, 0x9e, 0xf7, 0xcc, 0xc8, 0x3d, 0xd7, 0x06, 0xa2, 0x29, 0xc8, 0x7d, 0x54, + /* (2^211)P */ 0x06, 0x9b, 0xc3, 0x80, 0xcd, 0xa6, 0x22, 0xb8, 0xc6, 0xd4, 0x00, 0x20, 0x73, 0x54, 0x6d, 0xe9, 0x4d, 0x3b, 0x46, 0x91, 0x6f, 0x5b, 0x53, 0x28, 0x1d, 0x6e, 0x48, 0xe2, 0x60, 0x46, 0x8f, 0x22, + /* (2^212)P */ 0xbf, 0x3a, 0x8d, 0xde, 0x38, 0x95, 0x79, 0x98, 0x6e, 0xca, 0xeb, 0x45, 0x00, 0x33, 0xd8, 0x8c, 0x38, 0xe7, 0x21, 0x82, 0x00, 0x2a, 0x95, 0x79, 0xbb, 0xd2, 0x5c, 0x53, 0xa7, 0xe1, 0x22, 0x43, + /* (2^213)P */ 0x1c, 0x80, 0xd1, 0x19, 0x18, 0xc1, 0x14, 0xb1, 0xc7, 0x5e, 0x3f, 0x4f, 0xd8, 0xe4, 0x16, 0x20, 0x4c, 0x0f, 0x26, 0x09, 0xf4, 0x2d, 0x0e, 0xdd, 0x66, 0x72, 0x5f, 0xae, 0xc0, 0x62, 0xc3, 0x5e, + /* (2^214)P */ 0xee, 0xb4, 0xb2, 0xb8, 0x18, 0x2b, 0x46, 0xc0, 0xfb, 0x1a, 0x4d, 0x27, 0x50, 0xd9, 0xc8, 0x7c, 0xd2, 0x02, 0x6b, 0x43, 0x05, 0x71, 0x5f, 0xf2, 0xd3, 0xcc, 0xf9, 0xbf, 0xdc, 0xf8, 0xbb, 0x43, + /* (2^215)P */ 0xdf, 0xe9, 0x39, 0xa0, 0x67, 0x17, 0xad, 0xb6, 0x83, 0x35, 0x9d, 0xf6, 0xa8, 0x4d, 0x71, 0xb0, 0xf5, 0x31, 0x29, 0xb4, 0x18, 0xfa, 0x55, 0x5e, 0x61, 0x09, 0xc6, 0x33, 0x8f, 0x55, 0xd5, 0x4e, + /* (2^216)P */ 0xdd, 0xa5, 0x47, 0xc6, 0x01, 0x79, 0xe3, 0x1f, 0x57, 0xd3, 0x81, 0x80, 0x1f, 0xdf, 0x3d, 0x59, 0xa6, 0xd7, 0x3f, 0x81, 0xfd, 0xa4, 0x49, 0x02, 0x61, 0xaf, 0x9c, 0x4e, 0x27, 0xca, 0xac, 0x69, + /* (2^217)P */ 0xc9, 0x21, 0x07, 0x33, 0xea, 0xa3, 0x7b, 0x04, 0xa0, 0x1e, 0x7e, 0x0e, 0xc2, 0x3f, 0x42, 0x83, 0x60, 0x4a, 0x31, 0x01, 0xaf, 0xc0, 0xf4, 0x1d, 0x27, 0x95, 0x28, 0x89, 0xab, 0x2d, 0xa6, 0x09, + /* (2^218)P */ 0x00, 0xcb, 0xc6, 0x9c, 0xa4, 0x25, 0xb3, 0xa5, 0xb6, 0x6c, 0xb5, 0x54, 0xc6, 0x5d, 0x4b, 0xe9, 0xa0, 0x94, 0xc9, 0xad, 0x79, 0x87, 0xe2, 0x3b, 0xad, 0x4a, 0x3a, 0xba, 0xf8, 0xe8, 0x96, 0x42, + /* (2^219)P */ 0xab, 0x1e, 0x45, 0x1e, 0x76, 0x89, 0x86, 0x32, 0x4a, 0x59, 0x59, 0xff, 0x8b, 0x59, 0x4d, 0x2e, 0x4a, 0x08, 0xa7, 0xd7, 0x53, 0x68, 0xb9, 0x49, 0xa8, 0x20, 0x14, 0x60, 0x19, 0xa3, 0x80, 0x49, + /* (2^220)P */ 0x42, 0x2c, 0x55, 0x2f, 0xe1, 0xb9, 0x65, 0x95, 0x96, 0xfe, 0x00, 0x71, 0xdb, 0x18, 0x53, 0x8a, 0xd7, 0xd0, 0xad, 0x43, 0x4d, 0x0b, 0xc9, 0x05, 0xda, 0x4e, 0x5d, 0x6a, 0xd6, 0x4c, 0x8b, 0x53, + /* (2^221)P */ 0x9f, 0x03, 0x9f, 0xe8, 0xc3, 0x4f, 0xe9, 0xf4, 0x45, 0x80, 0x61, 0x6f, 0xf2, 0x9a, 0x2c, 0x59, 0x50, 0x95, 0x4b, 0xfd, 0xb5, 0x6e, 0xa3, 0x08, 0x19, 0x14, 0xed, 0xc2, 0xf6, 0xfa, 0xff, 0x25, + /* (2^222)P */ 0x54, 0xd3, 0x79, 0xcc, 0x59, 0x44, 0x43, 0x34, 0x6b, 0x47, 0xd5, 0xb1, 0xb4, 0xbf, 0xec, 0xee, 0x99, 0x5d, 0x61, 0x61, 0xa0, 0x34, 0xeb, 0xdd, 0x73, 0xb7, 0x64, 0xeb, 0xcc, 0xce, 0x29, 0x51, + /* (2^223)P */ 0x20, 0x35, 0x99, 0x94, 0x58, 0x21, 0x43, 0xee, 0x3b, 0x0b, 0x4c, 0xf1, 0x7c, 0x9c, 0x2f, 0x77, 0xd5, 0xda, 0xbe, 0x06, 0xe3, 0xfc, 0xe2, 0xd2, 0x97, 0x6a, 0xf0, 0x46, 0xb5, 0x42, 0x5f, 0x71, + /* (2^224)P */ 0x1a, 0x5f, 0x5b, 0xda, 0xce, 0xcd, 0x4e, 0x43, 0xa9, 0x41, 0x97, 0xa4, 0x15, 0x71, 0xa1, 0x0d, 0x2e, 0xad, 0xed, 0x73, 0x7c, 0xd7, 0x0b, 0x68, 0x41, 0x90, 0xdd, 0x4e, 0x35, 0x02, 0x7c, 0x48, + /* (2^225)P */ 0xc4, 0xd9, 0x0e, 0xa7, 0xf3, 0xef, 0xef, 0xb8, 0x02, 0xe3, 0x57, 0xe8, 0xa3, 0x2a, 0xa3, 0x56, 0xa0, 0xa5, 0xa2, 0x48, 0xbd, 0x68, 0x3a, 0xdf, 0x44, 0xc4, 0x76, 0x31, 0xb7, 0x50, 0xf6, 0x07, + /* (2^226)P */ 0xb1, 0xcc, 0xe0, 0x26, 0x16, 0x9b, 0x8b, 0xe3, 0x36, 0xfb, 0x09, 0x8b, 0xc1, 0x53, 0xe0, 0x79, 0x64, 0x49, 0xf9, 0xc9, 0x19, 0x03, 0xd9, 0x56, 0xc4, 0xf5, 0x9f, 0xac, 0xe7, 0x41, 0xa9, 0x1c, + /* (2^227)P */ 0xbb, 0xa0, 0x2f, 0x16, 0x29, 0xdf, 0xc4, 0x49, 0x05, 0x33, 0xb3, 0x82, 0x32, 0xcf, 0x88, 0x84, 0x7d, 0x43, 0xbb, 0xca, 0x14, 0xda, 0xdf, 0x95, 0x86, 0xad, 0xd5, 0x64, 0x82, 0xf7, 0x91, 0x33, + /* (2^228)P */ 0x5d, 0x09, 0xb5, 0xe2, 0x6a, 0xe0, 0x9a, 0x72, 0x46, 0xa9, 0x59, 0x32, 0xd7, 0x58, 0x8a, 0xd5, 0xed, 0x21, 0x39, 0xd1, 0x62, 0x42, 0x83, 0xe9, 0x92, 0xb5, 0x4b, 0xa5, 0xfa, 0xda, 0xfe, 0x27, + /* (2^229)P */ 0xbb, 0x48, 0xad, 0x29, 0xb8, 0xc5, 0x9d, 0xa9, 0x60, 0xe2, 0x9e, 0x49, 0x42, 0x57, 0x02, 0x5f, 0xfd, 0x13, 0x75, 0x5d, 0xcd, 0x8e, 0x2c, 0x80, 0x38, 0xd9, 0x6d, 0x3f, 0xef, 0xb3, 0xce, 0x78, + /* (2^230)P */ 0x94, 0x5d, 0x13, 0x8a, 0x4f, 0xf4, 0x42, 0xc3, 0xa3, 0xdd, 0x8c, 0x82, 0x44, 0xdb, 0x9e, 0x7b, 0xe7, 0xcf, 0x37, 0x05, 0x1a, 0xd1, 0x36, 0x94, 0xc8, 0xb4, 0x1a, 0xec, 0x64, 0xb1, 0x64, 0x50, + /* (2^231)P */ 0xfc, 0xb2, 0x7e, 0xd3, 0xcf, 0xec, 0x20, 0x70, 0xfc, 0x25, 0x0d, 0xd9, 0x3e, 0xea, 0x31, 0x1f, 0x34, 0xbb, 0xa1, 0xdf, 0x7b, 0x0d, 0x93, 0x1b, 0x44, 0x30, 0x11, 0x48, 0x7a, 0x46, 0x44, 0x53, + /* (2^232)P */ 0xfb, 0x6d, 0x5e, 0xf2, 0x70, 0x31, 0x07, 0x70, 0xc8, 0x4c, 0x11, 0x50, 0x1a, 0xdc, 0x85, 0xe3, 0x00, 0x4f, 0xfc, 0xc8, 0x8a, 0x69, 0x48, 0x23, 0xd8, 0x40, 0xdd, 0x84, 0x52, 0xa5, 0x77, 0x2a, + /* (2^233)P */ 0xe4, 0x6c, 0x8c, 0xc9, 0xe0, 0xaf, 0x06, 0xfe, 0xe4, 0xd6, 0xdf, 0xdd, 0x96, 0xdf, 0x35, 0xc2, 0xd3, 0x1e, 0xbf, 0x33, 0x1e, 0xd0, 0x28, 0x14, 0xaf, 0xbd, 0x00, 0x93, 0xec, 0x68, 0x57, 0x78, + /* (2^234)P */ 0x3b, 0xb6, 0xde, 0x91, 0x7a, 0xe5, 0x02, 0x97, 0x80, 0x8b, 0xce, 0xe5, 0xbf, 0xb8, 0xbd, 0x61, 0xac, 0x58, 0x1d, 0x3d, 0x6f, 0x42, 0x5b, 0x64, 0xbc, 0x57, 0xa5, 0x27, 0x22, 0xa8, 0x04, 0x48, + /* (2^235)P */ 0x01, 0x26, 0x4d, 0xb4, 0x8a, 0x04, 0x57, 0x8e, 0x35, 0x69, 0x3a, 0x4b, 0x1a, 0x50, 0xd6, 0x68, 0x93, 0xc2, 0xe1, 0xf9, 0xc3, 0x9e, 0x9c, 0xc3, 0xe2, 0x63, 0xde, 0xd4, 0x57, 0xf2, 0x72, 0x41, + /* (2^236)P */ 0x01, 0x64, 0x0c, 0x33, 0x50, 0xb4, 0x68, 0xd3, 0x91, 0x23, 0x8f, 0x41, 0x17, 0x30, 0x0d, 0x04, 0x0d, 0xd9, 0xb7, 0x90, 0x60, 0xbb, 0x34, 0x2c, 0x1f, 0xd5, 0xdf, 0x8f, 0x22, 0x49, 0xf6, 0x16, + /* (2^237)P */ 0xf5, 0x8e, 0x92, 0x2b, 0x8e, 0x81, 0xa6, 0xbe, 0x72, 0x1e, 0xc1, 0xcd, 0x91, 0xcf, 0x8c, 0xe2, 0xcd, 0x36, 0x7a, 0xe7, 0x68, 0xaa, 0x4a, 0x59, 0x0f, 0xfd, 0x7f, 0x6c, 0x80, 0x34, 0x30, 0x31, + /* (2^238)P */ 0x65, 0xbd, 0x49, 0x22, 0xac, 0x27, 0x9d, 0x8a, 0x12, 0x95, 0x8e, 0x01, 0x64, 0xb4, 0xa3, 0x19, 0xc7, 0x7e, 0xb3, 0x52, 0xf3, 0xcf, 0x6c, 0xc2, 0x21, 0x7b, 0x79, 0x1d, 0x34, 0x68, 0x6f, 0x05, + /* (2^239)P */ 0x27, 0x23, 0xfd, 0x7e, 0x75, 0xd6, 0x79, 0x5e, 0x15, 0xfe, 0x3a, 0x55, 0xb6, 0xbc, 0xbd, 0xfa, 0x60, 0x5a, 0xaf, 0x6e, 0x2c, 0x22, 0xe7, 0xd3, 0x3b, 0x74, 0xae, 0x4d, 0x6d, 0xc7, 0x46, 0x70, + /* (2^240)P */ 0x55, 0x4a, 0x8d, 0xb1, 0x72, 0xe8, 0x0b, 0x66, 0x96, 0x14, 0x4e, 0x57, 0x18, 0x25, 0x99, 0x19, 0xbb, 0xdc, 0x2b, 0x30, 0x3a, 0x05, 0x03, 0xc1, 0x8e, 0x8e, 0x21, 0x0b, 0x80, 0xe9, 0xd8, 0x3e, + /* (2^241)P */ 0x3e, 0xe0, 0x75, 0xfa, 0x39, 0x92, 0x0b, 0x7b, 0x83, 0xc0, 0x33, 0x46, 0x68, 0xfb, 0xe9, 0xef, 0x93, 0x77, 0x1a, 0x39, 0xbe, 0x5f, 0xa3, 0x98, 0x34, 0xfe, 0xd0, 0xe2, 0x0f, 0x51, 0x65, 0x60, + /* (2^242)P */ 0x0c, 0xad, 0xab, 0x48, 0x85, 0x66, 0xcb, 0x55, 0x27, 0xe5, 0x87, 0xda, 0x48, 0x45, 0x58, 0xb4, 0xdd, 0xc1, 0x07, 0x01, 0xea, 0xec, 0x43, 0x2c, 0x35, 0xde, 0x72, 0x93, 0x80, 0x28, 0x60, 0x52, + /* (2^243)P */ 0x1f, 0x3b, 0x21, 0xf9, 0x6a, 0xc5, 0x15, 0x34, 0xdb, 0x98, 0x7e, 0x01, 0x4d, 0x1a, 0xee, 0x5b, 0x9b, 0x70, 0xcf, 0xb5, 0x05, 0xb1, 0xf6, 0x13, 0xb6, 0x9a, 0xb2, 0x82, 0x34, 0x0e, 0xf2, 0x5f, + /* (2^244)P */ 0x90, 0x6c, 0x2e, 0xcc, 0x75, 0x9c, 0xa2, 0x0a, 0x06, 0xe2, 0x70, 0x3a, 0xca, 0x73, 0x7d, 0xfc, 0x15, 0xc5, 0xb5, 0xc4, 0x8f, 0xc3, 0x9f, 0x89, 0x07, 0xc2, 0xff, 0x24, 0xb1, 0x86, 0x03, 0x25, + /* (2^245)P */ 0x56, 0x2b, 0x3d, 0xae, 0xd5, 0x28, 0xea, 0x54, 0xce, 0x60, 0xde, 0xd6, 0x9d, 0x14, 0x13, 0x99, 0xc1, 0xd6, 0x06, 0x8f, 0xc5, 0x4f, 0x69, 0x16, 0xc7, 0x8f, 0x01, 0xeb, 0x75, 0x39, 0xb2, 0x46, + /* (2^246)P */ 0xe2, 0xb4, 0xb7, 0xb4, 0x0f, 0x6a, 0x0a, 0x47, 0xde, 0x53, 0x72, 0x8f, 0x5a, 0x47, 0x92, 0x5d, 0xdb, 0x3a, 0xbd, 0x2f, 0xb5, 0xe5, 0xee, 0xab, 0x68, 0x69, 0x80, 0xa0, 0x01, 0x08, 0xa2, 0x7f, + /* (2^247)P */ 0xd2, 0x14, 0x77, 0x9f, 0xf1, 0xfa, 0xf3, 0x76, 0xc3, 0x60, 0x46, 0x2f, 0xc1, 0x40, 0xe8, 0xb3, 0x4e, 0x74, 0x12, 0xf2, 0x8d, 0xcd, 0xb4, 0x0f, 0xd2, 0x2d, 0x3a, 0x1d, 0x25, 0x5a, 0x06, 0x4b, + /* (2^248)P */ 0x4a, 0xcd, 0x77, 0x3d, 0x38, 0xde, 0xeb, 0x5c, 0xb1, 0x9c, 0x2c, 0x88, 0xdf, 0x39, 0xdf, 0x6a, 0x59, 0xf7, 0x9a, 0xb0, 0x2e, 0x24, 0xdd, 0xa2, 0x22, 0x64, 0x5f, 0x0e, 0xe5, 0xc0, 0x47, 0x31, + /* (2^249)P */ 0xdb, 0x50, 0x13, 0x1d, 0x10, 0xa5, 0x4c, 0x16, 0x62, 0xc9, 0x3f, 0xc3, 0x79, 0x34, 0xd1, 0xf8, 0x08, 0xda, 0xe5, 0x13, 0x4d, 0xce, 0x40, 0xe6, 0xba, 0xf8, 0x61, 0x50, 0xc4, 0xe0, 0xde, 0x4b, + /* (2^250)P */ 0xc9, 0xb1, 0xed, 0xa4, 0xc1, 0x6d, 0xc4, 0xd7, 0x8a, 0xd9, 0x7f, 0x43, 0xb6, 0xd7, 0x14, 0x55, 0x0b, 0xc0, 0xa1, 0xb2, 0x6b, 0x2f, 0x94, 0x58, 0x0e, 0x71, 0x70, 0x1d, 0xab, 0xb2, 0xff, 0x2d, + /* (2^251)P */ 0x68, 0x6d, 0x8b, 0xc1, 0x2f, 0xcf, 0xdf, 0xcc, 0x67, 0x61, 0x80, 0xb7, 0xa8, 0xcb, 0xeb, 0xa8, 0xe3, 0x37, 0x29, 0x5e, 0xf9, 0x97, 0x06, 0x98, 0x8c, 0x6e, 0x12, 0xd0, 0x1c, 0xba, 0xfb, 0x02, + /* (2^252)P */ 0x65, 0x45, 0xff, 0xad, 0x60, 0xc3, 0x98, 0xcb, 0x19, 0x15, 0xdb, 0x4b, 0xd2, 0x01, 0x71, 0x44, 0xd5, 0x15, 0xfb, 0x75, 0x74, 0xc8, 0xc4, 0x98, 0x7d, 0xa2, 0x22, 0x6e, 0x6d, 0xc7, 0xf8, 0x05, + /* (2^253)P */ 0x94, 0xf4, 0xb9, 0xfe, 0xdf, 0xe5, 0x69, 0xab, 0x75, 0x6b, 0x40, 0x18, 0x9d, 0xc7, 0x09, 0xae, 0x1d, 0x2d, 0xa4, 0x94, 0xfb, 0x45, 0x9b, 0x19, 0x84, 0xfa, 0x2a, 0xae, 0xeb, 0x0a, 0x71, 0x79, + /* (2^254)P */ 0xdf, 0xd2, 0x34, 0xf3, 0xa7, 0xed, 0xad, 0xa6, 0xb4, 0x57, 0x2a, 0xaf, 0x51, 0x9c, 0xde, 0x7b, 0xa8, 0xea, 0xdc, 0x86, 0x4f, 0xc6, 0x8f, 0xa9, 0x7b, 0xd0, 0x0e, 0xc2, 0x35, 0x03, 0xbe, 0x6b, + /* (2^255)P */ 0x44, 0x43, 0x98, 0x53, 0xbe, 0xdc, 0x7f, 0x66, 0xa8, 0x49, 0x59, 0x00, 0x1c, 0xbc, 0x72, 0x07, 0x8e, 0xd6, 0xbe, 0x4e, 0x9f, 0xa4, 0x07, 0xba, 0xbf, 0x30, 0xdf, 0xba, 0x85, 0xb0, 0xa7, 0x1f, +} diff --git a/vendor/github.com/cloudflare/circl/dh/x448/curve.go b/vendor/github.com/cloudflare/circl/dh/x448/curve.go new file mode 100644 index 00000000..d59564e4 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x448/curve.go @@ -0,0 +1,104 @@ +package x448 + +import ( + fp "github.com/cloudflare/circl/math/fp448" +) + +// ladderJoye calculates a fixed-point multiplication with the generator point. +// The algorithm is the right-to-left Joye's ladder as described +// in "How to precompute a ladder" in SAC'2017. +func ladderJoye(k *Key) { + w := [5]fp.Elt{} // [mu,x1,z1,x2,z2] order must be preserved. + w[1] = fp.Elt{ // x1 = S + 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + } + fp.SetOne(&w[2]) // z1 = 1 + w[3] = fp.Elt{ // x2 = G-S + 0x20, 0x27, 0x9d, 0xc9, 0x7d, 0x19, 0xb1, 0xac, + 0xf8, 0xba, 0x69, 0x1c, 0xff, 0x33, 0xac, 0x23, + 0x51, 0x1b, 0xce, 0x3a, 0x64, 0x65, 0xbd, 0xf1, + 0x23, 0xf8, 0xc1, 0x84, 0x9d, 0x45, 0x54, 0x29, + 0x67, 0xb9, 0x81, 0x1c, 0x03, 0xd1, 0xcd, 0xda, + 0x7b, 0xeb, 0xff, 0x1a, 0x88, 0x03, 0xcf, 0x3a, + 0x42, 0x44, 0x32, 0x01, 0x25, 0xb7, 0xfa, 0xf0, + } + fp.SetOne(&w[4]) // z2 = 1 + + const n = 448 + const h = 2 + swap := uint(1) + for s := 0; s < n-h; s++ { + i := (s + h) / 8 + j := (s + h) % 8 + bit := uint((k[i] >> uint(j)) & 1) + copy(w[0][:], tableGenerator[s*Size:(s+1)*Size]) + diffAdd(&w, swap^bit) + swap = bit + } + for s := 0; s < h; s++ { + double(&w[1], &w[2]) + } + toAffine((*[fp.Size]byte)(k), &w[1], &w[2]) +} + +// ladderMontgomery calculates a generic scalar point multiplication +// The algorithm implemented is the left-to-right Montgomery's ladder. +func ladderMontgomery(k, xP *Key) { + w := [5]fp.Elt{} // [x1, x2, z2, x3, z3] order must be preserved. + w[0] = *(*fp.Elt)(xP) // x1 = xP + fp.SetOne(&w[1]) // x2 = 1 + w[3] = *(*fp.Elt)(xP) // x3 = xP + fp.SetOne(&w[4]) // z3 = 1 + + move := uint(0) + for s := 448 - 1; s >= 0; s-- { + i := s / 8 + j := s % 8 + bit := uint((k[i] >> uint(j)) & 1) + ladderStep(&w, move^bit) + move = bit + } + toAffine((*[fp.Size]byte)(k), &w[1], &w[2]) +} + +func toAffine(k *[fp.Size]byte, x, z *fp.Elt) { + fp.Inv(z, z) + fp.Mul(x, x, z) + _ = fp.ToBytes(k[:], x) +} + +var lowOrderPoints = [3]fp.Elt{ + { /* (0,_,1) point of order 2 on Curve448 */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + }, + { /* (1,_,1) a point of order 4 on the twist of Curve448 */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + }, + { /* (-1,_,1) point of order 4 on Curve448 */ + 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + }, +} diff --git a/vendor/github.com/cloudflare/circl/dh/x448/curve_amd64.go b/vendor/github.com/cloudflare/circl/dh/x448/curve_amd64.go new file mode 100644 index 00000000..a0622666 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x448/curve_amd64.go @@ -0,0 +1,30 @@ +//go:build amd64 && !purego +// +build amd64,!purego + +package x448 + +import ( + fp "github.com/cloudflare/circl/math/fp448" + "golang.org/x/sys/cpu" +) + +var hasBmi2Adx = cpu.X86.HasBMI2 && cpu.X86.HasADX + +var _ = hasBmi2Adx + +func double(x, z *fp.Elt) { doubleAmd64(x, z) } +func diffAdd(w *[5]fp.Elt, b uint) { diffAddAmd64(w, b) } +func ladderStep(w *[5]fp.Elt, b uint) { ladderStepAmd64(w, b) } +func mulA24(z, x *fp.Elt) { mulA24Amd64(z, x) } + +//go:noescape +func doubleAmd64(x, z *fp.Elt) + +//go:noescape +func diffAddAmd64(w *[5]fp.Elt, b uint) + +//go:noescape +func ladderStepAmd64(w *[5]fp.Elt, b uint) + +//go:noescape +func mulA24Amd64(z, x *fp.Elt) diff --git a/vendor/github.com/cloudflare/circl/dh/x448/curve_amd64.h b/vendor/github.com/cloudflare/circl/dh/x448/curve_amd64.h new file mode 100644 index 00000000..8c1ae4d0 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x448/curve_amd64.h @@ -0,0 +1,111 @@ +#define ladderStepLeg \ + addSub(x2,z2) \ + addSub(x3,z3) \ + integerMulLeg(b0,x2,z3) \ + integerMulLeg(b1,x3,z2) \ + reduceFromDoubleLeg(t0,b0) \ + reduceFromDoubleLeg(t1,b1) \ + addSub(t0,t1) \ + cselect(x2,x3,regMove) \ + cselect(z2,z3,regMove) \ + integerSqrLeg(b0,t0) \ + integerSqrLeg(b1,t1) \ + reduceFromDoubleLeg(x3,b0) \ + reduceFromDoubleLeg(z3,b1) \ + integerMulLeg(b0,x1,z3) \ + reduceFromDoubleLeg(z3,b0) \ + integerSqrLeg(b0,x2) \ + integerSqrLeg(b1,z2) \ + reduceFromDoubleLeg(x2,b0) \ + reduceFromDoubleLeg(z2,b1) \ + subtraction(t0,x2,z2) \ + multiplyA24Leg(t1,t0) \ + additionLeg(t1,t1,z2) \ + integerMulLeg(b0,x2,z2) \ + integerMulLeg(b1,t0,t1) \ + reduceFromDoubleLeg(x2,b0) \ + reduceFromDoubleLeg(z2,b1) + +#define ladderStepBmi2Adx \ + addSub(x2,z2) \ + addSub(x3,z3) \ + integerMulAdx(b0,x2,z3) \ + integerMulAdx(b1,x3,z2) \ + reduceFromDoubleAdx(t0,b0) \ + reduceFromDoubleAdx(t1,b1) \ + addSub(t0,t1) \ + cselect(x2,x3,regMove) \ + cselect(z2,z3,regMove) \ + integerSqrAdx(b0,t0) \ + integerSqrAdx(b1,t1) \ + reduceFromDoubleAdx(x3,b0) \ + reduceFromDoubleAdx(z3,b1) \ + integerMulAdx(b0,x1,z3) \ + reduceFromDoubleAdx(z3,b0) \ + integerSqrAdx(b0,x2) \ + integerSqrAdx(b1,z2) \ + reduceFromDoubleAdx(x2,b0) \ + reduceFromDoubleAdx(z2,b1) \ + subtraction(t0,x2,z2) \ + multiplyA24Adx(t1,t0) \ + additionAdx(t1,t1,z2) \ + integerMulAdx(b0,x2,z2) \ + integerMulAdx(b1,t0,t1) \ + reduceFromDoubleAdx(x2,b0) \ + reduceFromDoubleAdx(z2,b1) + +#define difAddLeg \ + addSub(x1,z1) \ + integerMulLeg(b0,z1,ui) \ + reduceFromDoubleLeg(z1,b0) \ + addSub(x1,z1) \ + integerSqrLeg(b0,x1) \ + integerSqrLeg(b1,z1) \ + reduceFromDoubleLeg(x1,b0) \ + reduceFromDoubleLeg(z1,b1) \ + integerMulLeg(b0,x1,z2) \ + integerMulLeg(b1,z1,x2) \ + reduceFromDoubleLeg(x1,b0) \ + reduceFromDoubleLeg(z1,b1) + +#define difAddBmi2Adx \ + addSub(x1,z1) \ + integerMulAdx(b0,z1,ui) \ + reduceFromDoubleAdx(z1,b0) \ + addSub(x1,z1) \ + integerSqrAdx(b0,x1) \ + integerSqrAdx(b1,z1) \ + reduceFromDoubleAdx(x1,b0) \ + reduceFromDoubleAdx(z1,b1) \ + integerMulAdx(b0,x1,z2) \ + integerMulAdx(b1,z1,x2) \ + reduceFromDoubleAdx(x1,b0) \ + reduceFromDoubleAdx(z1,b1) + +#define doubleLeg \ + addSub(x1,z1) \ + integerSqrLeg(b0,x1) \ + integerSqrLeg(b1,z1) \ + reduceFromDoubleLeg(x1,b0) \ + reduceFromDoubleLeg(z1,b1) \ + subtraction(t0,x1,z1) \ + multiplyA24Leg(t1,t0) \ + additionLeg(t1,t1,z1) \ + integerMulLeg(b0,x1,z1) \ + integerMulLeg(b1,t0,t1) \ + reduceFromDoubleLeg(x1,b0) \ + reduceFromDoubleLeg(z1,b1) + +#define doubleBmi2Adx \ + addSub(x1,z1) \ + integerSqrAdx(b0,x1) \ + integerSqrAdx(b1,z1) \ + reduceFromDoubleAdx(x1,b0) \ + reduceFromDoubleAdx(z1,b1) \ + subtraction(t0,x1,z1) \ + multiplyA24Adx(t1,t0) \ + additionAdx(t1,t1,z1) \ + integerMulAdx(b0,x1,z1) \ + integerMulAdx(b1,t0,t1) \ + reduceFromDoubleAdx(x1,b0) \ + reduceFromDoubleAdx(z1,b1) diff --git a/vendor/github.com/cloudflare/circl/dh/x448/curve_amd64.s b/vendor/github.com/cloudflare/circl/dh/x448/curve_amd64.s new file mode 100644 index 00000000..810aa9e6 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x448/curve_amd64.s @@ -0,0 +1,193 @@ +// +build amd64 + +#include "textflag.h" + +// Depends on circl/math/fp448 package +#include "../../math/fp448/fp_amd64.h" +#include "curve_amd64.h" + +// CTE_A24 is (A+2)/4 from Curve448 +#define CTE_A24 39082 + +#define Size 56 + +// multiplyA24Leg multiplies x times CTE_A24 and stores in z +// Uses: AX, DX, R8-R15, FLAGS +// Instr: x86_64, cmov, adx +#define multiplyA24Leg(z,x) \ + MOVQ $CTE_A24, R15; \ + MOVQ 0+x, AX; MULQ R15; MOVQ AX, R8; ;;;;;;;;;;;; MOVQ DX, R9; \ + MOVQ 8+x, AX; MULQ R15; ADDQ AX, R9; ADCQ $0, DX; MOVQ DX, R10; \ + MOVQ 16+x, AX; MULQ R15; ADDQ AX, R10; ADCQ $0, DX; MOVQ DX, R11; \ + MOVQ 24+x, AX; MULQ R15; ADDQ AX, R11; ADCQ $0, DX; MOVQ DX, R12; \ + MOVQ 32+x, AX; MULQ R15; ADDQ AX, R12; ADCQ $0, DX; MOVQ DX, R13; \ + MOVQ 40+x, AX; MULQ R15; ADDQ AX, R13; ADCQ $0, DX; MOVQ DX, R14; \ + MOVQ 48+x, AX; MULQ R15; ADDQ AX, R14; ADCQ $0, DX; \ + MOVQ DX, AX; \ + SHLQ $32, AX; \ + ADDQ DX, R8; MOVQ $0, DX; \ + ADCQ $0, R9; \ + ADCQ $0, R10; \ + ADCQ AX, R11; \ + ADCQ $0, R12; \ + ADCQ $0, R13; \ + ADCQ $0, R14; \ + ADCQ $0, DX; \ + MOVQ DX, AX; \ + SHLQ $32, AX; \ + ADDQ DX, R8; \ + ADCQ $0, R9; \ + ADCQ $0, R10; \ + ADCQ AX, R11; \ + ADCQ $0, R12; \ + ADCQ $0, R13; \ + ADCQ $0, R14; \ + MOVQ R8, 0+z; \ + MOVQ R9, 8+z; \ + MOVQ R10, 16+z; \ + MOVQ R11, 24+z; \ + MOVQ R12, 32+z; \ + MOVQ R13, 40+z; \ + MOVQ R14, 48+z; + +// multiplyA24Adx multiplies x times CTE_A24 and stores in z +// Uses: AX, DX, R8-R14, FLAGS +// Instr: x86_64, bmi2 +#define multiplyA24Adx(z,x) \ + MOVQ $CTE_A24, DX; \ + MULXQ 0+x, R8, R9; \ + MULXQ 8+x, AX, R10; ADDQ AX, R9; \ + MULXQ 16+x, AX, R11; ADCQ AX, R10; \ + MULXQ 24+x, AX, R12; ADCQ AX, R11; \ + MULXQ 32+x, AX, R13; ADCQ AX, R12; \ + MULXQ 40+x, AX, R14; ADCQ AX, R13; \ + MULXQ 48+x, AX, DX; ADCQ AX, R14; \ + ;;;;;;;;;;;;;;;;;;;; ADCQ $0, DX; \ + MOVQ DX, AX; \ + SHLQ $32, AX; \ + ADDQ DX, R8; MOVQ $0, DX; \ + ADCQ $0, R9; \ + ADCQ $0, R10; \ + ADCQ AX, R11; \ + ADCQ $0, R12; \ + ADCQ $0, R13; \ + ADCQ $0, R14; \ + ADCQ $0, DX; \ + MOVQ DX, AX; \ + SHLQ $32, AX; \ + ADDQ DX, R8; \ + ADCQ $0, R9; \ + ADCQ $0, R10; \ + ADCQ AX, R11; \ + ADCQ $0, R12; \ + ADCQ $0, R13; \ + ADCQ $0, R14; \ + MOVQ R8, 0+z; \ + MOVQ R9, 8+z; \ + MOVQ R10, 16+z; \ + MOVQ R11, 24+z; \ + MOVQ R12, 32+z; \ + MOVQ R13, 40+z; \ + MOVQ R14, 48+z; + +#define mulA24Legacy \ + multiplyA24Leg(0(DI),0(SI)) +#define mulA24Bmi2Adx \ + multiplyA24Adx(0(DI),0(SI)) + +// func mulA24Amd64(z, x *fp448.Elt) +TEXT ·mulA24Amd64(SB),NOSPLIT,$0-16 + MOVQ z+0(FP), DI + MOVQ x+8(FP), SI + CHECK_BMI2ADX(LMA24, mulA24Legacy, mulA24Bmi2Adx) + +// func ladderStepAmd64(w *[5]fp448.Elt, b uint) +// ladderStepAmd64 calculates a point addition and doubling as follows: +// (x2,z2) = 2*(x2,z2) and (x3,z3) = (x2,z2)+(x3,z3) using as a difference (x1,-). +// w = {x1,x2,z2,x3,z4} are five fp255.Elt of 56 bytes. +// stack = (t0,t1) are two fp.Elt of fp.Size bytes, and +// (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes. +TEXT ·ladderStepAmd64(SB),NOSPLIT,$336-16 + // Parameters + #define regWork DI + #define regMove SI + #define x1 0*Size(regWork) + #define x2 1*Size(regWork) + #define z2 2*Size(regWork) + #define x3 3*Size(regWork) + #define z3 4*Size(regWork) + // Local variables + #define t0 0*Size(SP) + #define t1 1*Size(SP) + #define b0 2*Size(SP) + #define b1 4*Size(SP) + MOVQ w+0(FP), regWork + MOVQ b+8(FP), regMove + CHECK_BMI2ADX(LLADSTEP, ladderStepLeg, ladderStepBmi2Adx) + #undef regWork + #undef regMove + #undef x1 + #undef x2 + #undef z2 + #undef x3 + #undef z3 + #undef t0 + #undef t1 + #undef b0 + #undef b1 + +// func diffAddAmd64(work *[5]fp.Elt, swap uint) +// diffAddAmd64 calculates a differential point addition using a precomputed point. +// (x1,z1) = (x1,z1)+(mu) using a difference point (x2,z2) +// work = {mu,x1,z1,x2,z2} are five fp448.Elt of 56 bytes, and +// stack = (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes. +// This is Equation 7 at https://eprint.iacr.org/2017/264. +TEXT ·diffAddAmd64(SB),NOSPLIT,$224-16 + // Parameters + #define regWork DI + #define regSwap SI + #define ui 0*Size(regWork) + #define x1 1*Size(regWork) + #define z1 2*Size(regWork) + #define x2 3*Size(regWork) + #define z2 4*Size(regWork) + // Local variables + #define b0 0*Size(SP) + #define b1 2*Size(SP) + MOVQ w+0(FP), regWork + MOVQ b+8(FP), regSwap + cswap(x1,x2,regSwap) + cswap(z1,z2,regSwap) + CHECK_BMI2ADX(LDIFADD, difAddLeg, difAddBmi2Adx) + #undef regWork + #undef regSwap + #undef ui + #undef x1 + #undef z1 + #undef x2 + #undef z2 + #undef b0 + #undef b1 + +// func doubleAmd64(x, z *fp448.Elt) +// doubleAmd64 calculates a point doubling (x1,z1) = 2*(x1,z1). +// stack = (t0,t1) are two fp.Elt of fp.Size bytes, and +// (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes. +TEXT ·doubleAmd64(SB),NOSPLIT,$336-16 + // Parameters + #define x1 0(DI) + #define z1 0(SI) + // Local variables + #define t0 0*Size(SP) + #define t1 1*Size(SP) + #define b0 2*Size(SP) + #define b1 4*Size(SP) + MOVQ x+0(FP), DI + MOVQ z+8(FP), SI + CHECK_BMI2ADX(LDOUB,doubleLeg,doubleBmi2Adx) + #undef x1 + #undef z1 + #undef t0 + #undef t1 + #undef b0 + #undef b1 diff --git a/vendor/github.com/cloudflare/circl/dh/x448/curve_generic.go b/vendor/github.com/cloudflare/circl/dh/x448/curve_generic.go new file mode 100644 index 00000000..b0b65ccf --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x448/curve_generic.go @@ -0,0 +1,100 @@ +package x448 + +import ( + "encoding/binary" + "math/bits" + + "github.com/cloudflare/circl/math/fp448" +) + +func doubleGeneric(x, z *fp448.Elt) { + t0, t1 := &fp448.Elt{}, &fp448.Elt{} + fp448.AddSub(x, z) + fp448.Sqr(x, x) + fp448.Sqr(z, z) + fp448.Sub(t0, x, z) + mulA24Generic(t1, t0) + fp448.Add(t1, t1, z) + fp448.Mul(x, x, z) + fp448.Mul(z, t0, t1) +} + +func diffAddGeneric(w *[5]fp448.Elt, b uint) { + mu, x1, z1, x2, z2 := &w[0], &w[1], &w[2], &w[3], &w[4] + fp448.Cswap(x1, x2, b) + fp448.Cswap(z1, z2, b) + fp448.AddSub(x1, z1) + fp448.Mul(z1, z1, mu) + fp448.AddSub(x1, z1) + fp448.Sqr(x1, x1) + fp448.Sqr(z1, z1) + fp448.Mul(x1, x1, z2) + fp448.Mul(z1, z1, x2) +} + +func ladderStepGeneric(w *[5]fp448.Elt, b uint) { + x1, x2, z2, x3, z3 := &w[0], &w[1], &w[2], &w[3], &w[4] + t0 := &fp448.Elt{} + t1 := &fp448.Elt{} + fp448.AddSub(x2, z2) + fp448.AddSub(x3, z3) + fp448.Mul(t0, x2, z3) + fp448.Mul(t1, x3, z2) + fp448.AddSub(t0, t1) + fp448.Cmov(x2, x3, b) + fp448.Cmov(z2, z3, b) + fp448.Sqr(x3, t0) + fp448.Sqr(z3, t1) + fp448.Mul(z3, x1, z3) + fp448.Sqr(x2, x2) + fp448.Sqr(z2, z2) + fp448.Sub(t0, x2, z2) + mulA24Generic(t1, t0) + fp448.Add(t1, t1, z2) + fp448.Mul(x2, x2, z2) + fp448.Mul(z2, t0, t1) +} + +func mulA24Generic(z, x *fp448.Elt) { + const A24 = 39082 + const n = 8 + var xx [7]uint64 + for i := range xx { + xx[i] = binary.LittleEndian.Uint64(x[i*n : (i+1)*n]) + } + h0, l0 := bits.Mul64(xx[0], A24) + h1, l1 := bits.Mul64(xx[1], A24) + h2, l2 := bits.Mul64(xx[2], A24) + h3, l3 := bits.Mul64(xx[3], A24) + h4, l4 := bits.Mul64(xx[4], A24) + h5, l5 := bits.Mul64(xx[5], A24) + h6, l6 := bits.Mul64(xx[6], A24) + + l1, c0 := bits.Add64(h0, l1, 0) + l2, c1 := bits.Add64(h1, l2, c0) + l3, c2 := bits.Add64(h2, l3, c1) + l4, c3 := bits.Add64(h3, l4, c2) + l5, c4 := bits.Add64(h4, l5, c3) + l6, c5 := bits.Add64(h5, l6, c4) + l7, _ := bits.Add64(h6, 0, c5) + + l0, c0 = bits.Add64(l0, l7, 0) + l1, c1 = bits.Add64(l1, 0, c0) + l2, c2 = bits.Add64(l2, 0, c1) + l3, c3 = bits.Add64(l3, l7<<32, c2) + l4, c4 = bits.Add64(l4, 0, c3) + l5, c5 = bits.Add64(l5, 0, c4) + l6, l7 = bits.Add64(l6, 0, c5) + + xx[0], c0 = bits.Add64(l0, l7, 0) + xx[1], c1 = bits.Add64(l1, 0, c0) + xx[2], c2 = bits.Add64(l2, 0, c1) + xx[3], c3 = bits.Add64(l3, l7<<32, c2) + xx[4], c4 = bits.Add64(l4, 0, c3) + xx[5], c5 = bits.Add64(l5, 0, c4) + xx[6], _ = bits.Add64(l6, 0, c5) + + for i := range xx { + binary.LittleEndian.PutUint64(z[i*n:(i+1)*n], xx[i]) + } +} diff --git a/vendor/github.com/cloudflare/circl/dh/x448/curve_noasm.go b/vendor/github.com/cloudflare/circl/dh/x448/curve_noasm.go new file mode 100644 index 00000000..3755b7c8 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x448/curve_noasm.go @@ -0,0 +1,11 @@ +//go:build !amd64 || purego +// +build !amd64 purego + +package x448 + +import fp "github.com/cloudflare/circl/math/fp448" + +func double(x, z *fp.Elt) { doubleGeneric(x, z) } +func diffAdd(w *[5]fp.Elt, b uint) { diffAddGeneric(w, b) } +func ladderStep(w *[5]fp.Elt, b uint) { ladderStepGeneric(w, b) } +func mulA24(z, x *fp.Elt) { mulA24Generic(z, x) } diff --git a/vendor/github.com/cloudflare/circl/dh/x448/doc.go b/vendor/github.com/cloudflare/circl/dh/x448/doc.go new file mode 100644 index 00000000..c02904fe --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x448/doc.go @@ -0,0 +1,19 @@ +/* +Package x448 provides Diffie-Hellman functions as specified in RFC-7748. + +Validation of public keys. + +The Diffie-Hellman function, as described in RFC-7748 [1], works for any +public key. However, if a different protocol requires contributory +behaviour [2,3], then the public keys must be validated against low-order +points [3,4]. To do that, the Shared function performs this validation +internally and returns false when the public key is invalid (i.e., it +is a low-order point). + +References: + - [1] RFC7748 by Langley, Hamburg, Turner (https://rfc-editor.org/rfc/rfc7748.txt) + - [2] Curve25519 by Bernstein (https://cr.yp.to/ecdh.html) + - [3] Bernstein (https://cr.yp.to/ecdh.html#validate) + - [4] Cremers&Jackson (https://eprint.iacr.org/2019/526) +*/ +package x448 diff --git a/vendor/github.com/cloudflare/circl/dh/x448/key.go b/vendor/github.com/cloudflare/circl/dh/x448/key.go new file mode 100644 index 00000000..82a07a2b --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x448/key.go @@ -0,0 +1,46 @@ +package x448 + +import ( + "crypto/subtle" + + fp "github.com/cloudflare/circl/math/fp448" +) + +// Size is the length in bytes of a X448 key. +const Size = 56 + +// Key represents a X448 key. +type Key [Size]byte + +func (k *Key) clamp(in *Key) *Key { + *k = *in + k[0] &= 252 + k[55] |= 128 + return k +} + +// isValidPubKey verifies if the public key is not a low-order point. +func (k *Key) isValidPubKey() bool { + fp.Modp((*fp.Elt)(k)) + isLowOrder := false + for _, P := range lowOrderPoints { + isLowOrder = isLowOrder || subtle.ConstantTimeCompare(P[:], k[:]) != 0 + } + return !isLowOrder +} + +// KeyGen obtains a public key given a secret key. +func KeyGen(public, secret *Key) { + ladderJoye(public.clamp(secret)) +} + +// Shared calculates Alice's shared key from Alice's secret key and Bob's +// public key returning true on success. A failure case happens when the public +// key is a low-order point, thus the shared key is all-zeros and the function +// returns false. +func Shared(shared, secret, public *Key) bool { + validPk := *public + ok := validPk.isValidPubKey() + ladderMontgomery(shared.clamp(secret), &validPk) + return ok +} diff --git a/vendor/github.com/cloudflare/circl/dh/x448/table.go b/vendor/github.com/cloudflare/circl/dh/x448/table.go new file mode 100644 index 00000000..eef53c30 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x448/table.go @@ -0,0 +1,460 @@ +package x448 + +import fp "github.com/cloudflare/circl/math/fp448" + +// tableGenerator contains the set of points: +// +// t[i] = (xi+1)/(xi-1), +// +// where (xi,yi) = 2^iG and G is the generator point +// Size = (448)*(448/8) = 25088 bytes. +var tableGenerator = [448 * fp.Size]byte{ + /* (2^ 0)P */ 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, + /* (2^ 1)P */ 0x37, 0xfa, 0xaa, 0x0d, 0x86, 0xa6, 0x24, 0xe9, 0x6c, 0x95, 0x08, 0x34, 0xba, 0x1a, 0x81, 0x3a, 0xae, 0x01, 0xa5, 0xa7, 0x05, 0x85, 0x96, 0x00, 0x06, 0x5a, 0xd7, 0xff, 0xee, 0x8e, 0x8f, 0x94, 0xd2, 0xdc, 0xd7, 0xfc, 0xe7, 0xe5, 0x99, 0x1d, 0x05, 0x46, 0x43, 0xe8, 0xbc, 0x12, 0xb7, 0xeb, 0x30, 0x5e, 0x7a, 0x85, 0x68, 0xed, 0x9d, 0x28, + /* (2^ 2)P */ 0xf1, 0x7d, 0x08, 0x2b, 0x32, 0x4a, 0x62, 0x80, 0x36, 0xe7, 0xa4, 0x76, 0x5a, 0x2a, 0x1e, 0xf7, 0x9e, 0x3c, 0x40, 0x46, 0x9a, 0x1b, 0x61, 0xc1, 0xbf, 0x1a, 0x1b, 0xae, 0x91, 0x80, 0xa3, 0x76, 0x6c, 0xd4, 0x8f, 0xa4, 0xee, 0x26, 0x39, 0x23, 0xa4, 0x80, 0xf4, 0x66, 0x92, 0xe4, 0xe1, 0x18, 0x76, 0xc5, 0xe2, 0x19, 0x87, 0xd5, 0xc3, 0xe8, + /* (2^ 3)P */ 0xfb, 0xc9, 0xf0, 0x07, 0xf2, 0x93, 0xd8, 0x50, 0x36, 0xed, 0xfb, 0xbd, 0xb2, 0xd3, 0xfc, 0xdf, 0xd5, 0x2a, 0x6e, 0x26, 0x09, 0xce, 0xd4, 0x07, 0x64, 0x9f, 0x40, 0x74, 0xad, 0x98, 0x2f, 0x1c, 0xb6, 0xdc, 0x2d, 0x42, 0xff, 0xbf, 0x97, 0xd8, 0xdb, 0xef, 0x99, 0xca, 0x73, 0x99, 0x1a, 0x04, 0x3b, 0x56, 0x2c, 0x1f, 0x87, 0x9d, 0x9f, 0x03, + /* (2^ 4)P */ 0x4c, 0x35, 0x97, 0xf7, 0x81, 0x2c, 0x84, 0xa6, 0xe0, 0xcb, 0xce, 0x37, 0x4c, 0x21, 0x1c, 0x67, 0xfa, 0xab, 0x18, 0x4d, 0xef, 0xd0, 0xf0, 0x44, 0xa9, 0xfb, 0xc0, 0x8e, 0xda, 0x57, 0xa1, 0xd8, 0xeb, 0x87, 0xf4, 0x17, 0xea, 0x66, 0x0f, 0x16, 0xea, 0xcd, 0x5f, 0x3e, 0x88, 0xea, 0x09, 0x68, 0x40, 0xdf, 0x43, 0xcc, 0x54, 0x61, 0x58, 0xaa, + /* (2^ 5)P */ 0x8d, 0xe7, 0x59, 0xd7, 0x5e, 0x63, 0x37, 0xa7, 0x3f, 0xd1, 0x49, 0x85, 0x01, 0xdd, 0x5e, 0xb3, 0xe6, 0x29, 0xcb, 0x25, 0x93, 0xdd, 0x08, 0x96, 0x83, 0x52, 0x76, 0x85, 0xf5, 0x5d, 0x02, 0xbf, 0xe9, 0x6d, 0x15, 0x27, 0xc1, 0x09, 0xd1, 0x14, 0x4d, 0x6e, 0xe8, 0xaf, 0x59, 0x58, 0x34, 0x9d, 0x2a, 0x99, 0x85, 0x26, 0xbe, 0x4b, 0x1e, 0xb9, + /* (2^ 6)P */ 0x8d, 0xce, 0x94, 0xe2, 0x18, 0x56, 0x0d, 0x82, 0x8e, 0xdf, 0x85, 0x01, 0x8f, 0x93, 0x3c, 0xc6, 0xbd, 0x61, 0xfb, 0xf4, 0x22, 0xc5, 0x16, 0x87, 0xd1, 0xb1, 0x9e, 0x09, 0xc5, 0x83, 0x2e, 0x4a, 0x07, 0x88, 0xee, 0xe0, 0x29, 0x8d, 0x2e, 0x1f, 0x88, 0xad, 0xfd, 0x18, 0x93, 0xb7, 0xed, 0x42, 0x86, 0x78, 0xf0, 0xb8, 0x70, 0xbe, 0x01, 0x67, + /* (2^ 7)P */ 0xdf, 0x62, 0x2d, 0x94, 0xc7, 0x35, 0x23, 0xda, 0x27, 0xbb, 0x2b, 0xdb, 0x30, 0x80, 0x68, 0x16, 0xa3, 0xae, 0xd7, 0xd2, 0xa7, 0x7c, 0xbf, 0x6a, 0x1d, 0x83, 0xde, 0x96, 0x0a, 0x43, 0xb6, 0x30, 0x37, 0xd6, 0xee, 0x63, 0x59, 0x9a, 0xbf, 0xa3, 0x30, 0x6c, 0xaf, 0x0c, 0xee, 0x3d, 0xcb, 0x35, 0x4b, 0x55, 0x5f, 0x84, 0x85, 0xcb, 0x4f, 0x1e, + /* (2^ 8)P */ 0x9d, 0x04, 0x68, 0x89, 0xa4, 0xa9, 0x0d, 0x87, 0xc1, 0x70, 0xf1, 0xeb, 0xfb, 0x47, 0x0a, 0xf0, 0xde, 0x67, 0xb7, 0x94, 0xcd, 0x36, 0x43, 0xa5, 0x49, 0x43, 0x67, 0xc3, 0xee, 0x3c, 0x6b, 0xec, 0xd0, 0x1a, 0xf4, 0xad, 0xef, 0x06, 0x4a, 0xe8, 0x46, 0x24, 0xd7, 0x93, 0xbf, 0xf0, 0xe3, 0x81, 0x61, 0xec, 0xea, 0x64, 0xfe, 0x67, 0xeb, 0xc7, + /* (2^ 9)P */ 0x95, 0x45, 0x79, 0xcf, 0x2c, 0xfd, 0x9b, 0xfe, 0x84, 0x46, 0x4b, 0x8f, 0xa1, 0xcf, 0xc3, 0x04, 0x94, 0x78, 0xdb, 0xc9, 0xa6, 0x01, 0x75, 0xa4, 0xb4, 0x93, 0x72, 0x43, 0xa7, 0x7d, 0xda, 0x31, 0x38, 0x54, 0xab, 0x4e, 0x3f, 0x89, 0xa6, 0xab, 0x57, 0xc0, 0x16, 0x65, 0xdb, 0x92, 0x96, 0xe4, 0xc8, 0xae, 0xe7, 0x4c, 0x7a, 0xeb, 0xbb, 0x5a, + /* (2^ 10)P */ 0xbe, 0xfe, 0x86, 0xc3, 0x97, 0xe0, 0x6a, 0x18, 0x20, 0x21, 0xca, 0x22, 0x55, 0xa1, 0xeb, 0xf5, 0x74, 0xe5, 0xc9, 0x59, 0xa7, 0x92, 0x65, 0x15, 0x08, 0x71, 0xd1, 0x09, 0x7e, 0x83, 0xfc, 0xbc, 0x5a, 0x93, 0x38, 0x0d, 0x43, 0x42, 0xfd, 0x76, 0x30, 0xe8, 0x63, 0x60, 0x09, 0x8d, 0x6c, 0xd3, 0xf8, 0x56, 0x3d, 0x68, 0x47, 0xab, 0xa0, 0x1d, + /* (2^ 11)P */ 0x38, 0x50, 0x1c, 0xb1, 0xac, 0x88, 0x8f, 0x38, 0xe3, 0x69, 0xe6, 0xfc, 0x4f, 0x8f, 0xe1, 0x9b, 0xb1, 0x1a, 0x09, 0x39, 0x19, 0xdf, 0xcd, 0x98, 0x7b, 0x64, 0x42, 0xf6, 0x11, 0xea, 0xc7, 0xe8, 0x92, 0x65, 0x00, 0x2c, 0x75, 0xb5, 0x94, 0x1e, 0x5b, 0xa6, 0x66, 0x81, 0x77, 0xf3, 0x39, 0x94, 0xac, 0xbd, 0xe4, 0x2a, 0x66, 0x84, 0x9c, 0x60, + /* (2^ 12)P */ 0xb5, 0xb6, 0xd9, 0x03, 0x67, 0xa4, 0xa8, 0x0a, 0x4a, 0x2b, 0x9d, 0xfa, 0x13, 0xe1, 0x99, 0x25, 0x4a, 0x5c, 0x67, 0xb9, 0xb2, 0xb7, 0xdd, 0x1e, 0xaf, 0xeb, 0x63, 0x41, 0xb6, 0xb9, 0xa0, 0x87, 0x0a, 0xe0, 0x06, 0x07, 0xaa, 0x97, 0xf8, 0xf9, 0x38, 0x4f, 0xdf, 0x0c, 0x40, 0x7c, 0xc3, 0x98, 0xa9, 0x74, 0xf1, 0x5d, 0xda, 0xd1, 0xc0, 0x0a, + /* (2^ 13)P */ 0xf2, 0x0a, 0xab, 0xab, 0x94, 0x50, 0xf0, 0xa3, 0x6f, 0xc6, 0x66, 0xba, 0xa6, 0xdc, 0x44, 0xdd, 0xd6, 0x08, 0xf4, 0xd3, 0xed, 0xb1, 0x40, 0x93, 0xee, 0xf6, 0xb8, 0x8e, 0xb4, 0x7c, 0xb9, 0x82, 0xc9, 0x9d, 0x45, 0x3b, 0x8e, 0x10, 0xcb, 0x70, 0x1e, 0xba, 0x3c, 0x62, 0x50, 0xda, 0xa9, 0x93, 0xb5, 0xd7, 0xd0, 0x6f, 0x29, 0x52, 0x95, 0xae, + /* (2^ 14)P */ 0x14, 0x68, 0x69, 0x23, 0xa8, 0x44, 0x87, 0x9e, 0x22, 0x91, 0xe8, 0x92, 0xdf, 0xf7, 0xae, 0xba, 0x1c, 0x96, 0xe1, 0xc3, 0x94, 0xed, 0x6c, 0x95, 0xae, 0x96, 0xa7, 0x15, 0x9f, 0xf1, 0x17, 0x11, 0x92, 0x42, 0xd5, 0xcd, 0x18, 0xe7, 0xa9, 0xb5, 0x2f, 0xcd, 0xde, 0x6c, 0xc9, 0x7d, 0xfc, 0x7e, 0xbd, 0x7f, 0x10, 0x3d, 0x01, 0x00, 0x8d, 0x95, + /* (2^ 15)P */ 0x3b, 0x76, 0x72, 0xae, 0xaf, 0x84, 0xf2, 0xf7, 0xd1, 0x6d, 0x13, 0x9c, 0x47, 0xe1, 0xb7, 0xa3, 0x19, 0x16, 0xee, 0x75, 0x45, 0xf6, 0x1a, 0x7b, 0x78, 0x49, 0x79, 0x05, 0x86, 0xf0, 0x7f, 0x9f, 0xfc, 0xc4, 0xbd, 0x86, 0xf3, 0x41, 0xa7, 0xfe, 0x01, 0xd5, 0x67, 0x16, 0x10, 0x5b, 0xa5, 0x16, 0xf3, 0x7f, 0x60, 0xce, 0xd2, 0x0c, 0x8e, 0x4b, + /* (2^ 16)P */ 0x4a, 0x07, 0x99, 0x4a, 0x0f, 0x74, 0x91, 0x14, 0x68, 0xb9, 0x48, 0xb7, 0x44, 0x77, 0x9b, 0x4a, 0xe0, 0x68, 0x0e, 0x43, 0x4d, 0x98, 0x98, 0xbf, 0xa8, 0x3a, 0xb7, 0x6d, 0x2a, 0x9a, 0x77, 0x5f, 0x62, 0xf5, 0x6b, 0x4a, 0xb7, 0x7d, 0xe5, 0x09, 0x6b, 0xc0, 0x8b, 0x9c, 0x88, 0x37, 0x33, 0xf2, 0x41, 0xac, 0x22, 0x1f, 0xcf, 0x3b, 0x82, 0x34, + /* (2^ 17)P */ 0x00, 0xc3, 0x78, 0x42, 0x32, 0x2e, 0xdc, 0xda, 0xb1, 0x96, 0x21, 0xa4, 0xe4, 0xbb, 0xe9, 0x9d, 0xbb, 0x0f, 0x93, 0xed, 0x26, 0x3d, 0xb5, 0xdb, 0x94, 0x31, 0x37, 0x07, 0xa2, 0xb2, 0xd5, 0x99, 0x0d, 0x93, 0xe1, 0xce, 0x3f, 0x0b, 0x96, 0x82, 0x47, 0xfe, 0x60, 0x6f, 0x8f, 0x61, 0x88, 0xd7, 0x05, 0x95, 0x0b, 0x46, 0x06, 0xb7, 0x32, 0x06, + /* (2^ 18)P */ 0x44, 0xf5, 0x34, 0xdf, 0x2f, 0x9c, 0x5d, 0x9f, 0x53, 0x5c, 0x42, 0x8f, 0xc9, 0xdc, 0xd8, 0x40, 0xa2, 0xe7, 0x6a, 0x4a, 0x05, 0xf7, 0x86, 0x77, 0x2b, 0xae, 0x37, 0xed, 0x48, 0xfb, 0xf7, 0x62, 0x7c, 0x17, 0x59, 0x92, 0x41, 0x61, 0x93, 0x38, 0x30, 0xd1, 0xef, 0x54, 0x54, 0x03, 0x17, 0x57, 0x91, 0x15, 0x11, 0x33, 0xb5, 0xfa, 0xfb, 0x17, + /* (2^ 19)P */ 0x29, 0xbb, 0xd4, 0xb4, 0x9c, 0xf1, 0x72, 0x94, 0xce, 0x6a, 0x29, 0xa8, 0x89, 0x18, 0x19, 0xf7, 0xb7, 0xcc, 0xee, 0x9a, 0x02, 0xe3, 0xc0, 0xb1, 0xe0, 0xee, 0x83, 0x78, 0xb4, 0x9e, 0x07, 0x87, 0xdf, 0xb0, 0x82, 0x26, 0x4e, 0xa4, 0x0c, 0x33, 0xaf, 0x40, 0x59, 0xb6, 0xdd, 0x52, 0x45, 0xf0, 0xb4, 0xf6, 0xe8, 0x4e, 0x4e, 0x79, 0x1a, 0x5d, + /* (2^ 20)P */ 0x27, 0x33, 0x4d, 0x4c, 0x6b, 0x4f, 0x75, 0xb1, 0xbc, 0x1f, 0xab, 0x5b, 0x2b, 0xf0, 0x1c, 0x57, 0x86, 0xdd, 0xfd, 0x60, 0xb0, 0x8c, 0xe7, 0x9a, 0xe5, 0x5c, 0xeb, 0x11, 0x3a, 0xda, 0x22, 0x25, 0x99, 0x06, 0x8d, 0xf4, 0xaf, 0x29, 0x7a, 0xc9, 0xe5, 0xd2, 0x16, 0x9e, 0xd4, 0x63, 0x1d, 0x64, 0xa6, 0x47, 0x96, 0x37, 0x6f, 0x93, 0x2c, 0xcc, + /* (2^ 21)P */ 0xc1, 0x94, 0x74, 0x86, 0x75, 0xf2, 0x91, 0x58, 0x23, 0x85, 0x63, 0x76, 0x54, 0xc7, 0xb4, 0x8c, 0xbc, 0x4e, 0xc4, 0xa7, 0xba, 0xa0, 0x55, 0x26, 0x71, 0xd5, 0x33, 0x72, 0xc9, 0xad, 0x1e, 0xf9, 0x5d, 0x78, 0x70, 0x93, 0x4e, 0x85, 0xfc, 0x39, 0x06, 0x73, 0x76, 0xff, 0xe8, 0x64, 0x69, 0x42, 0x45, 0xb2, 0x69, 0xb5, 0x32, 0xe7, 0x2c, 0xde, + /* (2^ 22)P */ 0xde, 0x16, 0xd8, 0x33, 0x49, 0x32, 0xe9, 0x0e, 0x3a, 0x60, 0xee, 0x2e, 0x24, 0x75, 0xe3, 0x9c, 0x92, 0x07, 0xdb, 0xad, 0x92, 0xf5, 0x11, 0xdf, 0xdb, 0xb0, 0x17, 0x5c, 0xd6, 0x1a, 0x70, 0x00, 0xb7, 0xe2, 0x18, 0xec, 0xdc, 0xc2, 0x02, 0x93, 0xb3, 0xc8, 0x3f, 0x4f, 0x1b, 0x96, 0xe6, 0x33, 0x8c, 0xfb, 0xcc, 0xa5, 0x4e, 0xe8, 0xe7, 0x11, + /* (2^ 23)P */ 0x05, 0x7a, 0x74, 0x52, 0xf8, 0xdf, 0x0d, 0x7c, 0x6a, 0x1a, 0x4e, 0x9a, 0x02, 0x1d, 0xae, 0x77, 0xf8, 0x8e, 0xf9, 0xa2, 0x38, 0x54, 0x50, 0xb2, 0x2c, 0x08, 0x9d, 0x9b, 0x9f, 0xfb, 0x2b, 0x06, 0xde, 0x9d, 0xc2, 0x03, 0x0b, 0x22, 0x2b, 0x10, 0x5b, 0x3a, 0x73, 0x29, 0x8e, 0x3e, 0x37, 0x08, 0x2c, 0x3b, 0xf8, 0x80, 0xc1, 0x66, 0x1e, 0x98, + /* (2^ 24)P */ 0xd8, 0xd6, 0x3e, 0xcd, 0x63, 0x8c, 0x2b, 0x41, 0x81, 0xc0, 0x0c, 0x06, 0x87, 0xd6, 0xe7, 0x92, 0xfe, 0xf1, 0x0c, 0x4a, 0x84, 0x5b, 0xaf, 0x40, 0x53, 0x6f, 0x60, 0xd6, 0x6b, 0x76, 0x4b, 0xc2, 0xad, 0xc9, 0xb6, 0xb6, 0x6a, 0xa2, 0xb3, 0xf5, 0xf5, 0xc2, 0x55, 0x83, 0xb2, 0xd3, 0xe9, 0x41, 0x6c, 0x63, 0x51, 0xb8, 0x81, 0x74, 0xc8, 0x2c, + /* (2^ 25)P */ 0xb2, 0xaf, 0x1c, 0xee, 0x07, 0xb0, 0x58, 0xa8, 0x2c, 0x6a, 0xc9, 0x2d, 0x62, 0x28, 0x75, 0x0c, 0x40, 0xb6, 0x11, 0x33, 0x96, 0x80, 0x28, 0x6d, 0xd5, 0x9e, 0x87, 0x90, 0x01, 0x66, 0x1d, 0x1c, 0xf8, 0xb4, 0x92, 0xac, 0x38, 0x18, 0x05, 0xc2, 0x4c, 0x4b, 0x54, 0x7d, 0x80, 0x46, 0x87, 0x2d, 0x99, 0x8e, 0x70, 0x80, 0x69, 0x71, 0x8b, 0xed, + /* (2^ 26)P */ 0x37, 0xa7, 0x6b, 0x71, 0x36, 0x75, 0x8e, 0xff, 0x0f, 0x42, 0xda, 0x5a, 0x46, 0xa6, 0x97, 0x79, 0x7e, 0x30, 0xb3, 0x8f, 0xc7, 0x3a, 0xa0, 0xcb, 0x1d, 0x9c, 0x78, 0x77, 0x36, 0xc2, 0xe7, 0xf4, 0x2f, 0x29, 0x07, 0xb1, 0x07, 0xfd, 0xed, 0x1b, 0x39, 0x77, 0x06, 0x38, 0x77, 0x0f, 0x50, 0x31, 0x12, 0xbf, 0x92, 0xbf, 0x72, 0x79, 0x54, 0xa9, + /* (2^ 27)P */ 0xbd, 0x4d, 0x46, 0x6b, 0x1a, 0x80, 0x46, 0x2d, 0xed, 0xfd, 0x64, 0x6d, 0x94, 0xbc, 0x4a, 0x6e, 0x0c, 0x12, 0xf6, 0x12, 0xab, 0x54, 0x88, 0xd3, 0x85, 0xac, 0x51, 0xae, 0x6f, 0xca, 0xc4, 0xb7, 0xec, 0x22, 0x54, 0x6d, 0x80, 0xb2, 0x1c, 0x63, 0x33, 0x76, 0x6b, 0x8e, 0x6d, 0x59, 0xcd, 0x73, 0x92, 0x5f, 0xff, 0xad, 0x10, 0x35, 0x70, 0x5f, + /* (2^ 28)P */ 0xb3, 0x84, 0xde, 0xc8, 0x04, 0x43, 0x63, 0xfa, 0x29, 0xd9, 0xf0, 0x69, 0x65, 0x5a, 0x0c, 0xe8, 0x2e, 0x0b, 0xfe, 0xb0, 0x7a, 0x42, 0xb3, 0xc3, 0xfc, 0xe6, 0xb8, 0x92, 0x29, 0xae, 0xed, 0xec, 0xd5, 0xe8, 0x4a, 0xa1, 0xbd, 0x3b, 0xd3, 0xc0, 0x07, 0xab, 0x65, 0x65, 0x35, 0x9a, 0xa6, 0x5e, 0x78, 0x18, 0x76, 0x1c, 0x15, 0x49, 0xe6, 0x75, + /* (2^ 29)P */ 0x45, 0xb3, 0x92, 0xa9, 0xc3, 0xb8, 0x11, 0x68, 0x64, 0x3a, 0x83, 0x5d, 0xa8, 0x94, 0x6a, 0x9d, 0xaa, 0x27, 0x9f, 0x98, 0x5d, 0xc0, 0x29, 0xf0, 0xc0, 0x4b, 0x14, 0x3c, 0x05, 0xe7, 0xf8, 0xbd, 0x38, 0x22, 0x96, 0x75, 0x65, 0x5e, 0x0d, 0x3f, 0xbb, 0x6f, 0xe8, 0x3f, 0x96, 0x76, 0x9f, 0xba, 0xd9, 0x44, 0x92, 0x96, 0x22, 0xe7, 0x52, 0xe7, + /* (2^ 30)P */ 0xf4, 0xa3, 0x95, 0x90, 0x47, 0xdf, 0x7d, 0xdc, 0xf4, 0x13, 0x87, 0x67, 0x7d, 0x4f, 0x9d, 0xa0, 0x00, 0x46, 0x72, 0x08, 0xc3, 0xa2, 0x7a, 0x3e, 0xe7, 0x6d, 0x52, 0x7c, 0x11, 0x36, 0x50, 0x83, 0x89, 0x64, 0xcb, 0x1f, 0x08, 0x83, 0x46, 0xcb, 0xac, 0xa6, 0xd8, 0x9c, 0x1b, 0xe8, 0x05, 0x47, 0xc7, 0x26, 0x06, 0x83, 0x39, 0xe9, 0xb1, 0x1c, + /* (2^ 31)P */ 0x11, 0xe8, 0xc8, 0x42, 0xbf, 0x30, 0x9c, 0xa3, 0xf1, 0x85, 0x96, 0x95, 0x4f, 0x4f, 0x52, 0xa2, 0xf5, 0x8b, 0x68, 0x24, 0x16, 0xac, 0x9b, 0xa9, 0x27, 0x28, 0x0e, 0x84, 0x03, 0x46, 0x22, 0x5f, 0xf7, 0x0d, 0xa6, 0x85, 0x88, 0xc1, 0x45, 0x4b, 0x85, 0x1a, 0x10, 0x7f, 0xc9, 0x94, 0x20, 0xb0, 0x04, 0x28, 0x12, 0x30, 0xb9, 0xe6, 0x40, 0x6b, + /* (2^ 32)P */ 0xac, 0x1b, 0x57, 0xb6, 0x42, 0xdb, 0x81, 0x8d, 0x76, 0xfd, 0x9b, 0x1c, 0x29, 0x30, 0xd5, 0x3a, 0xcc, 0x53, 0xd9, 0x26, 0x7a, 0x0f, 0x9c, 0x2e, 0x79, 0xf5, 0x62, 0xeb, 0x61, 0x9d, 0x9b, 0x80, 0x39, 0xcd, 0x60, 0x2e, 0x1f, 0x08, 0x22, 0xbc, 0x19, 0xb3, 0x2a, 0x43, 0x44, 0xf2, 0x4e, 0x66, 0xf4, 0x36, 0xa6, 0xa7, 0xbc, 0xa4, 0x15, 0x7e, + /* (2^ 33)P */ 0xc1, 0x90, 0x8a, 0xde, 0xff, 0x78, 0xc3, 0x73, 0x16, 0xee, 0x76, 0xa0, 0x84, 0x60, 0x8d, 0xe6, 0x82, 0x0f, 0xde, 0x4e, 0xc5, 0x99, 0x34, 0x06, 0x90, 0x44, 0x55, 0xf8, 0x91, 0xd8, 0xe1, 0xe4, 0x2c, 0x8a, 0xde, 0x94, 0x1e, 0x78, 0x25, 0x3d, 0xfd, 0xd8, 0x59, 0x7d, 0xaf, 0x6e, 0xbe, 0x96, 0xbe, 0x3c, 0x16, 0x23, 0x0f, 0x4c, 0xa4, 0x28, + /* (2^ 34)P */ 0xba, 0x11, 0x35, 0x57, 0x03, 0xb6, 0xf4, 0x24, 0x89, 0xb8, 0x5a, 0x0d, 0x50, 0x9c, 0xaa, 0x51, 0x7f, 0xa4, 0x0e, 0xfc, 0x71, 0xb3, 0x3b, 0xf1, 0x96, 0x50, 0x23, 0x15, 0xf5, 0xf5, 0xd4, 0x23, 0xdc, 0x8b, 0x26, 0x9e, 0xae, 0xb7, 0x50, 0xcd, 0xc4, 0x25, 0xf6, 0x75, 0x40, 0x9c, 0x37, 0x79, 0x33, 0x60, 0xd4, 0x4b, 0x13, 0x32, 0xee, 0xe2, + /* (2^ 35)P */ 0x43, 0xb8, 0x56, 0x59, 0xf0, 0x68, 0x23, 0xb3, 0xea, 0x70, 0x58, 0x4c, 0x1e, 0x5a, 0x16, 0x54, 0x03, 0xb2, 0xf4, 0x73, 0xb6, 0xd9, 0x5c, 0x9c, 0x6f, 0xcf, 0x82, 0x2e, 0x54, 0x15, 0x46, 0x2c, 0xa3, 0xda, 0x4e, 0x87, 0xf5, 0x2b, 0xba, 0x91, 0xa3, 0xa0, 0x89, 0xba, 0x48, 0x2b, 0xfa, 0x64, 0x02, 0x7f, 0x78, 0x03, 0xd1, 0xe8, 0x3b, 0xe9, + /* (2^ 36)P */ 0x15, 0xa4, 0x71, 0xd4, 0x0c, 0x24, 0xe9, 0x07, 0xa1, 0x43, 0xf4, 0x7f, 0xbb, 0xa2, 0xa6, 0x6b, 0xfa, 0xb7, 0xea, 0x58, 0xd1, 0x96, 0xb0, 0x24, 0x5c, 0xc7, 0x37, 0x4e, 0x60, 0x0f, 0x40, 0xf2, 0x2f, 0x44, 0x70, 0xea, 0x80, 0x63, 0xfe, 0xfc, 0x46, 0x59, 0x12, 0x27, 0xb5, 0x27, 0xfd, 0xb7, 0x73, 0x0b, 0xca, 0x8b, 0xc2, 0xd3, 0x71, 0x08, + /* (2^ 37)P */ 0x26, 0x0e, 0xd7, 0x52, 0x6f, 0xf1, 0xf2, 0x9d, 0xb8, 0x3d, 0xbd, 0xd4, 0x75, 0x97, 0xd8, 0xbf, 0xa8, 0x86, 0x96, 0xa5, 0x80, 0xa0, 0x45, 0x75, 0xf6, 0x77, 0x71, 0xdb, 0x77, 0x96, 0x55, 0x99, 0x31, 0xd0, 0x4f, 0x34, 0xf4, 0x35, 0x39, 0x41, 0xd3, 0x7d, 0xf7, 0xe2, 0x74, 0xde, 0xbe, 0x5b, 0x1f, 0x39, 0x10, 0x21, 0xa3, 0x4d, 0x3b, 0xc8, + /* (2^ 38)P */ 0x04, 0x00, 0x2a, 0x45, 0xb2, 0xaf, 0x9b, 0x18, 0x6a, 0xeb, 0x96, 0x28, 0xa4, 0x77, 0xd0, 0x13, 0xcf, 0x17, 0x65, 0xe8, 0xc5, 0x81, 0x28, 0xad, 0x39, 0x7a, 0x0b, 0xaa, 0x55, 0x2b, 0xf3, 0xfc, 0x86, 0x40, 0xad, 0x0d, 0x1e, 0x28, 0xa2, 0x2d, 0xc5, 0xd6, 0x04, 0x15, 0xa2, 0x30, 0x3d, 0x12, 0x8e, 0xd6, 0xb5, 0xf7, 0x69, 0xbb, 0x84, 0x20, + /* (2^ 39)P */ 0xd7, 0x7a, 0x77, 0x2c, 0xfb, 0x81, 0x80, 0xe9, 0x1e, 0xc6, 0x36, 0x31, 0x79, 0xc3, 0x7c, 0xa9, 0x57, 0x6b, 0xb5, 0x70, 0xfb, 0xe4, 0xa1, 0xff, 0xfd, 0x21, 0xa5, 0x7c, 0xfa, 0x44, 0xba, 0x0d, 0x96, 0x3d, 0xc4, 0x5c, 0x39, 0x52, 0x87, 0xd7, 0x22, 0x0f, 0x52, 0x88, 0x91, 0x87, 0x96, 0xac, 0xfa, 0x3b, 0xdf, 0xdc, 0x83, 0x8c, 0x99, 0x29, + /* (2^ 40)P */ 0x98, 0x6b, 0x3a, 0x8d, 0x83, 0x17, 0xe1, 0x62, 0xd8, 0x80, 0x4c, 0x97, 0xce, 0x6b, 0xaa, 0x10, 0xa7, 0xc4, 0xe9, 0xeb, 0xa5, 0xfb, 0xc9, 0xdd, 0x2d, 0xeb, 0xfc, 0x9a, 0x71, 0xcd, 0x68, 0x6e, 0xc0, 0x35, 0x64, 0x62, 0x1b, 0x95, 0x12, 0xe8, 0x53, 0xec, 0xf0, 0xf4, 0x86, 0x86, 0x78, 0x18, 0xc4, 0xc6, 0xbc, 0x5a, 0x59, 0x8f, 0x7c, 0x7e, + /* (2^ 41)P */ 0x7f, 0xd7, 0x1e, 0xc5, 0x83, 0xdc, 0x1f, 0xbe, 0x0b, 0xcf, 0x2e, 0x01, 0x01, 0xed, 0xac, 0x17, 0x3b, 0xed, 0xa4, 0x30, 0x96, 0x0e, 0x14, 0x7e, 0x19, 0x2b, 0xa5, 0x67, 0x1e, 0xb3, 0x34, 0x03, 0xa8, 0xbb, 0x0a, 0x7d, 0x08, 0x2d, 0xd5, 0x53, 0x19, 0x6f, 0x13, 0xd5, 0xc0, 0x90, 0x8a, 0xcc, 0xc9, 0x5c, 0xab, 0x24, 0xd7, 0x03, 0xf6, 0x57, + /* (2^ 42)P */ 0x49, 0xcb, 0xb4, 0x96, 0x5f, 0xa6, 0xf8, 0x71, 0x6f, 0x59, 0xad, 0x05, 0x24, 0x2d, 0xaf, 0x67, 0xa8, 0xbe, 0x95, 0xdf, 0x0d, 0x28, 0x5a, 0x7f, 0x6e, 0x87, 0x8c, 0x6e, 0x67, 0x0c, 0xf4, 0xe0, 0x1c, 0x30, 0xc2, 0x66, 0xae, 0x20, 0xa1, 0x34, 0xec, 0x9c, 0xbc, 0xae, 0x3d, 0xa1, 0x28, 0x28, 0x95, 0x1d, 0xc9, 0x3a, 0xa8, 0xfd, 0xfc, 0xa1, + /* (2^ 43)P */ 0xe2, 0x2b, 0x9d, 0xed, 0x02, 0x99, 0x67, 0xbb, 0x2e, 0x16, 0x62, 0x05, 0x70, 0xc7, 0x27, 0xb9, 0x1c, 0x3f, 0xf2, 0x11, 0x01, 0xd8, 0x51, 0xa4, 0x18, 0x92, 0xa9, 0x5d, 0xfb, 0xa9, 0xe4, 0x42, 0xba, 0x38, 0x34, 0x1a, 0x4a, 0xc5, 0x6a, 0x37, 0xde, 0xa7, 0x0c, 0xb4, 0x7e, 0x7f, 0xde, 0xa6, 0xee, 0xcd, 0x55, 0x57, 0x05, 0x06, 0xfd, 0x5d, + /* (2^ 44)P */ 0x2f, 0x32, 0xcf, 0x2e, 0x2c, 0x7b, 0xbe, 0x9a, 0x0c, 0x57, 0x35, 0xf8, 0x87, 0xda, 0x9c, 0xec, 0x48, 0xf2, 0xbb, 0xe2, 0xda, 0x10, 0x58, 0x20, 0xc6, 0xd3, 0x87, 0xe9, 0xc7, 0x26, 0xd1, 0x9a, 0x46, 0x87, 0x90, 0xda, 0xdc, 0xde, 0xc3, 0xb3, 0xf2, 0xe8, 0x6f, 0x4a, 0xe6, 0xe8, 0x9d, 0x98, 0x36, 0x20, 0x03, 0x47, 0x15, 0x3f, 0x64, 0x59, + /* (2^ 45)P */ 0xd4, 0x71, 0x49, 0x0a, 0x67, 0x97, 0xaa, 0x3f, 0xf4, 0x1b, 0x3a, 0x6e, 0x5e, 0x17, 0xcc, 0x0a, 0x8f, 0x81, 0x6a, 0x41, 0x38, 0x77, 0x40, 0x8a, 0x11, 0x42, 0x62, 0xd2, 0x50, 0x32, 0x79, 0x78, 0x28, 0xc2, 0x2e, 0x10, 0x01, 0x94, 0x30, 0x4f, 0x7f, 0x18, 0x17, 0x56, 0x85, 0x4e, 0xad, 0xf7, 0xcb, 0x87, 0x3c, 0x3f, 0x50, 0x2c, 0xc0, 0xba, + /* (2^ 46)P */ 0xbc, 0x30, 0x8e, 0x65, 0x8e, 0x57, 0x5b, 0x38, 0x7a, 0xd4, 0x95, 0x52, 0x7a, 0x32, 0x59, 0x69, 0xcd, 0x9d, 0x47, 0x34, 0x5b, 0x55, 0xa5, 0x24, 0x60, 0xdd, 0xc0, 0xc1, 0x62, 0x73, 0x44, 0xae, 0x4c, 0x9c, 0x65, 0x55, 0x1b, 0x9d, 0x8a, 0x29, 0xb0, 0x1a, 0x52, 0xa8, 0xf1, 0xe6, 0x9a, 0xb3, 0xf6, 0xa3, 0xc9, 0x0a, 0x70, 0x7d, 0x0f, 0xee, + /* (2^ 47)P */ 0x77, 0xd3, 0xe5, 0x8e, 0xfa, 0x00, 0xeb, 0x1b, 0x7f, 0xdc, 0x68, 0x3f, 0x92, 0xbd, 0xb7, 0x0b, 0xb7, 0xb5, 0x24, 0xdf, 0xc5, 0x67, 0x53, 0xd4, 0x36, 0x79, 0xc4, 0x7b, 0x57, 0xbc, 0x99, 0x97, 0x60, 0xef, 0xe4, 0x01, 0xa1, 0xa7, 0xaa, 0x12, 0x36, 0x29, 0xb1, 0x03, 0xc2, 0x83, 0x1c, 0x2b, 0x83, 0xef, 0x2e, 0x2c, 0x23, 0x92, 0xfd, 0xd1, + /* (2^ 48)P */ 0x94, 0xef, 0x03, 0x59, 0xfa, 0x8a, 0x18, 0x76, 0xee, 0x58, 0x08, 0x4d, 0x44, 0xce, 0xf1, 0x52, 0x33, 0x49, 0xf6, 0x69, 0x71, 0xe3, 0xa9, 0xbc, 0x86, 0xe3, 0x43, 0xde, 0x33, 0x7b, 0x90, 0x8b, 0x3e, 0x7d, 0xd5, 0x4a, 0xf0, 0x23, 0x99, 0xa6, 0xea, 0x5f, 0x08, 0xe5, 0xb9, 0x49, 0x8b, 0x0d, 0x6a, 0x21, 0xab, 0x07, 0x62, 0xcd, 0xc4, 0xbe, + /* (2^ 49)P */ 0x61, 0xbf, 0x70, 0x14, 0xfa, 0x4e, 0x9e, 0x7c, 0x0c, 0xf8, 0xb2, 0x48, 0x71, 0x62, 0x83, 0xd6, 0xd1, 0xdc, 0x9c, 0x29, 0x66, 0xb1, 0x34, 0x9c, 0x8d, 0xe6, 0x88, 0xaf, 0xbe, 0xdc, 0x4d, 0xeb, 0xb0, 0xe7, 0x28, 0xae, 0xb2, 0x05, 0x56, 0xc6, 0x0e, 0x10, 0x26, 0xab, 0x2c, 0x59, 0x72, 0x03, 0x66, 0xfe, 0x8f, 0x2c, 0x51, 0x2d, 0xdc, 0xae, + /* (2^ 50)P */ 0xdc, 0x63, 0xf1, 0x8b, 0x5c, 0x65, 0x0b, 0xf1, 0xa6, 0x22, 0xe2, 0xd9, 0xdb, 0x49, 0xb1, 0x3c, 0x47, 0xc2, 0xfe, 0xac, 0x86, 0x07, 0x52, 0xec, 0xb0, 0x08, 0x69, 0xfb, 0xd1, 0x06, 0xdc, 0x48, 0x5c, 0x3d, 0xb2, 0x4d, 0xb8, 0x1a, 0x4e, 0xda, 0xb9, 0xc1, 0x2b, 0xab, 0x4b, 0x62, 0x81, 0x21, 0x9a, 0xfc, 0x3d, 0x39, 0x83, 0x11, 0x36, 0xeb, + /* (2^ 51)P */ 0x94, 0xf3, 0x17, 0xef, 0xf9, 0x60, 0x54, 0xc3, 0xd7, 0x27, 0x35, 0xc5, 0x98, 0x5e, 0xf6, 0x63, 0x6c, 0xa0, 0x4a, 0xd3, 0xa3, 0x98, 0xd9, 0x42, 0xe3, 0xf1, 0xf8, 0x81, 0x96, 0xa9, 0xea, 0x6d, 0x4b, 0x8e, 0x33, 0xca, 0x94, 0x0d, 0xa0, 0xf7, 0xbb, 0x64, 0xa3, 0x36, 0x6f, 0xdc, 0x5a, 0x94, 0x42, 0xca, 0x06, 0xb2, 0x2b, 0x9a, 0x9f, 0x71, + /* (2^ 52)P */ 0xec, 0xdb, 0xa6, 0x1f, 0xdf, 0x15, 0x36, 0xa3, 0xda, 0x8a, 0x7a, 0xb6, 0xa7, 0xe3, 0xaf, 0x52, 0xe0, 0x8d, 0xe8, 0xf2, 0x44, 0x20, 0xeb, 0xa1, 0x20, 0xc4, 0x65, 0x3c, 0x7c, 0x6c, 0x49, 0xed, 0x2f, 0x66, 0x23, 0x68, 0x61, 0x91, 0x40, 0x9f, 0x50, 0x19, 0xd1, 0x84, 0xa7, 0xe2, 0xed, 0x34, 0x37, 0xe3, 0xe4, 0x11, 0x7f, 0x87, 0x55, 0x0f, + /* (2^ 53)P */ 0xb3, 0xa1, 0x0f, 0xb0, 0x48, 0xc0, 0x4d, 0x96, 0xa7, 0xcf, 0x5a, 0x81, 0xb8, 0x4a, 0x46, 0xef, 0x0a, 0xd3, 0x40, 0x7e, 0x02, 0xe3, 0x63, 0xaa, 0x50, 0xd1, 0x2a, 0x37, 0x22, 0x4a, 0x7f, 0x4f, 0xb6, 0xf9, 0x01, 0x82, 0x78, 0x3d, 0x93, 0x14, 0x11, 0x8a, 0x90, 0x60, 0xcd, 0x45, 0x4e, 0x7b, 0x42, 0xb9, 0x3e, 0x6e, 0x68, 0x1f, 0x36, 0x41, + /* (2^ 54)P */ 0x13, 0x73, 0x0e, 0x4f, 0x79, 0x93, 0x9e, 0x29, 0x70, 0x7b, 0x4a, 0x59, 0x1a, 0x9a, 0xf4, 0x55, 0x08, 0xf0, 0xdb, 0x17, 0x58, 0xec, 0x64, 0xad, 0x7f, 0x29, 0xeb, 0x3f, 0x85, 0x4e, 0x60, 0x28, 0x98, 0x1f, 0x73, 0x4e, 0xe6, 0xa8, 0xab, 0xd5, 0xd6, 0xfc, 0xa1, 0x36, 0x6d, 0x15, 0xc6, 0x13, 0x83, 0xa0, 0xc2, 0x6e, 0xd9, 0xdb, 0xc9, 0xcc, + /* (2^ 55)P */ 0xff, 0xd8, 0x52, 0xa3, 0xdc, 0x99, 0xcf, 0x3e, 0x19, 0xb3, 0x68, 0xd0, 0xb5, 0x0d, 0xb8, 0xee, 0x3f, 0xef, 0x6e, 0xc0, 0x38, 0x28, 0x44, 0x92, 0x78, 0x91, 0x1a, 0x08, 0x78, 0x6c, 0x65, 0x24, 0xf3, 0xa2, 0x3d, 0xf2, 0xe5, 0x79, 0x62, 0x69, 0x29, 0xf4, 0x22, 0xc5, 0xdb, 0x6a, 0xae, 0xf4, 0x44, 0xa3, 0x6f, 0xc7, 0x86, 0xab, 0xef, 0xef, + /* (2^ 56)P */ 0xbf, 0x54, 0x9a, 0x09, 0x5d, 0x17, 0xd0, 0xde, 0xfb, 0xf5, 0xca, 0xff, 0x13, 0x20, 0x88, 0x82, 0x3a, 0xe2, 0xd0, 0x3b, 0xfb, 0x05, 0x76, 0xd1, 0xc0, 0x02, 0x71, 0x3b, 0x94, 0xe8, 0xc9, 0x84, 0xcf, 0xa4, 0xe9, 0x28, 0x7b, 0xf5, 0x09, 0xc3, 0x2b, 0x22, 0x40, 0xf1, 0x68, 0x24, 0x24, 0x7d, 0x9f, 0x6e, 0xcd, 0xfe, 0xb0, 0x19, 0x61, 0xf5, + /* (2^ 57)P */ 0xe8, 0x63, 0x51, 0xb3, 0x95, 0x6b, 0x7b, 0x74, 0x92, 0x52, 0x45, 0xa4, 0xed, 0xea, 0x0e, 0x0d, 0x2b, 0x01, 0x1e, 0x2c, 0xbc, 0x91, 0x06, 0x69, 0xdb, 0x1f, 0xb5, 0x77, 0x1d, 0x56, 0xf5, 0xb4, 0x02, 0x80, 0x49, 0x56, 0x12, 0xce, 0x86, 0x05, 0xc9, 0xd9, 0xae, 0xf3, 0x6d, 0xe6, 0x3f, 0x40, 0x52, 0xe9, 0x49, 0x2b, 0x31, 0x06, 0x86, 0x14, + /* (2^ 58)P */ 0xf5, 0x09, 0x3b, 0xd2, 0xff, 0xdf, 0x11, 0xa5, 0x1c, 0x99, 0xe8, 0x1b, 0xa4, 0x2c, 0x7d, 0x8e, 0xc8, 0xf7, 0x03, 0x46, 0xfa, 0xb6, 0xde, 0x73, 0x91, 0x7e, 0x5a, 0x7a, 0xd7, 0x9a, 0x5b, 0x80, 0x24, 0x62, 0x5e, 0x92, 0xf1, 0xa3, 0x45, 0xa3, 0x43, 0x92, 0x8a, 0x2a, 0x5b, 0x0c, 0xb4, 0xc8, 0xad, 0x1c, 0xb6, 0x6c, 0x5e, 0x81, 0x18, 0x91, + /* (2^ 59)P */ 0x96, 0xb3, 0xca, 0x2b, 0xe3, 0x7a, 0x59, 0x72, 0x17, 0x74, 0x29, 0x21, 0xe7, 0x78, 0x07, 0xad, 0xda, 0xb6, 0xcd, 0xf9, 0x27, 0x4d, 0xc8, 0xf2, 0x98, 0x22, 0xca, 0xf2, 0x33, 0x74, 0x7a, 0xdd, 0x1e, 0x71, 0xec, 0xe3, 0x3f, 0xe2, 0xa2, 0xd2, 0x38, 0x75, 0xb0, 0xd0, 0x0a, 0xcf, 0x7d, 0x36, 0xdc, 0x49, 0x38, 0x25, 0x34, 0x4f, 0x20, 0x9a, + /* (2^ 60)P */ 0x2b, 0x6e, 0x04, 0x0d, 0x4f, 0x3d, 0x3b, 0x24, 0xf6, 0x4e, 0x5e, 0x0a, 0xbd, 0x48, 0x96, 0xba, 0x81, 0x8f, 0x39, 0x82, 0x13, 0xe6, 0x72, 0xf3, 0x0f, 0xb6, 0x94, 0xf4, 0xc5, 0x90, 0x74, 0x91, 0xa8, 0xf2, 0xc9, 0xca, 0x9a, 0x4d, 0x98, 0xf2, 0xdf, 0x52, 0x4e, 0x97, 0x2f, 0xeb, 0x84, 0xd3, 0xaf, 0xc2, 0xcc, 0xfb, 0x4c, 0x26, 0x4b, 0xe4, + /* (2^ 61)P */ 0x12, 0x9e, 0xfb, 0x9d, 0x78, 0x79, 0x99, 0xdd, 0xb3, 0x0b, 0x2e, 0x56, 0x41, 0x8e, 0x3f, 0x39, 0xb8, 0x97, 0x89, 0x53, 0x9b, 0x8a, 0x3c, 0x40, 0x9d, 0xa4, 0x6c, 0x2e, 0x31, 0x71, 0xc6, 0x0a, 0x41, 0xd4, 0x95, 0x06, 0x5e, 0xc1, 0xab, 0xc2, 0x14, 0xc4, 0xc7, 0x15, 0x08, 0x3a, 0xad, 0x7a, 0xb4, 0x62, 0xa3, 0x0c, 0x90, 0xf4, 0x47, 0x08, + /* (2^ 62)P */ 0x7f, 0xec, 0x09, 0x82, 0xf5, 0x94, 0x09, 0x93, 0x32, 0xd3, 0xdc, 0x56, 0x80, 0x7b, 0x5b, 0x22, 0x80, 0x6a, 0x96, 0x72, 0xb1, 0xc2, 0xd9, 0xa1, 0x8b, 0x66, 0x42, 0x16, 0xe2, 0x07, 0xb3, 0x2d, 0xf1, 0x75, 0x35, 0x72, 0xc7, 0x98, 0xbe, 0x63, 0x3b, 0x20, 0x75, 0x05, 0xc1, 0x3e, 0x31, 0x5a, 0xf7, 0xaa, 0xae, 0x4b, 0xdb, 0x1d, 0xd0, 0x74, + /* (2^ 63)P */ 0x36, 0x5c, 0x74, 0xe6, 0x5d, 0x59, 0x3f, 0x15, 0x4b, 0x4d, 0x4e, 0x67, 0x41, 0xfe, 0x98, 0x1f, 0x49, 0x76, 0x91, 0x0f, 0x9b, 0xf4, 0xaf, 0x86, 0xaf, 0x66, 0x19, 0xed, 0x46, 0xf1, 0x05, 0x9a, 0xcc, 0xd1, 0x14, 0x1f, 0x82, 0x12, 0x8e, 0xe6, 0xf4, 0xc3, 0x42, 0x5c, 0x4e, 0x33, 0x93, 0xbe, 0x30, 0xe7, 0x64, 0xa9, 0x35, 0x00, 0x4d, 0xf9, + /* (2^ 64)P */ 0x1f, 0xc1, 0x1e, 0xb7, 0xe3, 0x7c, 0xfa, 0xa3, 0x6b, 0x76, 0xaf, 0x9c, 0x05, 0x85, 0x4a, 0xa9, 0xfb, 0xe3, 0x7e, 0xf2, 0x49, 0x56, 0xdc, 0x2f, 0x57, 0x10, 0xba, 0x37, 0xb2, 0x62, 0xf5, 0x6b, 0xe5, 0x8f, 0x0a, 0x87, 0xd1, 0x6a, 0xcb, 0x9d, 0x07, 0xd0, 0xf6, 0x38, 0x99, 0x2c, 0x61, 0x4a, 0x4e, 0xd8, 0xd2, 0x88, 0x29, 0x99, 0x11, 0x95, + /* (2^ 65)P */ 0x6f, 0xdc, 0xd5, 0xd6, 0xd6, 0xa7, 0x4c, 0x46, 0x93, 0x65, 0x62, 0x23, 0x95, 0x32, 0x9c, 0xde, 0x40, 0x41, 0x68, 0x2c, 0x18, 0x4e, 0x5a, 0x8c, 0xc0, 0xc5, 0xc5, 0xea, 0x5c, 0x45, 0x0f, 0x60, 0x78, 0x39, 0xb6, 0x36, 0x23, 0x12, 0xbc, 0x21, 0x9a, 0xf8, 0x91, 0xac, 0xc4, 0x70, 0xdf, 0x85, 0x8e, 0x3c, 0xec, 0x22, 0x04, 0x98, 0xa8, 0xaa, + /* (2^ 66)P */ 0xcc, 0x52, 0x10, 0x5b, 0x4b, 0x6c, 0xc5, 0xfa, 0x3e, 0xd4, 0xf8, 0x1c, 0x04, 0x14, 0x48, 0x33, 0xd9, 0xfc, 0x5f, 0xb0, 0xa5, 0x48, 0x8c, 0x45, 0x8a, 0xee, 0x3e, 0xa7, 0xc1, 0x2e, 0x34, 0xca, 0xf6, 0xc9, 0xeb, 0x10, 0xbb, 0xe1, 0x59, 0x84, 0x25, 0xe8, 0x81, 0x70, 0xc0, 0x09, 0x42, 0xa7, 0x3b, 0x0d, 0x33, 0x00, 0xb5, 0x77, 0xbe, 0x25, + /* (2^ 67)P */ 0xcd, 0x1f, 0xbc, 0x7d, 0xef, 0xe5, 0xca, 0x91, 0xaf, 0xa9, 0x59, 0x6a, 0x09, 0xca, 0xd6, 0x1b, 0x3d, 0x55, 0xde, 0xa2, 0x6a, 0x80, 0xd6, 0x95, 0x47, 0xe4, 0x5f, 0x68, 0x54, 0x08, 0xdf, 0x29, 0xba, 0x2a, 0x02, 0x84, 0xe8, 0xe9, 0x00, 0x77, 0x99, 0x36, 0x03, 0xf6, 0x4a, 0x3e, 0x21, 0x81, 0x7d, 0xb8, 0xa4, 0x8a, 0xa2, 0x05, 0xef, 0xbc, + /* (2^ 68)P */ 0x7c, 0x59, 0x5f, 0x66, 0xd9, 0xb7, 0x83, 0x43, 0x8a, 0xa1, 0x8d, 0x51, 0x70, 0xba, 0xf2, 0x9b, 0x95, 0xc0, 0x4b, 0x4c, 0xa0, 0x14, 0xd3, 0xa4, 0x5d, 0x4a, 0x37, 0x36, 0x97, 0x31, 0x1e, 0x12, 0xe7, 0xbb, 0x08, 0x67, 0xa5, 0x23, 0xd7, 0xfb, 0x97, 0xd8, 0x6a, 0x03, 0xb1, 0xf8, 0x7f, 0xda, 0x58, 0xd9, 0x3f, 0x73, 0x4a, 0x53, 0xe1, 0x7b, + /* (2^ 69)P */ 0x55, 0x83, 0x98, 0x78, 0x6c, 0x56, 0x5e, 0xed, 0xf7, 0x23, 0x3e, 0x4c, 0x7d, 0x09, 0x2d, 0x09, 0x9c, 0x58, 0x8b, 0x32, 0xca, 0xfe, 0xbf, 0x47, 0x03, 0xeb, 0x4d, 0xe7, 0xeb, 0x9c, 0x83, 0x05, 0x68, 0xaa, 0x80, 0x89, 0x44, 0xf9, 0xd4, 0xdc, 0xdb, 0xb1, 0xdb, 0x77, 0xac, 0xf9, 0x2a, 0xae, 0x35, 0xac, 0x74, 0xb5, 0x95, 0x62, 0x18, 0x85, + /* (2^ 70)P */ 0xab, 0x82, 0x7e, 0x10, 0xd7, 0xe6, 0x57, 0xd1, 0x66, 0x12, 0x31, 0x9c, 0x9c, 0xa6, 0x27, 0x59, 0x71, 0x2e, 0xeb, 0xa0, 0x68, 0xc5, 0x87, 0x51, 0xf4, 0xca, 0x3f, 0x98, 0x56, 0xb0, 0x89, 0xb1, 0xc7, 0x7b, 0x46, 0xb3, 0xae, 0x36, 0xf2, 0xee, 0x15, 0x1a, 0x60, 0xf4, 0x50, 0x76, 0x4f, 0xc4, 0x53, 0x0d, 0x36, 0x4d, 0x31, 0xb1, 0x20, 0x51, + /* (2^ 71)P */ 0xf7, 0x1d, 0x8c, 0x1b, 0x5e, 0xe5, 0x02, 0x6f, 0xc5, 0xa5, 0xe0, 0x5f, 0xc6, 0xb6, 0x63, 0x43, 0xaf, 0x3c, 0x19, 0x6c, 0xf4, 0xaf, 0xa4, 0x33, 0xb1, 0x0a, 0x37, 0x3d, 0xd9, 0x4d, 0xe2, 0x29, 0x24, 0x26, 0x94, 0x7c, 0x02, 0xe4, 0xe2, 0xf2, 0xbe, 0xbd, 0xac, 0x1b, 0x48, 0xb8, 0xdd, 0xe9, 0x0d, 0x9a, 0x50, 0x1a, 0x98, 0x71, 0x6e, 0xdc, + /* (2^ 72)P */ 0x9f, 0x40, 0xb1, 0xb3, 0x66, 0x28, 0x6c, 0xfe, 0xa6, 0x7d, 0xf8, 0x3e, 0xb8, 0xf3, 0xde, 0x52, 0x76, 0x52, 0xa3, 0x92, 0x98, 0x23, 0xab, 0x4f, 0x88, 0x97, 0xfc, 0x22, 0xe1, 0x6b, 0x67, 0xcd, 0x13, 0x95, 0xda, 0x65, 0xdd, 0x3b, 0x67, 0x3f, 0x5f, 0x4c, 0xf2, 0x8a, 0xad, 0x98, 0xa7, 0x94, 0x24, 0x45, 0x87, 0x11, 0x7c, 0x75, 0x79, 0x85, + /* (2^ 73)P */ 0x70, 0xbf, 0xf9, 0x3b, 0xa9, 0x44, 0x57, 0x72, 0x96, 0xc9, 0xa4, 0x98, 0x65, 0xbf, 0x87, 0xb3, 0x3a, 0x39, 0x12, 0xde, 0xe5, 0x39, 0x01, 0x4f, 0xf7, 0xc0, 0x71, 0x52, 0x36, 0x85, 0xb3, 0x18, 0xf8, 0x14, 0xc0, 0x6d, 0xae, 0x9e, 0x4f, 0xb0, 0x72, 0x87, 0xac, 0x5c, 0xd1, 0x6c, 0x41, 0x6c, 0x90, 0x9d, 0x22, 0x81, 0xe4, 0x2b, 0xea, 0xe5, + /* (2^ 74)P */ 0xfc, 0xea, 0x1a, 0x65, 0xd9, 0x49, 0x6a, 0x39, 0xb5, 0x96, 0x72, 0x7b, 0x32, 0xf1, 0xd0, 0xe9, 0x45, 0xd9, 0x31, 0x55, 0xc7, 0x34, 0xe9, 0x5a, 0xec, 0x73, 0x0b, 0x03, 0xc4, 0xb3, 0xe6, 0xc9, 0x5e, 0x0a, 0x17, 0xfe, 0x53, 0x66, 0x7f, 0x21, 0x18, 0x74, 0x54, 0x1b, 0xc9, 0x49, 0x16, 0xd2, 0x48, 0xaf, 0x5b, 0x47, 0x7b, 0xeb, 0xaa, 0xc9, + /* (2^ 75)P */ 0x47, 0x04, 0xf5, 0x5a, 0x87, 0x77, 0x9e, 0x21, 0x34, 0x4e, 0x83, 0x88, 0xaf, 0x02, 0x1d, 0xb0, 0x5a, 0x1d, 0x1d, 0x7d, 0x8d, 0x2c, 0xd3, 0x8d, 0x63, 0xa9, 0x45, 0xfb, 0x15, 0x6d, 0x86, 0x45, 0xcd, 0x38, 0x0e, 0xf7, 0x37, 0x79, 0xed, 0x6d, 0x5a, 0xbc, 0x32, 0xcc, 0x66, 0xf1, 0x3a, 0xb2, 0x87, 0x6f, 0x70, 0x71, 0xd9, 0xf2, 0xfa, 0x7b, + /* (2^ 76)P */ 0x68, 0x07, 0xdc, 0x61, 0x40, 0xe4, 0xec, 0x32, 0xc8, 0xbe, 0x66, 0x30, 0x54, 0x80, 0xfd, 0x13, 0x7a, 0xef, 0xae, 0xed, 0x2e, 0x00, 0x6d, 0x3f, 0xbd, 0xfc, 0x91, 0x24, 0x53, 0x7f, 0x63, 0x9d, 0x2e, 0xe3, 0x76, 0xe0, 0xf3, 0xe1, 0x8f, 0x7a, 0xc4, 0x77, 0x0c, 0x91, 0xc0, 0xc2, 0x18, 0x6b, 0x04, 0xad, 0xb6, 0x70, 0x9a, 0x64, 0xc5, 0x82, + /* (2^ 77)P */ 0x7f, 0xea, 0x13, 0xd8, 0x9e, 0xfc, 0x5b, 0x06, 0xb5, 0x4f, 0xda, 0x38, 0xe0, 0x9c, 0xd2, 0x3a, 0xc1, 0x1c, 0x62, 0x70, 0x7f, 0xc6, 0x24, 0x0a, 0x47, 0x04, 0x01, 0xc4, 0x55, 0x09, 0xd1, 0x7a, 0x07, 0xba, 0xa3, 0x80, 0x4f, 0xc1, 0x65, 0x36, 0x6d, 0xc0, 0x10, 0xcf, 0x94, 0xa9, 0xa2, 0x01, 0x44, 0xd1, 0xf9, 0x1c, 0x4c, 0xfb, 0xf8, 0x99, + /* (2^ 78)P */ 0x6c, 0xb9, 0x6b, 0xee, 0x43, 0x5b, 0xb9, 0xbb, 0xee, 0x2e, 0x52, 0xc1, 0xc6, 0xb9, 0x61, 0xd2, 0x93, 0xa5, 0xaf, 0x52, 0xf4, 0xa4, 0x1a, 0x51, 0x61, 0xa7, 0xcb, 0x9e, 0xbb, 0x56, 0x65, 0xe2, 0xbf, 0x75, 0xb9, 0x9c, 0x50, 0x96, 0x60, 0x81, 0x74, 0x47, 0xc0, 0x04, 0x88, 0x71, 0x76, 0x39, 0x9a, 0xa7, 0xb1, 0x4e, 0x43, 0x15, 0xe0, 0xbb, + /* (2^ 79)P */ 0xbb, 0xce, 0xe2, 0xbb, 0xf9, 0x17, 0x0f, 0x82, 0x40, 0xad, 0x73, 0xe3, 0xeb, 0x3b, 0x06, 0x1a, 0xcf, 0x8e, 0x6e, 0x28, 0xb8, 0x26, 0xd9, 0x5b, 0xb7, 0xb3, 0xcf, 0xb4, 0x6a, 0x1c, 0xbf, 0x7f, 0xb8, 0xb5, 0x79, 0xcf, 0x45, 0x68, 0x7d, 0xc5, 0xeb, 0xf3, 0xbe, 0x39, 0x40, 0xfc, 0x07, 0x90, 0x7a, 0x62, 0xad, 0x86, 0x08, 0x71, 0x25, 0xe1, + /* (2^ 80)P */ 0x9b, 0x46, 0xac, 0xef, 0xc1, 0x4e, 0xa1, 0x97, 0x95, 0x76, 0xf9, 0x1b, 0xc2, 0xb2, 0x6a, 0x41, 0xea, 0x80, 0x3d, 0xe9, 0x08, 0x52, 0x5a, 0xe3, 0xf2, 0x08, 0xc5, 0xea, 0x39, 0x3f, 0x44, 0x71, 0x4d, 0xea, 0x0d, 0x05, 0x23, 0xe4, 0x2e, 0x3c, 0x89, 0xfe, 0x12, 0x8a, 0x95, 0x42, 0x0a, 0x68, 0xea, 0x5a, 0x28, 0x06, 0x9e, 0xe3, 0x5f, 0xe0, + /* (2^ 81)P */ 0x00, 0x61, 0x6c, 0x98, 0x9b, 0xe7, 0xb9, 0x06, 0x1c, 0xc5, 0x1b, 0xed, 0xbe, 0xc8, 0xb3, 0xea, 0x87, 0xf0, 0xc4, 0x24, 0x7d, 0xbb, 0x5d, 0xa4, 0x1d, 0x7a, 0x16, 0x00, 0x55, 0x94, 0x67, 0x78, 0xbd, 0x58, 0x02, 0x82, 0x90, 0x53, 0x76, 0xd4, 0x72, 0x99, 0x51, 0x6f, 0x7b, 0xcf, 0x80, 0x30, 0x31, 0x3b, 0x01, 0xc7, 0xc1, 0xef, 0xe6, 0x42, + /* (2^ 82)P */ 0xe2, 0x35, 0xaf, 0x4b, 0x79, 0xc6, 0x12, 0x24, 0x99, 0xc0, 0x68, 0xb0, 0x43, 0x3e, 0xe5, 0xef, 0xe2, 0x29, 0xea, 0xb8, 0xb3, 0xbc, 0x6a, 0x53, 0x2c, 0x69, 0x18, 0x5a, 0xf9, 0x15, 0xae, 0x66, 0x58, 0x18, 0xd3, 0x2d, 0x4b, 0x00, 0xfd, 0x84, 0xab, 0x4f, 0xae, 0x70, 0x6b, 0x9e, 0x9a, 0xdf, 0x83, 0xfd, 0x2e, 0x3c, 0xcf, 0xf8, 0x88, 0x5b, + /* (2^ 83)P */ 0xa4, 0x90, 0x31, 0x85, 0x13, 0xcd, 0xdf, 0x64, 0xc9, 0xa1, 0x0b, 0xe7, 0xb6, 0x73, 0x8a, 0x1b, 0x22, 0x78, 0x4c, 0xd4, 0xae, 0x48, 0x18, 0x00, 0x00, 0xa8, 0x9f, 0x06, 0xf9, 0xfb, 0x2d, 0xc3, 0xb1, 0x2a, 0xbc, 0x13, 0x99, 0x57, 0xaf, 0xf0, 0x8d, 0x61, 0x54, 0x29, 0xd5, 0xf2, 0x72, 0x00, 0x96, 0xd1, 0x85, 0x12, 0x8a, 0xf0, 0x23, 0xfb, + /* (2^ 84)P */ 0x69, 0xc7, 0xdb, 0xd9, 0x92, 0x75, 0x08, 0x9b, 0xeb, 0xa5, 0x93, 0xd1, 0x1a, 0xf4, 0xf5, 0xaf, 0xe6, 0xc4, 0x4a, 0x0d, 0x35, 0x26, 0x39, 0x9d, 0xd3, 0x17, 0x3e, 0xae, 0x2d, 0xbf, 0x73, 0x9f, 0xb7, 0x74, 0x91, 0xd1, 0xd8, 0x5c, 0x14, 0xf9, 0x75, 0xdf, 0xeb, 0xc2, 0x22, 0xd8, 0x14, 0x8d, 0x86, 0x23, 0x4d, 0xd1, 0x2d, 0xdb, 0x6b, 0x42, + /* (2^ 85)P */ 0x8c, 0xda, 0xc6, 0xf8, 0x71, 0xba, 0x2b, 0x06, 0x78, 0xae, 0xcc, 0x3a, 0xe3, 0xe3, 0xa1, 0x8b, 0xe2, 0x34, 0x6d, 0x28, 0x9e, 0x46, 0x13, 0x4d, 0x9e, 0xa6, 0x73, 0x49, 0x65, 0x79, 0x88, 0xb9, 0x3a, 0xd1, 0x6d, 0x2f, 0x48, 0x2b, 0x0a, 0x7f, 0x58, 0x20, 0x37, 0xf4, 0x0e, 0xbb, 0x4a, 0x95, 0x58, 0x0c, 0x88, 0x30, 0xc4, 0x74, 0xdd, 0xfd, + /* (2^ 86)P */ 0x6d, 0x13, 0x4e, 0x89, 0x2d, 0xa9, 0xa3, 0xed, 0x09, 0xe3, 0x0e, 0x71, 0x3e, 0x4a, 0xab, 0x90, 0xde, 0x03, 0xeb, 0x56, 0x46, 0x60, 0x06, 0xf5, 0x71, 0xe5, 0xee, 0x9b, 0xef, 0xff, 0xc4, 0x2c, 0x9f, 0x37, 0x48, 0x45, 0x94, 0x12, 0x41, 0x81, 0x15, 0x70, 0x91, 0x99, 0x5e, 0x56, 0x6b, 0xf4, 0xa6, 0xc9, 0xf5, 0x69, 0x9d, 0x78, 0x37, 0x57, + /* (2^ 87)P */ 0xf3, 0x51, 0x57, 0x7e, 0x43, 0x6f, 0xc6, 0x67, 0x59, 0x0c, 0xcf, 0x94, 0xe6, 0x3d, 0xb5, 0x07, 0xc9, 0x77, 0x48, 0xc9, 0x68, 0x0d, 0x98, 0x36, 0x62, 0x35, 0x38, 0x1c, 0xf5, 0xc5, 0xec, 0x66, 0x78, 0xfe, 0x47, 0xab, 0x26, 0xd6, 0x44, 0xb6, 0x06, 0x0f, 0x89, 0xe3, 0x19, 0x40, 0x1a, 0xe7, 0xd8, 0x65, 0x55, 0xf7, 0x1a, 0xfc, 0xa3, 0x0e, + /* (2^ 88)P */ 0x0e, 0x30, 0xa6, 0xb7, 0x58, 0x60, 0x62, 0x2a, 0x6c, 0x13, 0xa8, 0x14, 0x9b, 0xb8, 0xf2, 0x70, 0xd8, 0xb1, 0x71, 0x88, 0x8c, 0x18, 0x31, 0x25, 0x93, 0x90, 0xb4, 0xc7, 0x49, 0xd8, 0xd4, 0xdb, 0x1e, 0x1e, 0x7f, 0xaa, 0xba, 0xc9, 0xf2, 0x5d, 0xa9, 0x3a, 0x43, 0xb4, 0x5c, 0xee, 0x7b, 0xc7, 0x97, 0xb7, 0x66, 0xd7, 0x23, 0xd9, 0x22, 0x59, + /* (2^ 89)P */ 0x28, 0x19, 0xa6, 0xf9, 0x89, 0x20, 0x78, 0xd4, 0x6d, 0xcb, 0x79, 0x8f, 0x61, 0x6f, 0xb2, 0x5c, 0x4f, 0xa6, 0x54, 0x84, 0x95, 0x24, 0x36, 0x64, 0xcb, 0x39, 0xe7, 0x8f, 0x97, 0x9c, 0x5c, 0x3c, 0xfb, 0x51, 0x11, 0x01, 0x17, 0xdb, 0xc9, 0x9b, 0x51, 0x03, 0x9a, 0xe9, 0xe5, 0x24, 0x1e, 0xf5, 0xda, 0xe0, 0x48, 0x02, 0x23, 0xd0, 0x2c, 0x81, + /* (2^ 90)P */ 0x42, 0x1b, 0xe4, 0x91, 0x85, 0x2a, 0x0c, 0xd2, 0x28, 0x66, 0x57, 0x9e, 0x33, 0x8d, 0x25, 0x71, 0x10, 0x65, 0x76, 0xa2, 0x8c, 0x21, 0x86, 0x81, 0x15, 0xc2, 0x27, 0xeb, 0x54, 0x2d, 0x4f, 0x6c, 0xe6, 0xd6, 0x24, 0x9c, 0x1a, 0x12, 0xb8, 0x81, 0xe2, 0x0a, 0xf3, 0xd3, 0xf0, 0xd3, 0xe1, 0x74, 0x1f, 0x9b, 0x11, 0x47, 0xd0, 0xcf, 0xb6, 0x54, + /* (2^ 91)P */ 0x26, 0x45, 0xa2, 0x10, 0xd4, 0x2d, 0xae, 0xc0, 0xb0, 0xe8, 0x86, 0xb3, 0xc7, 0xea, 0x70, 0x87, 0x61, 0xb5, 0xa5, 0x55, 0xbe, 0x88, 0x1d, 0x7a, 0xd9, 0x6f, 0xeb, 0x83, 0xe2, 0x44, 0x7f, 0x98, 0x04, 0xd6, 0x50, 0x9d, 0xa7, 0x86, 0x66, 0x09, 0x63, 0xe1, 0xed, 0x72, 0xb1, 0xe4, 0x1d, 0x3a, 0xfd, 0x47, 0xce, 0x1c, 0xaa, 0x3b, 0x8f, 0x1b, + /* (2^ 92)P */ 0xf4, 0x3c, 0x4a, 0xb6, 0xc2, 0x9c, 0xe0, 0x2e, 0xb7, 0x38, 0xea, 0x61, 0x35, 0x97, 0x10, 0x90, 0xae, 0x22, 0x48, 0xb3, 0xa9, 0xc6, 0x7a, 0xbb, 0x23, 0xf2, 0xf8, 0x1b, 0xa7, 0xa1, 0x79, 0xcc, 0xc4, 0xf8, 0x08, 0x76, 0x8a, 0x5a, 0x1c, 0x1b, 0xc5, 0x33, 0x91, 0xa9, 0xb8, 0xb9, 0xd3, 0xf8, 0x49, 0xcd, 0xe5, 0x82, 0x43, 0xf7, 0xca, 0x68, + /* (2^ 93)P */ 0x38, 0xba, 0xae, 0x44, 0xfe, 0x57, 0x64, 0x56, 0x7c, 0x0e, 0x9c, 0xca, 0xff, 0xa9, 0x82, 0xbb, 0x38, 0x4a, 0xa7, 0xf7, 0x47, 0xab, 0xbe, 0x6d, 0x23, 0x0b, 0x8a, 0xed, 0xc2, 0xb9, 0x8f, 0xf1, 0xec, 0x91, 0x44, 0x73, 0x64, 0xba, 0xd5, 0x8f, 0x37, 0x38, 0x0d, 0xd5, 0xf8, 0x73, 0x57, 0xb6, 0xc2, 0x45, 0xdc, 0x25, 0xb2, 0xb6, 0xea, 0xd9, + /* (2^ 94)P */ 0xbf, 0xe9, 0x1a, 0x40, 0x4d, 0xcc, 0xe6, 0x1d, 0x70, 0x1a, 0x65, 0xcc, 0x34, 0x2c, 0x37, 0x2c, 0x2d, 0x6b, 0x6d, 0xe5, 0x2f, 0x19, 0x9e, 0xe4, 0xe1, 0xaa, 0xd4, 0xab, 0x54, 0xf4, 0xa8, 0xe4, 0x69, 0x2d, 0x8e, 0x4d, 0xd7, 0xac, 0xb0, 0x5b, 0xfe, 0xe3, 0x26, 0x07, 0xc3, 0xf8, 0x1b, 0x43, 0xa8, 0x1d, 0x64, 0xa5, 0x25, 0x88, 0xbb, 0x77, + /* (2^ 95)P */ 0x92, 0xcd, 0x6e, 0xa0, 0x79, 0x04, 0x18, 0xf4, 0x11, 0x58, 0x48, 0xb5, 0x3c, 0x7b, 0xd1, 0xcc, 0xd3, 0x14, 0x2c, 0xa0, 0xdd, 0x04, 0x44, 0x11, 0xb3, 0x6d, 0x2f, 0x0d, 0xf5, 0x2a, 0x75, 0x5d, 0x1d, 0xda, 0x86, 0x8d, 0x7d, 0x6b, 0x32, 0x68, 0xb6, 0x6c, 0x64, 0x9e, 0xde, 0x80, 0x88, 0xce, 0x08, 0xbf, 0x0b, 0xe5, 0x8e, 0x4f, 0x1d, 0xfb, + /* (2^ 96)P */ 0xaf, 0xe8, 0x85, 0xbf, 0x7f, 0x37, 0x8d, 0x66, 0x7c, 0xd5, 0xd3, 0x96, 0xa5, 0x81, 0x67, 0x95, 0xff, 0x48, 0xde, 0xde, 0xd7, 0x7a, 0x46, 0x34, 0xb1, 0x13, 0x70, 0x29, 0xed, 0x87, 0x90, 0xb0, 0x40, 0x2c, 0xa6, 0x43, 0x6e, 0xb6, 0xbc, 0x48, 0x8a, 0xc1, 0xae, 0xb8, 0xd4, 0xe2, 0xc0, 0x32, 0xb2, 0xa6, 0x2a, 0x8f, 0xb5, 0x16, 0x9e, 0xc3, + /* (2^ 97)P */ 0xff, 0x4d, 0xd2, 0xd6, 0x74, 0xef, 0x2c, 0x96, 0xc1, 0x11, 0xa8, 0xb8, 0xfe, 0x94, 0x87, 0x3e, 0xa0, 0xfb, 0x57, 0xa3, 0xfc, 0x7a, 0x7e, 0x6a, 0x59, 0x6c, 0x54, 0xbb, 0xbb, 0xa2, 0x25, 0x38, 0x1b, 0xdf, 0x5d, 0x7b, 0x94, 0x14, 0xde, 0x07, 0x6e, 0xd3, 0xab, 0x02, 0x26, 0x74, 0x16, 0x12, 0xdf, 0x2e, 0x2a, 0xa7, 0xb0, 0xe8, 0x29, 0xc0, + /* (2^ 98)P */ 0x6a, 0x38, 0x0b, 0xd3, 0xba, 0x45, 0x23, 0xe0, 0x04, 0x3b, 0x83, 0x39, 0xc5, 0x11, 0xe6, 0xcf, 0x39, 0x0a, 0xb3, 0xb0, 0x3b, 0x27, 0x29, 0x63, 0x1c, 0xf3, 0x00, 0xe6, 0xd2, 0x55, 0x21, 0x1f, 0x84, 0x97, 0x9f, 0x01, 0x49, 0x43, 0x30, 0x5f, 0xe0, 0x1d, 0x24, 0xc4, 0x4e, 0xa0, 0x2b, 0x0b, 0x12, 0x55, 0xc3, 0x27, 0xae, 0x08, 0x83, 0x7c, + /* (2^ 99)P */ 0x5d, 0x1a, 0xb7, 0xa9, 0xf5, 0xfd, 0xec, 0xad, 0xb7, 0x87, 0x02, 0x5f, 0x0d, 0x30, 0x4d, 0xe2, 0x65, 0x87, 0xa4, 0x41, 0x45, 0x1d, 0x67, 0xe0, 0x30, 0x5c, 0x13, 0x87, 0xf6, 0x2e, 0x08, 0xc1, 0xc7, 0x12, 0x45, 0xc8, 0x9b, 0xad, 0xb8, 0xd5, 0x57, 0xbb, 0x5c, 0x48, 0x3a, 0xe1, 0x91, 0x5e, 0xf6, 0x4d, 0x8a, 0x63, 0x75, 0x69, 0x0c, 0x01, + /* (2^100)P */ 0x8f, 0x53, 0x2d, 0xa0, 0x71, 0x3d, 0xfc, 0x45, 0x10, 0x96, 0xcf, 0x56, 0xf9, 0xbb, 0x40, 0x3c, 0x86, 0x52, 0x76, 0xbe, 0x84, 0xf9, 0xa6, 0x9d, 0x3d, 0x27, 0xbe, 0xb4, 0x00, 0x49, 0x94, 0xf5, 0x5d, 0xe1, 0x62, 0x85, 0x66, 0xe5, 0xb8, 0x20, 0x2c, 0x09, 0x7d, 0x9d, 0x3d, 0x6e, 0x74, 0x39, 0xab, 0xad, 0xa0, 0x90, 0x97, 0x5f, 0xbb, 0xa7, + /* (2^101)P */ 0xdb, 0x2d, 0x99, 0x08, 0x16, 0x46, 0x83, 0x7a, 0xa8, 0xea, 0x3d, 0x28, 0x5b, 0x49, 0xfc, 0xb9, 0x6d, 0x00, 0x9e, 0x54, 0x4f, 0x47, 0x64, 0x9b, 0x58, 0x4d, 0x07, 0x0c, 0x6f, 0x29, 0x56, 0x0b, 0x00, 0x14, 0x85, 0x96, 0x41, 0x04, 0xb9, 0x5c, 0xa4, 0xf6, 0x16, 0x73, 0x6a, 0xc7, 0x62, 0x0c, 0x65, 0x2f, 0x93, 0xbf, 0xf7, 0xb9, 0xb7, 0xf1, + /* (2^102)P */ 0xeb, 0x6d, 0xb3, 0x46, 0x32, 0xd2, 0xcb, 0x08, 0x94, 0x14, 0xbf, 0x3f, 0xc5, 0xcb, 0x5f, 0x9f, 0x8a, 0x89, 0x0c, 0x1b, 0x45, 0xad, 0x4c, 0x50, 0xb4, 0xe1, 0xa0, 0x6b, 0x11, 0x92, 0xaf, 0x1f, 0x00, 0xcc, 0xe5, 0x13, 0x7e, 0xe4, 0x2e, 0xa0, 0x57, 0xf3, 0xa7, 0x84, 0x79, 0x7a, 0xc2, 0xb7, 0xb7, 0xfc, 0x5d, 0xa5, 0xa9, 0x64, 0xcc, 0xd8, + /* (2^103)P */ 0xa9, 0xc4, 0x12, 0x8b, 0x34, 0x78, 0x3e, 0x38, 0xfd, 0x3f, 0x87, 0xfa, 0x88, 0x94, 0xd5, 0xd9, 0x7f, 0xeb, 0x58, 0xff, 0xb9, 0x45, 0xdb, 0xa1, 0xed, 0x22, 0x28, 0x1d, 0x00, 0x6d, 0x79, 0x85, 0x7a, 0x75, 0x5d, 0xf0, 0xb1, 0x9e, 0x47, 0x28, 0x8c, 0x62, 0xdf, 0xfb, 0x4c, 0x7b, 0xc5, 0x1a, 0x42, 0x95, 0xef, 0x9a, 0xb7, 0x27, 0x7e, 0xda, + /* (2^104)P */ 0xca, 0xd5, 0xc0, 0x17, 0xa1, 0x66, 0x79, 0x9c, 0x2a, 0xb7, 0x0a, 0xfe, 0x62, 0xe4, 0x26, 0x78, 0x90, 0xa7, 0xcb, 0xb0, 0x4f, 0x6d, 0xf9, 0x8f, 0xf7, 0x7d, 0xac, 0xb8, 0x78, 0x1f, 0x41, 0xea, 0x97, 0x1e, 0x62, 0x97, 0x43, 0x80, 0x58, 0x80, 0xb6, 0x69, 0x7d, 0xee, 0x16, 0xd2, 0xa1, 0x81, 0xd7, 0xb1, 0x27, 0x03, 0x48, 0xda, 0xab, 0xec, + /* (2^105)P */ 0x5b, 0xed, 0x40, 0x8e, 0x8c, 0xc1, 0x66, 0x90, 0x7f, 0x0c, 0xb2, 0xfc, 0xbd, 0x16, 0xac, 0x7d, 0x4c, 0x6a, 0xf9, 0xae, 0xe7, 0x4e, 0x11, 0x12, 0xe9, 0xbe, 0x17, 0x09, 0xc6, 0xc1, 0x5e, 0xb5, 0x7b, 0x50, 0x5c, 0x27, 0xfb, 0x80, 0xab, 0x01, 0xfa, 0x5b, 0x9b, 0x75, 0x16, 0x6e, 0xb2, 0x5c, 0x8c, 0x2f, 0xa5, 0x6a, 0x1a, 0x68, 0xa6, 0x90, + /* (2^106)P */ 0x75, 0xfe, 0xb6, 0x96, 0x96, 0x87, 0x4c, 0x12, 0xa9, 0xd1, 0xd8, 0x03, 0xa3, 0xc1, 0x15, 0x96, 0xe8, 0xa0, 0x75, 0x82, 0xa0, 0x6d, 0xea, 0x54, 0xdc, 0x5f, 0x0d, 0x7e, 0xf6, 0x70, 0xb5, 0xdc, 0x7a, 0xf6, 0xc4, 0xd4, 0x21, 0x49, 0xf5, 0xd4, 0x14, 0x6d, 0x48, 0x1d, 0x7c, 0x99, 0x42, 0xdf, 0x78, 0x6b, 0x9d, 0xb9, 0x30, 0x3c, 0xd0, 0x29, + /* (2^107)P */ 0x85, 0xd6, 0xd8, 0xf3, 0x91, 0x74, 0xdd, 0xbd, 0x72, 0x96, 0x10, 0xe4, 0x76, 0x02, 0x5a, 0x72, 0x67, 0xd3, 0x17, 0x72, 0x14, 0x9a, 0x20, 0x5b, 0x0f, 0x8d, 0xed, 0x6d, 0x4e, 0xe3, 0xd9, 0x82, 0xc2, 0x99, 0xee, 0x39, 0x61, 0x69, 0x8a, 0x24, 0x01, 0x92, 0x15, 0xe7, 0xfc, 0xf9, 0x4d, 0xac, 0xf1, 0x30, 0x49, 0x01, 0x0b, 0x6e, 0x0f, 0x20, + /* (2^108)P */ 0xd8, 0x25, 0x94, 0x5e, 0x43, 0x29, 0xf5, 0xcc, 0xe8, 0xe3, 0x55, 0x41, 0x3c, 0x9f, 0x58, 0x5b, 0x00, 0xeb, 0xc5, 0xdf, 0xcf, 0xfb, 0xfd, 0x6e, 0x92, 0xec, 0x99, 0x30, 0xd6, 0x05, 0xdd, 0x80, 0x7a, 0x5d, 0x6d, 0x16, 0x85, 0xd8, 0x9d, 0x43, 0x65, 0xd8, 0x2c, 0x33, 0x2f, 0x5c, 0x41, 0xea, 0xb7, 0x95, 0x77, 0xf2, 0x9e, 0x59, 0x09, 0xe8, + /* (2^109)P */ 0x00, 0xa0, 0x03, 0x80, 0xcd, 0x60, 0xe5, 0x17, 0xd4, 0x15, 0x99, 0xdd, 0x4f, 0xbf, 0x66, 0xb8, 0xc0, 0xf5, 0xf9, 0xfc, 0x6d, 0x42, 0x18, 0x34, 0x1c, 0x7d, 0x5b, 0xb5, 0x09, 0xd0, 0x99, 0x57, 0x81, 0x0b, 0x62, 0xb3, 0xa2, 0xf9, 0x0b, 0xae, 0x95, 0xb8, 0xc2, 0x3b, 0x0d, 0x5b, 0x00, 0xf1, 0xed, 0xbc, 0x05, 0x9d, 0x61, 0xbc, 0x73, 0x9d, + /* (2^110)P */ 0xd4, 0xdb, 0x29, 0xe5, 0x85, 0xe9, 0xc6, 0x89, 0x2a, 0xa8, 0x54, 0xab, 0xb3, 0x7f, 0x88, 0xc0, 0x4d, 0xe0, 0xd1, 0x74, 0x6e, 0xa3, 0xa7, 0x39, 0xd5, 0xcc, 0xa1, 0x8a, 0xcb, 0x5b, 0x34, 0xad, 0x92, 0xb4, 0xd8, 0xd5, 0x17, 0xf6, 0x77, 0x18, 0x9e, 0xaf, 0x45, 0x3b, 0x03, 0xe2, 0xf8, 0x52, 0x60, 0xdc, 0x15, 0x20, 0x9e, 0xdf, 0xd8, 0x5d, + /* (2^111)P */ 0x02, 0xc1, 0xac, 0x1a, 0x15, 0x8e, 0x6c, 0xf5, 0x1e, 0x1e, 0xba, 0x7e, 0xc2, 0xda, 0x7d, 0x02, 0xda, 0x43, 0xae, 0x04, 0x70, 0x28, 0x54, 0x78, 0x94, 0xf5, 0x4f, 0x07, 0x84, 0x8f, 0xed, 0xaa, 0xc0, 0xb8, 0xcd, 0x7f, 0x7e, 0x33, 0xa3, 0xbe, 0x21, 0x29, 0xc8, 0x56, 0x34, 0xc0, 0x76, 0x87, 0x8f, 0xc7, 0x73, 0x58, 0x90, 0x16, 0xfc, 0xd6, + /* (2^112)P */ 0xb8, 0x3f, 0xe1, 0xdf, 0x3a, 0x91, 0x25, 0x0c, 0xf6, 0x47, 0xa8, 0x89, 0xc4, 0xc6, 0x61, 0xec, 0x86, 0x2c, 0xfd, 0xbe, 0xa4, 0x6f, 0xc2, 0xd4, 0x46, 0x19, 0x70, 0x5d, 0x09, 0x02, 0x86, 0xd3, 0x4b, 0xe9, 0x16, 0x7b, 0xf0, 0x0d, 0x6c, 0xff, 0x91, 0x05, 0xbf, 0x55, 0xb4, 0x00, 0x8d, 0xe5, 0x6d, 0x68, 0x20, 0x90, 0x12, 0xb5, 0x5c, 0x32, + /* (2^113)P */ 0x80, 0x45, 0xc8, 0x51, 0x87, 0xba, 0x1c, 0x5c, 0xcf, 0x5f, 0x4b, 0x3c, 0x9e, 0x3b, 0x36, 0xd2, 0x26, 0xa2, 0x7f, 0xab, 0xb7, 0xbf, 0xda, 0x68, 0x23, 0x8f, 0xc3, 0xa0, 0xfd, 0xad, 0xf1, 0x56, 0x3b, 0xd0, 0x75, 0x2b, 0x44, 0x61, 0xd8, 0xf4, 0xf1, 0x05, 0x49, 0x53, 0x07, 0xee, 0x47, 0xef, 0xc0, 0x7c, 0x9d, 0xe4, 0x15, 0x88, 0xc5, 0x47, + /* (2^114)P */ 0x2d, 0xb5, 0x09, 0x80, 0xb9, 0xd3, 0xd8, 0xfe, 0x4c, 0xd2, 0xa6, 0x6e, 0xd3, 0x75, 0xcf, 0xb0, 0x99, 0xcb, 0x50, 0x8d, 0xe9, 0x67, 0x9b, 0x20, 0xe8, 0x57, 0xd8, 0x14, 0x85, 0x73, 0x6a, 0x74, 0xe0, 0x99, 0xf0, 0x6b, 0x6e, 0x59, 0x30, 0x31, 0x33, 0x96, 0x5f, 0xa1, 0x0c, 0x1b, 0xf4, 0xca, 0x09, 0xe1, 0x9b, 0xb5, 0xcf, 0x6d, 0x0b, 0xeb, + /* (2^115)P */ 0x1a, 0xde, 0x50, 0xa9, 0xac, 0x3e, 0x10, 0x43, 0x4f, 0x82, 0x4f, 0xc0, 0xfe, 0x3f, 0x33, 0xd2, 0x64, 0x86, 0x50, 0xa9, 0x51, 0x76, 0x5e, 0x50, 0x97, 0x6c, 0x73, 0x8d, 0x77, 0xa3, 0x75, 0x03, 0xbc, 0xc9, 0xfb, 0x50, 0xd9, 0x6d, 0x16, 0xad, 0x5d, 0x32, 0x3d, 0xac, 0x44, 0xdf, 0x51, 0xf7, 0x19, 0xd4, 0x0b, 0x57, 0x78, 0x0b, 0x81, 0x4e, + /* (2^116)P */ 0x32, 0x24, 0xf1, 0x6c, 0x55, 0x62, 0x1d, 0xb3, 0x1f, 0xda, 0xfa, 0x6a, 0x8f, 0x98, 0x01, 0x16, 0xde, 0x44, 0x50, 0x0d, 0x2e, 0x6c, 0x0b, 0xa2, 0xd3, 0x74, 0x0e, 0xa9, 0xbf, 0x8d, 0xa9, 0xc8, 0xc8, 0x2f, 0x62, 0xc1, 0x35, 0x5e, 0xfd, 0x3a, 0xb3, 0x83, 0x2d, 0xee, 0x4e, 0xfd, 0x5c, 0x5e, 0xad, 0x85, 0xa5, 0x10, 0xb5, 0x4f, 0x34, 0xa7, + /* (2^117)P */ 0xd1, 0x58, 0x6f, 0xe6, 0x54, 0x2c, 0xc2, 0xcd, 0xcf, 0x83, 0xdc, 0x88, 0x0c, 0xb9, 0xb4, 0x62, 0x18, 0x89, 0x65, 0x28, 0xe9, 0x72, 0x4b, 0x65, 0xcf, 0xd6, 0x90, 0x88, 0xd7, 0x76, 0x17, 0x4f, 0x74, 0x64, 0x1e, 0xcb, 0xd3, 0xf5, 0x4b, 0xaa, 0x2e, 0x4d, 0x2d, 0x7c, 0x13, 0x1f, 0xfd, 0xd9, 0x60, 0x83, 0x7e, 0xda, 0x64, 0x1c, 0xdc, 0x9f, + /* (2^118)P */ 0xad, 0xef, 0xac, 0x1b, 0xc1, 0x30, 0x5a, 0x15, 0xc9, 0x1f, 0xac, 0xf1, 0xca, 0x44, 0x95, 0x95, 0xea, 0xf2, 0x22, 0xe7, 0x8d, 0x25, 0xf0, 0xff, 0xd8, 0x71, 0xf7, 0xf8, 0x8f, 0x8f, 0xcd, 0xf4, 0x1e, 0xfe, 0x6c, 0x68, 0x04, 0xb8, 0x78, 0xa1, 0x5f, 0xa6, 0x5d, 0x5e, 0xf9, 0x8d, 0xea, 0x80, 0xcb, 0xf3, 0x17, 0xa6, 0x03, 0xc9, 0x38, 0xd5, + /* (2^119)P */ 0x79, 0x14, 0x31, 0xc3, 0x38, 0xe5, 0xaa, 0xbf, 0x17, 0xa3, 0x04, 0x4e, 0x80, 0x59, 0x9c, 0x9f, 0x19, 0x39, 0xe4, 0x2d, 0x23, 0x54, 0x4a, 0x7f, 0x3e, 0xf3, 0xd9, 0xc7, 0xba, 0x6c, 0x8f, 0x6b, 0xfa, 0x34, 0xb5, 0x23, 0x17, 0x1d, 0xff, 0x1d, 0xea, 0x1f, 0xd7, 0xba, 0x61, 0xb2, 0xe0, 0x38, 0x6a, 0xe9, 0xcf, 0x48, 0x5d, 0x6a, 0x10, 0x9c, + /* (2^120)P */ 0xc8, 0xbb, 0x13, 0x1c, 0x3f, 0x3c, 0x34, 0xfd, 0xac, 0x37, 0x52, 0x44, 0x25, 0xa8, 0xde, 0x1d, 0x63, 0xf4, 0x81, 0x9a, 0xbe, 0x0b, 0x74, 0x2e, 0xc8, 0x51, 0x16, 0xd3, 0xac, 0x4a, 0xaf, 0xe2, 0x5f, 0x3a, 0x89, 0x32, 0xd1, 0x9b, 0x7c, 0x90, 0x0d, 0xac, 0xdc, 0x8b, 0x73, 0x45, 0x45, 0x97, 0xb1, 0x90, 0x2c, 0x1b, 0x31, 0xca, 0xb1, 0x94, + /* (2^121)P */ 0x07, 0x28, 0xdd, 0x10, 0x14, 0xa5, 0x95, 0x7e, 0xf3, 0xe4, 0xd4, 0x14, 0xb4, 0x7e, 0x76, 0xdb, 0x42, 0xd6, 0x94, 0x3e, 0xeb, 0x44, 0x64, 0x88, 0x0d, 0xec, 0xc1, 0x21, 0xf0, 0x79, 0xe0, 0x83, 0x67, 0x55, 0x53, 0xc2, 0xf6, 0xc5, 0xc5, 0x89, 0x39, 0xe8, 0x42, 0xd0, 0x17, 0xbd, 0xff, 0x35, 0x59, 0x0e, 0xc3, 0x06, 0x86, 0xd4, 0x64, 0xcf, + /* (2^122)P */ 0x91, 0xa8, 0xdb, 0x57, 0x9b, 0xe2, 0x96, 0x31, 0x10, 0x6e, 0xd7, 0x9a, 0x97, 0xb3, 0xab, 0xb5, 0x15, 0x66, 0xbe, 0xcc, 0x6d, 0x9a, 0xac, 0x06, 0xb3, 0x0d, 0xaa, 0x4b, 0x9c, 0x96, 0x79, 0x6c, 0x34, 0xee, 0x9e, 0x53, 0x4d, 0x6e, 0xbd, 0x88, 0x02, 0xbf, 0x50, 0x54, 0x12, 0x5d, 0x01, 0x02, 0x46, 0xc6, 0x74, 0x02, 0x8c, 0x24, 0xae, 0xb1, + /* (2^123)P */ 0xf5, 0x22, 0xea, 0xac, 0x7d, 0x9c, 0x33, 0x8a, 0xa5, 0x36, 0x79, 0x6a, 0x4f, 0xa4, 0xdc, 0xa5, 0x73, 0x64, 0xc4, 0x6f, 0x43, 0x02, 0x3b, 0x94, 0x66, 0xd2, 0x4b, 0x4f, 0xf6, 0x45, 0x33, 0x5d, 0x10, 0x33, 0x18, 0x1e, 0xa3, 0xfc, 0xf7, 0xd2, 0xb8, 0xc8, 0xa7, 0xe0, 0x76, 0x8a, 0xcd, 0xff, 0x4f, 0x99, 0x34, 0x47, 0x84, 0x91, 0x96, 0x9f, + /* (2^124)P */ 0x8a, 0x48, 0x3b, 0x48, 0x4a, 0xbc, 0xac, 0xe2, 0x80, 0xd6, 0xd2, 0x35, 0xde, 0xd0, 0x56, 0x42, 0x33, 0xb3, 0x56, 0x5a, 0xcd, 0xb8, 0x3d, 0xb5, 0x25, 0xc1, 0xed, 0xff, 0x87, 0x0b, 0x79, 0xff, 0xf2, 0x62, 0xe1, 0x76, 0xc6, 0xa2, 0x0f, 0xa8, 0x9b, 0x0d, 0xcc, 0x3f, 0x3d, 0x35, 0x27, 0x8d, 0x0b, 0x74, 0xb0, 0xc3, 0x78, 0x8c, 0xcc, 0xc8, + /* (2^125)P */ 0xfc, 0x9a, 0x0c, 0xa8, 0x49, 0x42, 0xb8, 0xdf, 0xcf, 0xb3, 0x19, 0xa6, 0x64, 0x57, 0xfe, 0xe8, 0xf8, 0xa6, 0x4b, 0x86, 0xa1, 0xd5, 0x83, 0x7f, 0x14, 0x99, 0x18, 0x0c, 0x7d, 0x5b, 0xf7, 0x3d, 0xf9, 0x4b, 0x79, 0xb1, 0x86, 0x30, 0xb4, 0x5e, 0x6a, 0xe8, 0x9d, 0xfa, 0x8a, 0x41, 0xc4, 0x30, 0xfc, 0x56, 0x74, 0x14, 0x42, 0xc8, 0x96, 0x0e, + /* (2^126)P */ 0xdf, 0x66, 0xec, 0xbc, 0x44, 0xdb, 0x19, 0xce, 0xd4, 0xb5, 0x49, 0x40, 0x07, 0x49, 0xe0, 0x3a, 0x61, 0x10, 0xfb, 0x7d, 0xba, 0xb1, 0xe0, 0x28, 0x5b, 0x99, 0x59, 0x96, 0xa2, 0xee, 0xe0, 0x23, 0x37, 0x39, 0x1f, 0xe6, 0x57, 0x9f, 0xf8, 0xf8, 0xdc, 0x74, 0xf6, 0x8f, 0x4f, 0x5e, 0x51, 0xa4, 0x12, 0xac, 0xbe, 0xe4, 0xf3, 0xd1, 0xf0, 0x24, + /* (2^127)P */ 0x1e, 0x3e, 0x9a, 0x5f, 0xdf, 0x9f, 0xd6, 0x4e, 0x8a, 0x28, 0xc3, 0xcd, 0x96, 0x9d, 0x57, 0xc7, 0x61, 0x81, 0x90, 0xff, 0xae, 0xb1, 0x4f, 0xc2, 0x96, 0x8b, 0x1a, 0x18, 0xf4, 0x50, 0xcb, 0x31, 0xe1, 0x57, 0xf4, 0x90, 0xa8, 0xea, 0xac, 0xe7, 0x61, 0x98, 0xb6, 0x15, 0xc1, 0x7b, 0x29, 0xa4, 0xc3, 0x18, 0xef, 0xb9, 0xd8, 0xdf, 0xf6, 0xac, + /* (2^128)P */ 0xca, 0xa8, 0x6c, 0xf1, 0xb4, 0xca, 0xfe, 0x31, 0xee, 0x48, 0x38, 0x8b, 0x0e, 0xbb, 0x7a, 0x30, 0xaa, 0xf9, 0xee, 0x27, 0x53, 0x24, 0xdc, 0x2e, 0x15, 0xa6, 0x48, 0x8f, 0xa0, 0x7e, 0xf1, 0xdc, 0x93, 0x87, 0x39, 0xeb, 0x7f, 0x38, 0x92, 0x92, 0x4c, 0x29, 0xe9, 0x57, 0xd8, 0x59, 0xfc, 0xe9, 0x9c, 0x44, 0xc0, 0x65, 0xcf, 0xac, 0x4b, 0xdc, + /* (2^129)P */ 0xa3, 0xd0, 0x37, 0x8f, 0x86, 0x2f, 0xc6, 0x47, 0x55, 0x46, 0x65, 0x26, 0x4b, 0x91, 0xe2, 0x18, 0x5c, 0x4f, 0x23, 0xc1, 0x37, 0x29, 0xb9, 0xc1, 0x27, 0xc5, 0x3c, 0xbf, 0x7e, 0x23, 0xdb, 0x73, 0x99, 0xbd, 0x1b, 0xb2, 0x31, 0x68, 0x3a, 0xad, 0xb7, 0xb0, 0x10, 0xc5, 0xe5, 0x11, 0x51, 0xba, 0xa7, 0x60, 0x66, 0x54, 0xf0, 0x08, 0xd7, 0x69, + /* (2^130)P */ 0x89, 0x41, 0x79, 0xcc, 0xeb, 0x0a, 0xf5, 0x4b, 0xa3, 0x4c, 0xce, 0x52, 0xb0, 0xa7, 0xe4, 0x41, 0x75, 0x7d, 0x04, 0xbb, 0x09, 0x4c, 0x50, 0x9f, 0xdf, 0xea, 0x74, 0x61, 0x02, 0xad, 0xb4, 0x9d, 0xb7, 0x05, 0xb9, 0xea, 0xeb, 0x91, 0x35, 0xe7, 0x49, 0xea, 0xd3, 0x4f, 0x3c, 0x60, 0x21, 0x7a, 0xde, 0xc7, 0xe2, 0x5a, 0xee, 0x8e, 0x93, 0xc7, + /* (2^131)P */ 0x00, 0xe8, 0xed, 0xd0, 0xb3, 0x0d, 0xaf, 0xb2, 0xde, 0x2c, 0xf6, 0x00, 0xe2, 0xea, 0x6d, 0xf8, 0x0e, 0xd9, 0x67, 0x59, 0xa9, 0x50, 0xbb, 0x17, 0x8f, 0xff, 0xb1, 0x9f, 0x17, 0xb6, 0xf2, 0xb5, 0xba, 0x80, 0xf7, 0x0f, 0xba, 0xd5, 0x09, 0x43, 0xaa, 0x4e, 0x3a, 0x67, 0x6a, 0x89, 0x9b, 0x18, 0x65, 0x35, 0xf8, 0x3a, 0x49, 0x91, 0x30, 0x51, + /* (2^132)P */ 0x8d, 0x25, 0xe9, 0x0e, 0x7d, 0x50, 0x76, 0xe4, 0x58, 0x7e, 0xb9, 0x33, 0xe6, 0x65, 0x90, 0xc2, 0x50, 0x9d, 0x50, 0x2e, 0x11, 0xad, 0xd5, 0x43, 0x52, 0x32, 0x41, 0x4f, 0x7b, 0xb6, 0xa0, 0xec, 0x81, 0x75, 0x36, 0x7c, 0x77, 0x85, 0x59, 0x70, 0xe4, 0xf9, 0xef, 0x66, 0x8d, 0x35, 0xc8, 0x2a, 0x6e, 0x5b, 0xc6, 0x0d, 0x0b, 0x29, 0x60, 0x68, + /* (2^133)P */ 0xf8, 0xce, 0xb0, 0x3a, 0x56, 0x7d, 0x51, 0x9a, 0x25, 0x73, 0xea, 0xdd, 0xe4, 0xe0, 0x0e, 0xf0, 0x07, 0xc0, 0x31, 0x00, 0x73, 0x35, 0xd0, 0x39, 0xc4, 0x9b, 0xb7, 0x95, 0xe0, 0x62, 0x70, 0x36, 0x0b, 0xcb, 0xa0, 0x42, 0xde, 0x51, 0xcf, 0x41, 0xe0, 0xb8, 0xb4, 0xc0, 0xe5, 0x46, 0x99, 0x9f, 0x02, 0x7f, 0x14, 0x8c, 0xc1, 0x4e, 0xef, 0xe8, + /* (2^134)P */ 0x10, 0x01, 0x57, 0x0a, 0xbe, 0x8b, 0x18, 0xc8, 0xca, 0x00, 0x28, 0x77, 0x4a, 0x9a, 0xc7, 0x55, 0x2a, 0xcc, 0x0c, 0x7b, 0xb9, 0xe9, 0xc8, 0x97, 0x7c, 0x02, 0xe3, 0x09, 0x2f, 0x62, 0x30, 0xb8, 0x40, 0x09, 0x65, 0xe9, 0x55, 0x63, 0xb5, 0x07, 0xca, 0x9f, 0x00, 0xdf, 0x9d, 0x5c, 0xc7, 0xee, 0x57, 0xa5, 0x90, 0x15, 0x1e, 0x22, 0xa0, 0x12, + /* (2^135)P */ 0x71, 0x2d, 0xc9, 0xef, 0x27, 0xb9, 0xd8, 0x12, 0x43, 0x6b, 0xa8, 0xce, 0x3b, 0x6d, 0x6e, 0x91, 0x43, 0x23, 0xbc, 0x32, 0xb3, 0xbf, 0xe1, 0xc7, 0x39, 0xcf, 0x7c, 0x42, 0x4c, 0xb1, 0x30, 0xe2, 0xdd, 0x69, 0x06, 0xe5, 0xea, 0xf0, 0x2a, 0x16, 0x50, 0x71, 0xca, 0x92, 0xdf, 0xc1, 0xcc, 0xec, 0xe6, 0x54, 0x07, 0xf3, 0x18, 0x8d, 0xd8, 0x29, + /* (2^136)P */ 0x98, 0x51, 0x48, 0x8f, 0xfa, 0x2e, 0x5e, 0x67, 0xb0, 0xc6, 0x17, 0x12, 0xb6, 0x7d, 0xc9, 0xad, 0x81, 0x11, 0xad, 0x0c, 0x1c, 0x2d, 0x45, 0xdf, 0xac, 0x66, 0xbd, 0x08, 0x6f, 0x7c, 0xc7, 0x06, 0x6e, 0x19, 0x08, 0x39, 0x64, 0xd7, 0xe4, 0xd1, 0x11, 0x5f, 0x1c, 0xf4, 0x67, 0xc3, 0x88, 0x6a, 0xe6, 0x07, 0xa3, 0x83, 0xd7, 0xfd, 0x2a, 0xf9, + /* (2^137)P */ 0x87, 0xed, 0xeb, 0xd9, 0xdf, 0xff, 0x43, 0x8b, 0xaa, 0x20, 0x58, 0xb0, 0xb4, 0x6b, 0x14, 0xb8, 0x02, 0xc5, 0x40, 0x20, 0x22, 0xbb, 0xf7, 0xb4, 0xf3, 0x05, 0x1e, 0x4d, 0x94, 0xff, 0xe3, 0xc5, 0x22, 0x82, 0xfe, 0xaf, 0x90, 0x42, 0x98, 0x6b, 0x76, 0x8b, 0x3e, 0x89, 0x3f, 0x42, 0x2a, 0xa7, 0x26, 0x00, 0xda, 0x5c, 0xa2, 0x2b, 0xec, 0xdd, + /* (2^138)P */ 0x5c, 0x21, 0x16, 0x0d, 0x46, 0xb8, 0xd0, 0xa7, 0x88, 0xe7, 0x25, 0xcb, 0x3e, 0x50, 0x73, 0x61, 0xe7, 0xaf, 0x5a, 0x3f, 0x47, 0x8b, 0x3d, 0x97, 0x79, 0x2c, 0xe6, 0x6d, 0x95, 0x74, 0x65, 0x70, 0x36, 0xfd, 0xd1, 0x9e, 0x13, 0x18, 0x63, 0xb1, 0x2d, 0x0b, 0xb5, 0x36, 0x3e, 0xe7, 0x35, 0x42, 0x3b, 0xe6, 0x1f, 0x4d, 0x9d, 0x59, 0xa2, 0x43, + /* (2^139)P */ 0x8c, 0x0c, 0x7c, 0x24, 0x9e, 0xe0, 0xf8, 0x05, 0x1c, 0x9e, 0x1f, 0x31, 0xc0, 0x70, 0xb3, 0xfb, 0x4e, 0xf8, 0x0a, 0x57, 0xb7, 0x49, 0xb5, 0x73, 0xa1, 0x5f, 0x9b, 0x6a, 0x07, 0x6c, 0x87, 0x71, 0x87, 0xd4, 0xbe, 0x98, 0x1e, 0x98, 0xee, 0x52, 0xc1, 0x7b, 0x95, 0x0f, 0x28, 0x32, 0x36, 0x28, 0xd0, 0x3a, 0x0f, 0x7d, 0x2a, 0xa9, 0x62, 0xb9, + /* (2^140)P */ 0x97, 0xe6, 0x18, 0x77, 0xf9, 0x34, 0xac, 0xbc, 0xe0, 0x62, 0x9f, 0x42, 0xde, 0xbd, 0x2f, 0xf7, 0x1f, 0xb7, 0x14, 0x52, 0x8a, 0x79, 0xb2, 0x3f, 0xd2, 0x95, 0x71, 0x01, 0xe8, 0xaf, 0x8c, 0xa4, 0xa4, 0xa7, 0x27, 0xf3, 0x5c, 0xdf, 0x3e, 0x57, 0x7a, 0xf1, 0x76, 0x49, 0xe6, 0x42, 0x3f, 0x8f, 0x1e, 0x63, 0x4a, 0x65, 0xb5, 0x41, 0xf5, 0x02, + /* (2^141)P */ 0x72, 0x85, 0xc5, 0x0b, 0xe1, 0x47, 0x64, 0x02, 0xc5, 0x4d, 0x81, 0x69, 0xb2, 0xcf, 0x0f, 0x6c, 0xd4, 0x6d, 0xd0, 0xc7, 0xb4, 0x1c, 0xd0, 0x32, 0x59, 0x89, 0xe2, 0xe0, 0x96, 0x8b, 0x12, 0x98, 0xbf, 0x63, 0x7a, 0x4c, 0x76, 0x7e, 0x58, 0x17, 0x8f, 0x5b, 0x0a, 0x59, 0x65, 0x75, 0xbc, 0x61, 0x1f, 0xbe, 0xc5, 0x6e, 0x0a, 0x57, 0x52, 0x70, + /* (2^142)P */ 0x92, 0x1c, 0x77, 0xbb, 0x62, 0x02, 0x6c, 0x25, 0x9c, 0x66, 0x07, 0x83, 0xab, 0xcc, 0x80, 0x5d, 0xd2, 0x76, 0x0c, 0xa4, 0xc5, 0xb4, 0x8a, 0x68, 0x23, 0x31, 0x32, 0x29, 0x8a, 0x47, 0x92, 0x12, 0x80, 0xb3, 0xfa, 0x18, 0xe4, 0x8d, 0xc0, 0x4d, 0xfe, 0x97, 0x5f, 0x72, 0x41, 0xb5, 0x5c, 0x7a, 0xbd, 0xf0, 0xcf, 0x5e, 0x97, 0xaa, 0x64, 0x32, + /* (2^143)P */ 0x35, 0x3f, 0x75, 0xc1, 0x7a, 0x75, 0x7e, 0xa9, 0xc6, 0x0b, 0x4e, 0x32, 0x62, 0xec, 0xe3, 0x5c, 0xfb, 0x01, 0x43, 0xb6, 0xd4, 0x5b, 0x75, 0xd2, 0xee, 0x7f, 0x5d, 0x23, 0x2b, 0xb3, 0x54, 0x34, 0x4c, 0xd3, 0xb4, 0x32, 0x84, 0x81, 0xb5, 0x09, 0x76, 0x19, 0xda, 0x58, 0xda, 0x7c, 0xdb, 0x2e, 0xdd, 0x4c, 0x8e, 0xdd, 0x5d, 0x89, 0x10, 0x10, + /* (2^144)P */ 0x57, 0x25, 0x6a, 0x08, 0x37, 0x92, 0xa8, 0xdf, 0x24, 0xef, 0x8f, 0x33, 0x34, 0x52, 0xa4, 0x4c, 0xf0, 0x77, 0x9f, 0x69, 0x77, 0xd5, 0x8f, 0xd2, 0x9a, 0xb3, 0xb6, 0x1d, 0x2d, 0xa6, 0xf7, 0x1f, 0xda, 0xd7, 0xcb, 0x75, 0x11, 0xc3, 0x6b, 0xc0, 0x38, 0xb1, 0xd5, 0x2d, 0x96, 0x84, 0x16, 0xfa, 0x26, 0xb9, 0xcc, 0x3f, 0x16, 0x47, 0x23, 0x74, + /* (2^145)P */ 0x9b, 0x61, 0x2a, 0x1c, 0xdd, 0x39, 0xa5, 0xfa, 0x1c, 0x7d, 0x63, 0x50, 0xca, 0xe6, 0x9d, 0xfa, 0xb7, 0xc4, 0x4c, 0x6a, 0x97, 0x5f, 0x36, 0x4e, 0x47, 0xdd, 0x17, 0xf7, 0xf9, 0x19, 0xce, 0x75, 0x17, 0xad, 0xce, 0x2a, 0xf3, 0xfe, 0x27, 0x8f, 0x3e, 0x48, 0xc0, 0x60, 0x87, 0x24, 0x19, 0xae, 0x59, 0xe4, 0x5a, 0x00, 0x2a, 0xba, 0xa2, 0x1f, + /* (2^146)P */ 0x26, 0x88, 0x42, 0x60, 0x9f, 0x6e, 0x2c, 0x7c, 0x39, 0x0f, 0x47, 0x6a, 0x0e, 0x02, 0xbb, 0x4b, 0x34, 0x29, 0x55, 0x18, 0x36, 0xcf, 0x3b, 0x47, 0xf1, 0x2e, 0xfc, 0x6e, 0x94, 0xff, 0xe8, 0x6b, 0x06, 0xd2, 0xba, 0x77, 0x5e, 0x60, 0xd7, 0x19, 0xef, 0x02, 0x9d, 0x3a, 0xc2, 0xb7, 0xa9, 0xd8, 0x57, 0xee, 0x7e, 0x2b, 0xf2, 0x6d, 0x28, 0xda, + /* (2^147)P */ 0xdf, 0xd9, 0x92, 0x11, 0x98, 0x23, 0xe2, 0x45, 0x2f, 0x74, 0x70, 0xee, 0x0e, 0x55, 0x65, 0x79, 0x86, 0x38, 0x17, 0x92, 0x85, 0x87, 0x99, 0x50, 0xd9, 0x7c, 0xdb, 0xa1, 0x10, 0xec, 0x30, 0xb7, 0x40, 0xa3, 0x23, 0x9b, 0x0e, 0x27, 0x49, 0x29, 0x03, 0x94, 0xff, 0x53, 0xdc, 0xd7, 0xed, 0x49, 0xa9, 0x5a, 0x3b, 0xee, 0xd7, 0xc7, 0x65, 0xaf, + /* (2^148)P */ 0xa0, 0xbd, 0xbe, 0x03, 0xee, 0x0c, 0xbe, 0x32, 0x00, 0x7b, 0x52, 0xcb, 0x92, 0x29, 0xbf, 0xa0, 0xc6, 0xd9, 0xd2, 0xd6, 0x15, 0xe8, 0x3a, 0x75, 0x61, 0x65, 0x56, 0xae, 0xad, 0x3c, 0x2a, 0x64, 0x14, 0x3f, 0x8e, 0xc1, 0x2d, 0x0c, 0x8d, 0x20, 0xdb, 0x58, 0x4b, 0xe5, 0x40, 0x15, 0x4b, 0xdc, 0xa8, 0xbd, 0xef, 0x08, 0xa7, 0xd1, 0xf4, 0xb0, + /* (2^149)P */ 0xa9, 0x0f, 0x05, 0x94, 0x66, 0xac, 0x1f, 0x65, 0x3f, 0xe1, 0xb8, 0xe1, 0x34, 0x5e, 0x1d, 0x8f, 0xe3, 0x93, 0x03, 0x15, 0xff, 0xb6, 0x65, 0xb6, 0x6e, 0xc0, 0x2f, 0xd4, 0x2e, 0xb9, 0x2c, 0x13, 0x3c, 0x99, 0x1c, 0xb5, 0x87, 0xba, 0x79, 0xcb, 0xf0, 0x18, 0x06, 0x86, 0x04, 0x14, 0x25, 0x09, 0xcd, 0x1c, 0x14, 0xda, 0x35, 0xd0, 0x38, 0x3b, + /* (2^150)P */ 0x1b, 0x04, 0xa3, 0x27, 0xb4, 0xd3, 0x37, 0x48, 0x1e, 0x8f, 0x69, 0xd3, 0x5a, 0x2f, 0x20, 0x02, 0x36, 0xbe, 0x06, 0x7b, 0x6b, 0x6c, 0x12, 0x5b, 0x80, 0x74, 0x44, 0xe6, 0xf8, 0xf5, 0x95, 0x59, 0x29, 0xab, 0x51, 0x47, 0x83, 0x28, 0xe0, 0xad, 0xde, 0xaa, 0xd3, 0xb1, 0x1a, 0xcb, 0xa3, 0xcd, 0x8b, 0x6a, 0xb1, 0xa7, 0x0a, 0xd1, 0xf9, 0xbe, + /* (2^151)P */ 0xce, 0x2f, 0x85, 0xca, 0x74, 0x6d, 0x49, 0xb8, 0xce, 0x80, 0x44, 0xe0, 0xda, 0x5b, 0xcf, 0x2f, 0x79, 0x74, 0xfe, 0xb4, 0x2c, 0x99, 0x20, 0x6e, 0x09, 0x04, 0xfb, 0x6d, 0x57, 0x5b, 0x95, 0x0c, 0x45, 0xda, 0x4f, 0x7f, 0x63, 0xcc, 0x85, 0x5a, 0x67, 0x50, 0x68, 0x71, 0xb4, 0x67, 0xb1, 0x2e, 0xc1, 0x1c, 0xdc, 0xff, 0x2a, 0x7c, 0x10, 0x5e, + /* (2^152)P */ 0xa6, 0xde, 0xf3, 0xd4, 0x22, 0x30, 0x24, 0x9e, 0x0b, 0x30, 0x54, 0x59, 0x7e, 0xa2, 0xeb, 0x89, 0x54, 0x65, 0x3e, 0x40, 0xd1, 0xde, 0xe6, 0xee, 0x4d, 0xbf, 0x5e, 0x40, 0x1d, 0xee, 0x4f, 0x68, 0xd9, 0xa7, 0x2f, 0xb3, 0x64, 0xb3, 0xf5, 0xc8, 0xd3, 0xaa, 0x70, 0x70, 0x3d, 0xef, 0xd3, 0x95, 0x54, 0xdb, 0x3e, 0x94, 0x95, 0x92, 0x1f, 0x45, + /* (2^153)P */ 0x22, 0x80, 0x1d, 0x9d, 0x96, 0xa5, 0x78, 0x6f, 0xe0, 0x1e, 0x1b, 0x66, 0x42, 0xc8, 0xae, 0x9e, 0x46, 0x45, 0x08, 0x41, 0xdf, 0x80, 0xae, 0x6f, 0xdb, 0x15, 0x5a, 0x21, 0x31, 0x7a, 0xd0, 0xf2, 0x54, 0x15, 0x88, 0xd3, 0x0f, 0x7f, 0x14, 0x5a, 0x14, 0x97, 0xab, 0xf4, 0x58, 0x6a, 0x9f, 0xea, 0x74, 0xe5, 0x6b, 0x90, 0x59, 0x2b, 0x48, 0xd9, + /* (2^154)P */ 0x12, 0x24, 0x04, 0xf5, 0x50, 0xc2, 0x8c, 0xb0, 0x7c, 0x46, 0x98, 0xd5, 0x24, 0xad, 0xf6, 0x72, 0xdc, 0x82, 0x1a, 0x60, 0xc1, 0xeb, 0x48, 0xef, 0x7f, 0x6e, 0xe6, 0xcc, 0xdb, 0x7b, 0xae, 0xbe, 0x5e, 0x1e, 0x5c, 0xe6, 0x0a, 0x70, 0xdf, 0xa4, 0xa3, 0x85, 0x1b, 0x1b, 0x7f, 0x72, 0xb9, 0x96, 0x6f, 0xdc, 0x03, 0x76, 0x66, 0xfb, 0xa0, 0x33, + /* (2^155)P */ 0x37, 0x40, 0xbb, 0xbc, 0x68, 0x58, 0x86, 0xca, 0xbb, 0xa5, 0x24, 0x76, 0x3d, 0x48, 0xd1, 0xad, 0xb4, 0xa8, 0xcf, 0xc3, 0xb6, 0xa8, 0xba, 0x1a, 0x3a, 0xbe, 0x33, 0x75, 0x04, 0x5c, 0x13, 0x8c, 0x0d, 0x70, 0x8d, 0xa6, 0x4e, 0x2a, 0xeb, 0x17, 0x3c, 0x22, 0xdd, 0x3e, 0x96, 0x40, 0x11, 0x9e, 0x4e, 0xae, 0x3d, 0xf8, 0x91, 0xd7, 0x50, 0xc8, + /* (2^156)P */ 0xd8, 0xca, 0xde, 0x19, 0xcf, 0x00, 0xe4, 0x73, 0x18, 0x7f, 0x9b, 0x9f, 0xf4, 0x5b, 0x49, 0x49, 0x99, 0xdc, 0xa4, 0x46, 0x21, 0xb5, 0xd7, 0x3e, 0xb7, 0x47, 0x1b, 0xa9, 0x9f, 0x4c, 0x69, 0x7d, 0xec, 0x33, 0xd6, 0x1c, 0x51, 0x7f, 0x47, 0x74, 0x7a, 0x6c, 0xf3, 0xd2, 0x2e, 0xbf, 0xdf, 0x6c, 0x9e, 0x77, 0x3b, 0x34, 0xf6, 0x73, 0x80, 0xed, + /* (2^157)P */ 0x16, 0xfb, 0x16, 0xc3, 0xc2, 0x83, 0xe4, 0xf4, 0x03, 0x7f, 0x52, 0xb0, 0x67, 0x51, 0x7b, 0x24, 0x5a, 0x51, 0xd3, 0xb6, 0x4e, 0x59, 0x76, 0xcd, 0x08, 0x7b, 0x1d, 0x7a, 0x9c, 0x65, 0xae, 0xce, 0xaa, 0xd2, 0x1c, 0x85, 0x66, 0x68, 0x06, 0x15, 0xa8, 0x06, 0xe6, 0x16, 0x37, 0xf4, 0x49, 0x9e, 0x0f, 0x50, 0x37, 0xb1, 0xb2, 0x93, 0x70, 0x43, + /* (2^158)P */ 0x18, 0x3a, 0x16, 0xe5, 0x8d, 0xc8, 0x35, 0xd6, 0x7b, 0x09, 0xec, 0x61, 0x5f, 0x5c, 0x2a, 0x19, 0x96, 0x2e, 0xc3, 0xfd, 0xab, 0xe6, 0x23, 0xae, 0xab, 0xc5, 0xcb, 0xb9, 0x7b, 0x2d, 0x34, 0x51, 0xb9, 0x41, 0x9e, 0x7d, 0xca, 0xda, 0x25, 0x45, 0x14, 0xb0, 0xc7, 0x4d, 0x26, 0x2b, 0xfe, 0x43, 0xb0, 0x21, 0x5e, 0xfa, 0xdc, 0x7c, 0xf9, 0x5a, + /* (2^159)P */ 0x94, 0xad, 0x42, 0x17, 0xf5, 0xcd, 0x1c, 0x0d, 0xf6, 0x41, 0xd2, 0x55, 0xbb, 0x50, 0xf1, 0xc6, 0xbc, 0xa6, 0xc5, 0x3a, 0xfd, 0x9b, 0x75, 0x3e, 0xf6, 0x1a, 0xa7, 0xb2, 0x6e, 0x64, 0x12, 0xdc, 0x3c, 0xe5, 0xf6, 0xfc, 0x3b, 0xfa, 0x43, 0x81, 0xd4, 0xa5, 0xee, 0xf5, 0x9c, 0x47, 0x2f, 0xd0, 0x9c, 0xde, 0xa1, 0x48, 0x91, 0x9a, 0x34, 0xc1, + /* (2^160)P */ 0x37, 0x1b, 0xb3, 0x88, 0xc9, 0x98, 0x4e, 0xfb, 0x84, 0x4f, 0x2b, 0x0a, 0xb6, 0x8f, 0x35, 0x15, 0xcd, 0x61, 0x7a, 0x5f, 0x5c, 0xa0, 0xca, 0x23, 0xa0, 0x93, 0x1f, 0xcc, 0x3c, 0x39, 0x3a, 0x24, 0xa7, 0x49, 0xad, 0x8d, 0x59, 0xcc, 0x94, 0x5a, 0x16, 0xf5, 0x70, 0xe8, 0x52, 0x1e, 0xee, 0x20, 0x30, 0x17, 0x7e, 0xf0, 0x4c, 0x93, 0x06, 0x5a, + /* (2^161)P */ 0x81, 0xba, 0x3b, 0xd7, 0x3e, 0xb4, 0x32, 0x3a, 0x22, 0x39, 0x2a, 0xfc, 0x19, 0xd9, 0xd2, 0xf6, 0xc5, 0x79, 0x6c, 0x0e, 0xde, 0xda, 0x01, 0xff, 0x52, 0xfb, 0xb6, 0x95, 0x4e, 0x7a, 0x10, 0xb8, 0x06, 0x86, 0x3c, 0xcd, 0x56, 0xd6, 0x15, 0xbf, 0x6e, 0x3e, 0x4f, 0x35, 0x5e, 0xca, 0xbc, 0xa5, 0x95, 0xa2, 0xdf, 0x2d, 0x1d, 0xaf, 0x59, 0xf9, + /* (2^162)P */ 0x69, 0xe5, 0xe2, 0xfa, 0xc9, 0x7f, 0xdd, 0x09, 0xf5, 0x6b, 0x4e, 0x2e, 0xbe, 0xb4, 0xbf, 0x3e, 0xb2, 0xf2, 0x81, 0x30, 0xe1, 0x07, 0xa8, 0x0d, 0x2b, 0xd2, 0x5a, 0x55, 0xbe, 0x4b, 0x86, 0x5d, 0xb0, 0x5e, 0x7c, 0x8f, 0xc1, 0x3c, 0x81, 0x4c, 0xf7, 0x6d, 0x7d, 0xe6, 0x4f, 0x8a, 0x85, 0xc2, 0x2f, 0x28, 0xef, 0x8c, 0x69, 0xc2, 0xc2, 0x1a, + /* (2^163)P */ 0xd9, 0xe4, 0x0e, 0x1e, 0xc2, 0xf7, 0x2f, 0x9f, 0xa1, 0x40, 0xfe, 0x46, 0x16, 0xaf, 0x2e, 0xd1, 0xec, 0x15, 0x9b, 0x61, 0x92, 0xce, 0xfc, 0x10, 0x43, 0x1d, 0x00, 0xf6, 0xbe, 0x20, 0x80, 0x80, 0x6f, 0x3c, 0x16, 0x94, 0x59, 0xba, 0x03, 0x53, 0x6e, 0xb6, 0xdd, 0x25, 0x7b, 0x86, 0xbf, 0x96, 0xf4, 0x2f, 0xa1, 0x96, 0x8d, 0xf9, 0xb3, 0x29, + /* (2^164)P */ 0x3b, 0x04, 0x60, 0x6e, 0xce, 0xab, 0xd2, 0x63, 0x18, 0x53, 0x88, 0x16, 0x4a, 0x6a, 0xab, 0x72, 0x03, 0x68, 0xa5, 0xd4, 0x0d, 0xb2, 0x82, 0x81, 0x1f, 0x2b, 0x5c, 0x75, 0xe8, 0xd2, 0x1d, 0x7f, 0xe7, 0x1b, 0x35, 0x02, 0xde, 0xec, 0xbd, 0xcb, 0xc7, 0x01, 0xd3, 0x95, 0x61, 0xfe, 0xb2, 0x7a, 0x66, 0x09, 0x4c, 0x6d, 0xfd, 0x39, 0xf7, 0x52, + /* (2^165)P */ 0x42, 0xc1, 0x5f, 0xf8, 0x35, 0x52, 0xc1, 0xfe, 0xc5, 0x11, 0x80, 0x1c, 0x11, 0x46, 0x31, 0x11, 0xbe, 0xd0, 0xc4, 0xb6, 0x07, 0x13, 0x38, 0xa0, 0x8d, 0x65, 0xf0, 0x56, 0x9e, 0x16, 0xbf, 0x9d, 0xcd, 0x51, 0x34, 0xf9, 0x08, 0x48, 0x7b, 0x76, 0x0c, 0x7b, 0x30, 0x07, 0xa8, 0x76, 0xaf, 0xa3, 0x29, 0x38, 0xb0, 0x58, 0xde, 0x72, 0x4b, 0x45, + /* (2^166)P */ 0xd4, 0x16, 0xa7, 0xc0, 0xb4, 0x9f, 0xdf, 0x1a, 0x37, 0xc8, 0x35, 0xed, 0xc5, 0x85, 0x74, 0x64, 0x09, 0x22, 0xef, 0xe9, 0x0c, 0xaf, 0x12, 0x4c, 0x9e, 0xf8, 0x47, 0x56, 0xe0, 0x7f, 0x4e, 0x24, 0x6b, 0x0c, 0xe7, 0xad, 0xc6, 0x47, 0x1d, 0xa4, 0x0d, 0x86, 0x89, 0x65, 0xe8, 0x5f, 0x71, 0xc7, 0xe9, 0xcd, 0xec, 0x6c, 0x62, 0xc7, 0xe3, 0xb3, + /* (2^167)P */ 0xb5, 0xea, 0x86, 0xe3, 0x15, 0x18, 0x3f, 0x6d, 0x7b, 0x05, 0x95, 0x15, 0x53, 0x26, 0x1c, 0xeb, 0xbe, 0x7e, 0x16, 0x42, 0x4b, 0xa2, 0x3d, 0xdd, 0x0e, 0xff, 0xba, 0x67, 0xb5, 0xae, 0x7a, 0x17, 0xde, 0x23, 0xad, 0x14, 0xcc, 0xd7, 0xaf, 0x57, 0x01, 0xe0, 0xdd, 0x48, 0xdd, 0xd7, 0xe3, 0xdf, 0xe9, 0x2d, 0xda, 0x67, 0xa4, 0x9f, 0x29, 0x04, + /* (2^168)P */ 0x16, 0x53, 0xe6, 0x9c, 0x4e, 0xe5, 0x1e, 0x70, 0x81, 0x25, 0x02, 0x9b, 0x47, 0x6d, 0xd2, 0x08, 0x73, 0xbe, 0x0a, 0xf1, 0x7b, 0xeb, 0x24, 0xeb, 0x38, 0x23, 0x5c, 0xb6, 0x3e, 0xce, 0x1e, 0xe3, 0xbc, 0x82, 0x35, 0x1f, 0xaf, 0x3a, 0x3a, 0xe5, 0x4e, 0xc1, 0xca, 0xbf, 0x47, 0xb4, 0xbb, 0xbc, 0x5f, 0xea, 0xc6, 0xca, 0xf3, 0xa0, 0xa2, 0x73, + /* (2^169)P */ 0xef, 0xa4, 0x7a, 0x4e, 0xe4, 0xc7, 0xb6, 0x43, 0x2e, 0xa5, 0xe4, 0xa5, 0xba, 0x1e, 0xa5, 0xfe, 0x9e, 0xce, 0xa9, 0x80, 0x04, 0xcb, 0x4f, 0xd8, 0x74, 0x05, 0x48, 0xfa, 0x99, 0x11, 0x5d, 0x97, 0x3b, 0x07, 0x0d, 0xdd, 0xe6, 0xb1, 0x74, 0x87, 0x1a, 0xd3, 0x26, 0xb7, 0x8f, 0xe1, 0x63, 0x3d, 0xec, 0x53, 0x93, 0xb0, 0x81, 0x78, 0x34, 0xa4, + /* (2^170)P */ 0xe1, 0xe7, 0xd4, 0x58, 0x9d, 0x0e, 0x8b, 0x65, 0x66, 0x37, 0x16, 0x48, 0x6f, 0xaa, 0x42, 0x37, 0x77, 0xad, 0xb1, 0x56, 0x48, 0xdf, 0x65, 0x36, 0x30, 0xb8, 0x00, 0x12, 0xd8, 0x32, 0x28, 0x7f, 0xc1, 0x71, 0xeb, 0x93, 0x0f, 0x48, 0x04, 0xe1, 0x5a, 0x6a, 0x96, 0xc1, 0xca, 0x89, 0x6d, 0x1b, 0x82, 0x4c, 0x18, 0x6d, 0x55, 0x4b, 0xea, 0xfd, + /* (2^171)P */ 0x62, 0x1a, 0x53, 0xb4, 0xb1, 0xbe, 0x6f, 0x15, 0x18, 0x88, 0xd4, 0x66, 0x61, 0xc7, 0x12, 0x69, 0x02, 0xbd, 0x03, 0x23, 0x2b, 0xef, 0xf9, 0x54, 0xa4, 0x85, 0xa8, 0xe3, 0xb7, 0xbd, 0xa9, 0xa3, 0xf3, 0x2a, 0xdd, 0xf1, 0xd4, 0x03, 0x0f, 0xa9, 0xa1, 0xd8, 0xa3, 0xcd, 0xb2, 0x71, 0x90, 0x4b, 0x35, 0x62, 0xf2, 0x2f, 0xce, 0x67, 0x1f, 0xaa, + /* (2^172)P */ 0x9e, 0x1e, 0xcd, 0x43, 0x7e, 0x87, 0x37, 0x94, 0x3a, 0x97, 0x4c, 0x7e, 0xee, 0xc9, 0x37, 0x85, 0xf1, 0xd9, 0x4f, 0xbf, 0xf9, 0x6f, 0x39, 0x9a, 0x39, 0x87, 0x2e, 0x25, 0x84, 0x42, 0xc3, 0x80, 0xcb, 0x07, 0x22, 0xae, 0x30, 0xd5, 0x50, 0xa1, 0x23, 0xcc, 0x31, 0x81, 0x9d, 0xf1, 0x30, 0xd9, 0x2b, 0x73, 0x41, 0x16, 0x50, 0xab, 0x2d, 0xa2, + /* (2^173)P */ 0xa4, 0x69, 0x4f, 0xa1, 0x4e, 0xb9, 0xbf, 0x14, 0xe8, 0x2b, 0x04, 0x93, 0xb7, 0x6e, 0x9f, 0x7d, 0x73, 0x0a, 0xc5, 0x14, 0xb8, 0xde, 0x8c, 0xc1, 0xfe, 0xc0, 0xa7, 0xa4, 0xcc, 0x42, 0x42, 0x81, 0x15, 0x65, 0x8a, 0x80, 0xb9, 0xde, 0x1f, 0x60, 0x33, 0x0e, 0xcb, 0xfc, 0xe0, 0xdb, 0x83, 0xa1, 0xe5, 0xd0, 0x16, 0x86, 0x2c, 0xe2, 0x87, 0xed, + /* (2^174)P */ 0x7a, 0xc0, 0xeb, 0x6b, 0xf6, 0x0d, 0x4c, 0x6d, 0x1e, 0xdb, 0xab, 0xe7, 0x19, 0x45, 0xc6, 0xe3, 0xb2, 0x06, 0xbb, 0xbc, 0x70, 0x99, 0x83, 0x33, 0xeb, 0x28, 0xc8, 0x77, 0xf6, 0x4d, 0x01, 0xb7, 0x59, 0xa0, 0xd2, 0xb3, 0x2a, 0x72, 0x30, 0xe7, 0x11, 0x39, 0xb6, 0x41, 0x29, 0x65, 0x5a, 0x14, 0xb9, 0x86, 0x08, 0xe0, 0x7d, 0x32, 0x8c, 0xf0, + /* (2^175)P */ 0x5c, 0x11, 0x30, 0x9e, 0x05, 0x27, 0xf5, 0x45, 0x0f, 0xb3, 0xc9, 0x75, 0xc3, 0xd7, 0xe1, 0x82, 0x3b, 0x8e, 0x87, 0x23, 0x00, 0x15, 0x19, 0x07, 0xd9, 0x21, 0x53, 0xc7, 0xf1, 0xa3, 0xbf, 0x70, 0x64, 0x15, 0x18, 0xca, 0x23, 0x9e, 0xd3, 0x08, 0xc3, 0x2a, 0x8b, 0xe5, 0x83, 0x04, 0x89, 0x14, 0xfd, 0x28, 0x25, 0x1c, 0xe3, 0x26, 0xa7, 0x22, + /* (2^176)P */ 0xdc, 0xd4, 0x75, 0x60, 0x99, 0x94, 0xea, 0x09, 0x8e, 0x8a, 0x3c, 0x1b, 0xf9, 0xbd, 0x33, 0x0d, 0x51, 0x3d, 0x12, 0x6f, 0x4e, 0x72, 0xe0, 0x17, 0x20, 0xe9, 0x75, 0xe6, 0x3a, 0xb2, 0x13, 0x83, 0x4e, 0x7a, 0x08, 0x9e, 0xd1, 0x04, 0x5f, 0x6b, 0x42, 0x0b, 0x76, 0x2a, 0x2d, 0x77, 0x53, 0x6c, 0x65, 0x6d, 0x8e, 0x25, 0x3c, 0xb6, 0x8b, 0x69, + /* (2^177)P */ 0xb9, 0x49, 0x28, 0xd0, 0xdc, 0x6c, 0x8f, 0x4c, 0xc9, 0x14, 0x8a, 0x38, 0xa3, 0xcb, 0xc4, 0x9d, 0x53, 0xcf, 0xe9, 0xe3, 0xcf, 0xe0, 0xb1, 0xf2, 0x1b, 0x4c, 0x7f, 0x83, 0x2a, 0x7a, 0xe9, 0x8b, 0x3b, 0x86, 0x61, 0x30, 0xe9, 0x99, 0xbd, 0xba, 0x19, 0x6e, 0x65, 0x2a, 0x12, 0x3e, 0x9c, 0xa8, 0xaf, 0xc3, 0xcf, 0xf8, 0x1f, 0x77, 0x86, 0xea, + /* (2^178)P */ 0x30, 0xde, 0xe7, 0xff, 0x54, 0xf7, 0xa2, 0x59, 0xf6, 0x0b, 0xfb, 0x7a, 0xf2, 0x39, 0xf0, 0xdb, 0x39, 0xbc, 0xf0, 0xfa, 0x60, 0xeb, 0x6b, 0x4f, 0x47, 0x17, 0xc8, 0x00, 0x65, 0x6d, 0x25, 0x1c, 0xd0, 0x48, 0x56, 0x53, 0x45, 0x11, 0x30, 0x02, 0x49, 0x20, 0x27, 0xac, 0xf2, 0x4c, 0xac, 0x64, 0x3d, 0x52, 0xb8, 0x89, 0xe0, 0x93, 0x16, 0x0f, + /* (2^179)P */ 0x84, 0x09, 0xba, 0x40, 0xb2, 0x2f, 0xa3, 0xa8, 0xc2, 0xba, 0x46, 0x33, 0x05, 0x9d, 0x62, 0xad, 0xa1, 0x3c, 0x33, 0xef, 0x0d, 0xeb, 0xf0, 0x77, 0x11, 0x5a, 0xb0, 0x21, 0x9c, 0xdf, 0x55, 0x24, 0x25, 0x35, 0x51, 0x61, 0x92, 0xf0, 0xb1, 0xce, 0xf5, 0xd4, 0x7b, 0x6c, 0x21, 0x9d, 0x56, 0x52, 0xf8, 0xa1, 0x4c, 0xe9, 0x27, 0x55, 0xac, 0x91, + /* (2^180)P */ 0x03, 0x3e, 0x30, 0xd2, 0x0a, 0xfa, 0x7d, 0x82, 0x3d, 0x1f, 0x8b, 0xcb, 0xb6, 0x04, 0x5c, 0xcc, 0x8b, 0xda, 0xe2, 0x68, 0x74, 0x08, 0x8c, 0x44, 0x83, 0x57, 0x6d, 0x6f, 0x80, 0xb0, 0x7e, 0xa9, 0x82, 0x91, 0x7b, 0x4c, 0x37, 0x97, 0xd1, 0x63, 0xd1, 0xbd, 0x45, 0xe6, 0x8a, 0x86, 0xd6, 0x89, 0x54, 0xfd, 0xd2, 0xb1, 0xd7, 0x54, 0xad, 0xaf, + /* (2^181)P */ 0x8b, 0x33, 0x62, 0x49, 0x9f, 0x63, 0xf9, 0x87, 0x42, 0x58, 0xbf, 0xb3, 0xe6, 0x68, 0x02, 0x60, 0x5c, 0x76, 0x62, 0xf7, 0x61, 0xd7, 0x36, 0x31, 0xf7, 0x9c, 0xb5, 0xe5, 0x13, 0x6c, 0xea, 0x78, 0xae, 0xcf, 0xde, 0xbf, 0xb6, 0xeb, 0x4f, 0xc8, 0x2a, 0xb4, 0x9a, 0x9f, 0xf3, 0xd1, 0x6a, 0xec, 0x0c, 0xbd, 0x85, 0x98, 0x40, 0x06, 0x1c, 0x2a, + /* (2^182)P */ 0x74, 0x3b, 0xe7, 0x81, 0xd5, 0xae, 0x54, 0x56, 0x03, 0xe8, 0x97, 0x16, 0x76, 0xcf, 0x24, 0x96, 0x96, 0x5b, 0xcc, 0x09, 0xab, 0x23, 0x6f, 0x54, 0xae, 0x8f, 0xe4, 0x12, 0xcb, 0xfd, 0xbc, 0xac, 0x93, 0x45, 0x3d, 0x68, 0x08, 0x22, 0x59, 0xc6, 0xf0, 0x47, 0x19, 0x8c, 0x79, 0x93, 0x1e, 0x0e, 0x30, 0xb0, 0x94, 0xfb, 0x17, 0x1d, 0x5a, 0x12, + /* (2^183)P */ 0x85, 0xff, 0x40, 0x18, 0x85, 0xff, 0x44, 0x37, 0x69, 0x23, 0x4d, 0x34, 0xe1, 0xeb, 0xa3, 0x1b, 0x55, 0x40, 0xc1, 0x64, 0xf4, 0xd4, 0x13, 0x0a, 0x9f, 0xb9, 0x19, 0xfc, 0x88, 0x7d, 0xc0, 0x72, 0xcf, 0x69, 0x2f, 0xd2, 0x0c, 0x82, 0x0f, 0xda, 0x08, 0xba, 0x0f, 0xaa, 0x3b, 0xe9, 0xe5, 0x83, 0x7a, 0x06, 0xe8, 0x1b, 0x38, 0x43, 0xc3, 0x54, + /* (2^184)P */ 0x14, 0xaa, 0xb3, 0x6e, 0xe6, 0x28, 0xee, 0xc5, 0x22, 0x6c, 0x7c, 0xf9, 0xa8, 0x71, 0xcc, 0xfe, 0x68, 0x7e, 0xd3, 0xb8, 0x37, 0x96, 0xca, 0x0b, 0xd9, 0xb6, 0x06, 0xa9, 0xf6, 0x71, 0xe8, 0x31, 0xf7, 0xd8, 0xf1, 0x5d, 0xab, 0xb9, 0xf0, 0x5c, 0x98, 0xcf, 0x22, 0xa2, 0x2a, 0xf6, 0xd0, 0x59, 0xf0, 0x9d, 0xd9, 0x6a, 0x4f, 0x59, 0x57, 0xad, + /* (2^185)P */ 0xd7, 0x2b, 0x3d, 0x38, 0x4c, 0x2e, 0x23, 0x4d, 0x49, 0xa2, 0x62, 0x62, 0xf9, 0x0f, 0xde, 0x08, 0xf3, 0x86, 0x71, 0xb6, 0xc7, 0xf9, 0x85, 0x9c, 0x33, 0xa1, 0xcf, 0x16, 0xaa, 0x60, 0xb9, 0xb7, 0xea, 0xed, 0x01, 0x1c, 0x59, 0xdb, 0x3f, 0x3f, 0x97, 0x2e, 0xf0, 0x09, 0x9f, 0x10, 0x85, 0x5f, 0x53, 0x39, 0xf3, 0x13, 0x40, 0x56, 0x95, 0xf9, + /* (2^186)P */ 0xb4, 0xe3, 0xda, 0xc6, 0x1f, 0x78, 0x8e, 0xac, 0xd4, 0x20, 0x1d, 0xa0, 0xbf, 0x4c, 0x09, 0x16, 0xa7, 0x30, 0xb5, 0x8d, 0x9e, 0xa1, 0x5f, 0x6d, 0x52, 0xf4, 0x71, 0xb6, 0x32, 0x2d, 0x21, 0x51, 0xc6, 0xfc, 0x2f, 0x08, 0xf4, 0x13, 0x6c, 0x55, 0xba, 0x72, 0x81, 0x24, 0x49, 0x0e, 0x4f, 0x06, 0x36, 0x39, 0x6a, 0xc5, 0x81, 0xfc, 0xeb, 0xb2, + /* (2^187)P */ 0x7d, 0x8d, 0xc8, 0x6c, 0xea, 0xb4, 0xb9, 0xe8, 0x40, 0xc9, 0x69, 0xc9, 0x30, 0x05, 0xfd, 0x34, 0x46, 0xfd, 0x94, 0x05, 0x16, 0xf5, 0x4b, 0x13, 0x3d, 0x24, 0x1a, 0xd6, 0x64, 0x2b, 0x9c, 0xe2, 0xa5, 0xd9, 0x98, 0xe0, 0xe8, 0xf4, 0xbc, 0x2c, 0xbd, 0xa2, 0x56, 0xe3, 0x9e, 0x14, 0xdb, 0xbf, 0x05, 0xbf, 0x9a, 0x13, 0x5d, 0xf7, 0x91, 0xa3, + /* (2^188)P */ 0x8b, 0xcb, 0x27, 0xf3, 0x15, 0x26, 0x05, 0x40, 0x0f, 0xa6, 0x15, 0x13, 0x71, 0x95, 0xa2, 0xc6, 0x38, 0x04, 0x67, 0xf8, 0x9a, 0x83, 0x06, 0xaa, 0x25, 0x36, 0x72, 0x01, 0x6f, 0x74, 0x5f, 0xe5, 0x6e, 0x44, 0x99, 0xce, 0x13, 0xbc, 0x82, 0xc2, 0x0d, 0xa4, 0x98, 0x50, 0x38, 0xf3, 0xa2, 0xc5, 0xe5, 0x24, 0x1f, 0x6f, 0x56, 0x3e, 0x07, 0xb2, + /* (2^189)P */ 0xbd, 0x0f, 0x32, 0x60, 0x07, 0xb1, 0xd7, 0x0b, 0x11, 0x07, 0x57, 0x02, 0x89, 0xe8, 0x8b, 0xe8, 0x5a, 0x1f, 0xee, 0x54, 0x6b, 0xff, 0xb3, 0x04, 0x07, 0x57, 0x13, 0x0b, 0x94, 0xa8, 0x4d, 0x81, 0xe2, 0x17, 0x16, 0x45, 0xd4, 0x4b, 0xf7, 0x7e, 0x64, 0x66, 0x20, 0xe8, 0x0b, 0x26, 0xfd, 0xa9, 0x8a, 0x47, 0x52, 0x89, 0x14, 0xd0, 0xd1, 0xa1, + /* (2^190)P */ 0xdc, 0x03, 0xe6, 0x20, 0x44, 0x47, 0x8f, 0x04, 0x16, 0x24, 0x22, 0xc1, 0x55, 0x5c, 0xbe, 0x43, 0xc3, 0x92, 0xc5, 0x54, 0x3d, 0x5d, 0xd1, 0x05, 0x9c, 0xc6, 0x7c, 0xbf, 0x23, 0x84, 0x1a, 0xba, 0x4f, 0x1f, 0xfc, 0xa1, 0xae, 0x1a, 0x64, 0x02, 0x51, 0xf1, 0xcb, 0x7a, 0x20, 0xce, 0xb2, 0x34, 0x3c, 0xca, 0xe0, 0xe4, 0xba, 0x22, 0xd4, 0x7b, + /* (2^191)P */ 0xca, 0xfd, 0xca, 0xd7, 0xde, 0x61, 0xae, 0xf0, 0x79, 0x0c, 0x20, 0xab, 0xbc, 0x6f, 0x4d, 0x61, 0xf0, 0xc7, 0x9c, 0x8d, 0x4b, 0x52, 0xf3, 0xb9, 0x48, 0x63, 0x0b, 0xb6, 0xd2, 0x25, 0x9a, 0x96, 0x72, 0xc1, 0x6b, 0x0c, 0xb5, 0xfb, 0x71, 0xaa, 0xad, 0x47, 0x5b, 0xe7, 0xc0, 0x0a, 0x55, 0xb2, 0xd4, 0x16, 0x2f, 0xb1, 0x01, 0xfd, 0xce, 0x27, + /* (2^192)P */ 0x64, 0x11, 0x4b, 0xab, 0x57, 0x09, 0xc6, 0x49, 0x4a, 0x37, 0xc3, 0x36, 0xc4, 0x7b, 0x81, 0x1f, 0x42, 0xed, 0xbb, 0xe0, 0xa0, 0x8d, 0x51, 0xe6, 0xca, 0x8b, 0xb9, 0xcd, 0x99, 0x2d, 0x91, 0x53, 0xa9, 0x47, 0xcb, 0x32, 0xc7, 0xa4, 0x92, 0xec, 0x46, 0x74, 0x44, 0x6d, 0x71, 0x9f, 0x6d, 0x0c, 0x69, 0xa4, 0xf8, 0xbe, 0x9f, 0x7f, 0xa0, 0xd7, + /* (2^193)P */ 0x5f, 0x33, 0xb6, 0x91, 0xc8, 0xa5, 0x3f, 0x5d, 0x7f, 0x38, 0x6e, 0x74, 0x20, 0x4a, 0xd6, 0x2b, 0x98, 0x2a, 0x41, 0x4b, 0x83, 0x64, 0x0b, 0x92, 0x7a, 0x06, 0x1e, 0xc6, 0x2c, 0xf6, 0xe4, 0x91, 0xe5, 0xb1, 0x2e, 0x6e, 0x4e, 0xa8, 0xc8, 0x14, 0x32, 0x57, 0x44, 0x1c, 0xe4, 0xb9, 0x7f, 0x54, 0x51, 0x08, 0x81, 0xaa, 0x4e, 0xce, 0xa1, 0x5d, + /* (2^194)P */ 0x5c, 0xd5, 0x9b, 0x5e, 0x7c, 0xb5, 0xb1, 0x52, 0x73, 0x00, 0x41, 0x56, 0x79, 0x08, 0x7e, 0x07, 0x28, 0x06, 0xa6, 0xfb, 0x7f, 0x69, 0xbd, 0x7a, 0x3c, 0xae, 0x9f, 0x39, 0xbb, 0x54, 0xa2, 0x79, 0xb9, 0x0e, 0x7f, 0xbb, 0xe0, 0xe6, 0xb7, 0x27, 0x64, 0x38, 0x45, 0xdb, 0x84, 0xe4, 0x61, 0x72, 0x3f, 0xe2, 0x24, 0xfe, 0x7a, 0x31, 0x9a, 0xc9, + /* (2^195)P */ 0xa1, 0xd2, 0xa4, 0xee, 0x24, 0x96, 0xe5, 0x5b, 0x79, 0x78, 0x3c, 0x7b, 0x82, 0x3b, 0x8b, 0x58, 0x0b, 0xa3, 0x63, 0x2d, 0xbc, 0x75, 0x46, 0xe8, 0x83, 0x1a, 0xc0, 0x2a, 0x92, 0x61, 0xa8, 0x75, 0x37, 0x3c, 0xbf, 0x0f, 0xef, 0x8f, 0x6c, 0x97, 0x75, 0x10, 0x05, 0x7a, 0xde, 0x23, 0xe8, 0x2a, 0x35, 0xeb, 0x41, 0x64, 0x7d, 0xcf, 0xe0, 0x52, + /* (2^196)P */ 0x4a, 0xd0, 0x49, 0x93, 0xae, 0xf3, 0x24, 0x8c, 0xe1, 0x09, 0x98, 0x45, 0xd8, 0xb9, 0xfe, 0x8e, 0x8c, 0xa8, 0x2c, 0xc9, 0x9f, 0xce, 0x01, 0xdc, 0x38, 0x11, 0xab, 0x85, 0xb9, 0xe8, 0x00, 0x51, 0xfd, 0x82, 0xe1, 0x9b, 0x4e, 0xfc, 0xb5, 0x2a, 0x0f, 0x8b, 0xda, 0x4e, 0x02, 0xca, 0xcc, 0xe3, 0x91, 0xc4, 0xe0, 0xcf, 0x7b, 0xd6, 0xe6, 0x6a, + /* (2^197)P */ 0xfe, 0x11, 0xd7, 0xaa, 0xe3, 0x0c, 0x52, 0x2e, 0x04, 0xe0, 0xe0, 0x61, 0xc8, 0x05, 0xd7, 0x31, 0x4c, 0xc3, 0x9b, 0x2d, 0xce, 0x59, 0xbe, 0x12, 0xb7, 0x30, 0x21, 0xfc, 0x81, 0xb8, 0x5e, 0x57, 0x73, 0xd0, 0xad, 0x8e, 0x9e, 0xe4, 0xeb, 0xcd, 0xcf, 0xd2, 0x0f, 0x01, 0x35, 0x16, 0xed, 0x7a, 0x43, 0x8e, 0x42, 0xdc, 0xea, 0x4c, 0xa8, 0x7c, + /* (2^198)P */ 0x37, 0x26, 0xcc, 0x76, 0x0b, 0xe5, 0x76, 0xdd, 0x3e, 0x19, 0x3c, 0xc4, 0x6c, 0x7f, 0xd0, 0x03, 0xc1, 0xb8, 0x59, 0x82, 0xca, 0x36, 0xc1, 0xe4, 0xc8, 0xb2, 0x83, 0x69, 0x9c, 0xc5, 0x9d, 0x12, 0x82, 0x1c, 0xea, 0xb2, 0x84, 0x9f, 0xf3, 0x52, 0x6b, 0xbb, 0xd8, 0x81, 0x56, 0x83, 0x04, 0x66, 0x05, 0x22, 0x49, 0x37, 0x93, 0xb1, 0xfd, 0xd5, + /* (2^199)P */ 0xaf, 0x96, 0xbf, 0x03, 0xbe, 0xe6, 0x5d, 0x78, 0x19, 0xba, 0x37, 0x46, 0x0a, 0x2b, 0x52, 0x7c, 0xd8, 0x51, 0x9e, 0x3d, 0x29, 0x42, 0xdb, 0x0e, 0x31, 0x20, 0x94, 0xf8, 0x43, 0x9a, 0x2d, 0x22, 0xd3, 0xe3, 0xa1, 0x79, 0x68, 0xfb, 0x2d, 0x7e, 0xd6, 0x79, 0xda, 0x0b, 0xc6, 0x5b, 0x76, 0x68, 0xf0, 0xfe, 0x72, 0x59, 0xbb, 0xa1, 0x9c, 0x74, + /* (2^200)P */ 0x0a, 0xd9, 0xec, 0xc5, 0xbd, 0xf0, 0xda, 0xcf, 0x82, 0xab, 0x46, 0xc5, 0x32, 0x13, 0xdc, 0x5b, 0xac, 0xc3, 0x53, 0x9a, 0x7f, 0xef, 0xa5, 0x40, 0x5a, 0x1f, 0xc1, 0x12, 0x91, 0x54, 0x83, 0x6a, 0xb0, 0x9a, 0x85, 0x4d, 0xbf, 0x36, 0x8e, 0xd3, 0xa2, 0x2b, 0xe5, 0xd6, 0xc6, 0xe1, 0x58, 0x5b, 0x82, 0x9b, 0xc8, 0xf2, 0x03, 0xba, 0xf5, 0x92, + /* (2^201)P */ 0xfb, 0x21, 0x7e, 0xde, 0xe7, 0xb4, 0xc0, 0x56, 0x86, 0x3a, 0x5b, 0x78, 0xf8, 0xf0, 0xf4, 0xe7, 0x5c, 0x00, 0xd2, 0xd7, 0xd6, 0xf8, 0x75, 0x5e, 0x0f, 0x3e, 0xd1, 0x4b, 0x77, 0xd8, 0xad, 0xb0, 0xc9, 0x8b, 0x59, 0x7d, 0x30, 0x76, 0x64, 0x7a, 0x76, 0xd9, 0x51, 0x69, 0xfc, 0xbd, 0x8e, 0xb5, 0x55, 0xe0, 0xd2, 0x07, 0x15, 0xa9, 0xf7, 0xa4, + /* (2^202)P */ 0xaa, 0x2d, 0x2f, 0x2b, 0x3c, 0x15, 0xdd, 0xcd, 0xe9, 0x28, 0x82, 0x4f, 0xa2, 0xaa, 0x31, 0x48, 0xcc, 0xfa, 0x07, 0x73, 0x8a, 0x34, 0x74, 0x0d, 0xab, 0x1a, 0xca, 0xd2, 0xbf, 0x3a, 0xdb, 0x1a, 0x5f, 0x50, 0x62, 0xf4, 0x6b, 0x83, 0x38, 0x43, 0x96, 0xee, 0x6b, 0x39, 0x1e, 0xf0, 0x17, 0x80, 0x1e, 0x9b, 0xed, 0x2b, 0x2f, 0xcc, 0x65, 0xf7, + /* (2^203)P */ 0x03, 0xb3, 0x23, 0x9c, 0x0d, 0xd1, 0xeb, 0x7e, 0x34, 0x17, 0x8a, 0x4c, 0xde, 0x54, 0x39, 0xc4, 0x11, 0x82, 0xd3, 0xa4, 0x00, 0x32, 0x95, 0x9c, 0xa6, 0x64, 0x76, 0x6e, 0xd6, 0x53, 0x27, 0xb4, 0x6a, 0x14, 0x8c, 0x54, 0xf6, 0x58, 0x9e, 0x22, 0x4a, 0x55, 0x18, 0x77, 0xd0, 0x08, 0x6b, 0x19, 0x8a, 0xb5, 0xe7, 0x19, 0xb8, 0x60, 0x92, 0xb1, + /* (2^204)P */ 0x66, 0xec, 0xf3, 0x12, 0xde, 0x67, 0x7f, 0xd4, 0x5b, 0xf6, 0x70, 0x64, 0x0a, 0xb5, 0xc2, 0xf9, 0xb3, 0x64, 0xab, 0x56, 0x46, 0xc7, 0x93, 0xc2, 0x8b, 0x2d, 0xd0, 0xd6, 0x39, 0x3b, 0x1f, 0xcd, 0xb3, 0xac, 0xcc, 0x2c, 0x27, 0x6a, 0xbc, 0xb3, 0x4b, 0xa8, 0x3c, 0x69, 0x20, 0xe2, 0x18, 0x35, 0x17, 0xe1, 0x8a, 0xd3, 0x11, 0x74, 0xaa, 0x4d, + /* (2^205)P */ 0x96, 0xc4, 0x16, 0x7e, 0xfd, 0xf5, 0xd0, 0x7d, 0x1f, 0x32, 0x1b, 0xdb, 0xa6, 0xfd, 0x51, 0x75, 0x4d, 0xd7, 0x00, 0xe5, 0x7f, 0x58, 0x5b, 0xeb, 0x4b, 0x6a, 0x78, 0xfe, 0xe5, 0xd6, 0x8f, 0x99, 0x17, 0xca, 0x96, 0x45, 0xf7, 0x52, 0xdf, 0x84, 0x06, 0x77, 0xb9, 0x05, 0x63, 0x5d, 0xe9, 0x91, 0xb1, 0x4b, 0x82, 0x5a, 0xdb, 0xd7, 0xca, 0x69, + /* (2^206)P */ 0x02, 0xd3, 0x38, 0x38, 0x87, 0xea, 0xbd, 0x9f, 0x11, 0xca, 0xf3, 0x21, 0xf1, 0x9b, 0x35, 0x97, 0x98, 0xff, 0x8e, 0x6d, 0x3d, 0xd6, 0xb2, 0xfa, 0x68, 0xcb, 0x7e, 0x62, 0x85, 0xbb, 0xc7, 0x5d, 0xee, 0x32, 0x30, 0x2e, 0x71, 0x96, 0x63, 0x43, 0x98, 0xc4, 0xa7, 0xde, 0x60, 0xb2, 0xd9, 0x43, 0x4a, 0xfa, 0x97, 0x2d, 0x5f, 0x21, 0xd4, 0xfe, + /* (2^207)P */ 0x3b, 0x20, 0x29, 0x07, 0x07, 0xb5, 0x78, 0xc3, 0xc7, 0xab, 0x56, 0xba, 0x40, 0xde, 0x1d, 0xcf, 0xc3, 0x00, 0x56, 0x21, 0x0c, 0xc8, 0x42, 0xd9, 0x0e, 0xcd, 0x02, 0x7c, 0x07, 0xb9, 0x11, 0xd7, 0x96, 0xaf, 0xff, 0xad, 0xc5, 0xba, 0x30, 0x6d, 0x82, 0x3a, 0xbf, 0xef, 0x7b, 0xf7, 0x0a, 0x74, 0xbd, 0x31, 0x0c, 0xe4, 0xec, 0x1a, 0xe5, 0xc5, + /* (2^208)P */ 0xcc, 0xf2, 0x28, 0x16, 0x12, 0xbf, 0xef, 0x85, 0xbc, 0xf7, 0xcb, 0x9f, 0xdb, 0xa8, 0xb2, 0x49, 0x53, 0x48, 0xa8, 0x24, 0xa8, 0x68, 0x8d, 0xbb, 0x21, 0x0a, 0x5a, 0xbd, 0xb2, 0x91, 0x61, 0x47, 0xc4, 0x43, 0x08, 0xa6, 0x19, 0xef, 0x8e, 0x88, 0x39, 0xc6, 0x33, 0x30, 0xf3, 0x0e, 0xc5, 0x92, 0x66, 0xd6, 0xfe, 0xc5, 0x12, 0xd9, 0x4c, 0x2d, + /* (2^209)P */ 0x30, 0x34, 0x07, 0xbf, 0x9c, 0x5a, 0x4e, 0x65, 0xf1, 0x39, 0x35, 0x38, 0xae, 0x7b, 0x55, 0xac, 0x6a, 0x92, 0x24, 0x7e, 0x50, 0xd3, 0xba, 0x78, 0x51, 0xfe, 0x4d, 0x32, 0x05, 0x11, 0xf5, 0x52, 0xf1, 0x31, 0x45, 0x39, 0x98, 0x7b, 0x28, 0x56, 0xc3, 0x5d, 0x4f, 0x07, 0x6f, 0x84, 0xb8, 0x1a, 0x58, 0x0b, 0xc4, 0x7c, 0xc4, 0x8d, 0x32, 0x8e, + /* (2^210)P */ 0x7e, 0xaf, 0x98, 0xce, 0xc5, 0x2b, 0x9d, 0xf6, 0xfa, 0x2c, 0xb6, 0x2a, 0x5a, 0x1d, 0xc0, 0x24, 0x8d, 0xa4, 0xce, 0xb1, 0x12, 0x01, 0xf9, 0x79, 0xc6, 0x79, 0x38, 0x0c, 0xd4, 0x07, 0xc9, 0xf7, 0x37, 0xa1, 0x0b, 0xfe, 0x72, 0xec, 0x5d, 0xd6, 0xb0, 0x1c, 0x70, 0xbe, 0x70, 0x01, 0x13, 0xe0, 0x86, 0x95, 0xc7, 0x2e, 0x12, 0x3b, 0xe6, 0xa6, + /* (2^211)P */ 0x24, 0x82, 0x67, 0xe0, 0x14, 0x7b, 0x56, 0x08, 0x38, 0x44, 0xdb, 0xa0, 0x3a, 0x05, 0x47, 0xb2, 0xc0, 0xac, 0xd1, 0xcc, 0x3f, 0x82, 0xb8, 0x8a, 0x88, 0xbc, 0xf5, 0x33, 0xa1, 0x35, 0x0f, 0xf6, 0xe2, 0xef, 0x6c, 0xf7, 0x37, 0x9e, 0xe8, 0x10, 0xca, 0xb0, 0x8e, 0x80, 0x86, 0x00, 0x23, 0xd0, 0x4a, 0x76, 0x9f, 0xf7, 0x2c, 0x52, 0x15, 0x0e, + /* (2^212)P */ 0x5e, 0x49, 0xe1, 0x2c, 0x9a, 0x01, 0x76, 0xa6, 0xb3, 0x07, 0x5b, 0xa4, 0x07, 0xef, 0x1d, 0xc3, 0x6a, 0xbb, 0x64, 0xbe, 0x71, 0x15, 0x6e, 0x32, 0x31, 0x46, 0x9a, 0x9e, 0x8f, 0x45, 0x73, 0xce, 0x0b, 0x94, 0x1a, 0x52, 0x07, 0xf4, 0x50, 0x30, 0x49, 0x53, 0x50, 0xfb, 0x71, 0x1f, 0x5a, 0x03, 0xa9, 0x76, 0xf2, 0x8f, 0x42, 0xff, 0xed, 0xed, + /* (2^213)P */ 0xed, 0x08, 0xdb, 0x91, 0x1c, 0xee, 0xa2, 0xb4, 0x47, 0xa2, 0xfa, 0xcb, 0x03, 0xd1, 0xff, 0x8c, 0xad, 0x64, 0x50, 0x61, 0xcd, 0xfc, 0x88, 0xa0, 0x31, 0x95, 0x30, 0xb9, 0x58, 0xdd, 0xd7, 0x43, 0xe4, 0x46, 0xc2, 0x16, 0xd9, 0x72, 0x4a, 0x56, 0x51, 0x70, 0x85, 0xf1, 0xa1, 0x80, 0x40, 0xd5, 0xba, 0x67, 0x81, 0xda, 0xcd, 0x03, 0xea, 0x51, + /* (2^214)P */ 0x42, 0x50, 0xf0, 0xef, 0x37, 0x61, 0x72, 0x85, 0xe1, 0xf1, 0xff, 0x6f, 0x3d, 0xe8, 0x7b, 0x21, 0x5c, 0xe5, 0x50, 0x03, 0xde, 0x00, 0xc1, 0xf7, 0x3a, 0x55, 0x12, 0x1c, 0x9e, 0x1e, 0xce, 0xd1, 0x2f, 0xaf, 0x05, 0x70, 0x5b, 0x47, 0xf2, 0x04, 0x7a, 0x89, 0xbc, 0x78, 0xa6, 0x65, 0x6c, 0xaa, 0x3c, 0xa2, 0x3c, 0x8b, 0x5c, 0xa9, 0x22, 0x48, + /* (2^215)P */ 0x7e, 0x8c, 0x8f, 0x2f, 0x60, 0xe3, 0x5a, 0x94, 0xd4, 0xce, 0xdd, 0x9d, 0x83, 0x3b, 0x77, 0x78, 0x43, 0x1d, 0xfd, 0x8f, 0xc8, 0xe8, 0x02, 0x90, 0xab, 0xf6, 0xc9, 0xfc, 0xf1, 0x63, 0xaa, 0x5f, 0x42, 0xf1, 0x78, 0x34, 0x64, 0x16, 0x75, 0x9c, 0x7d, 0xd0, 0xe4, 0x74, 0x5a, 0xa8, 0xfb, 0xcb, 0xac, 0x20, 0xa3, 0xc2, 0xa6, 0x20, 0xf8, 0x1b, + /* (2^216)P */ 0x00, 0x4f, 0x1e, 0x56, 0xb5, 0x34, 0xb2, 0x87, 0x31, 0xe5, 0xee, 0x8d, 0xf1, 0x41, 0x67, 0xb7, 0x67, 0x3a, 0x54, 0x86, 0x5c, 0xf0, 0x0b, 0x37, 0x2f, 0x1b, 0x92, 0x5d, 0x58, 0x93, 0xdc, 0xd8, 0x58, 0xcc, 0x9e, 0x67, 0xd0, 0x97, 0x3a, 0xaf, 0x49, 0x39, 0x2d, 0x3b, 0xd8, 0x98, 0xfb, 0x76, 0x6b, 0xe7, 0xaf, 0xc3, 0x45, 0x44, 0x53, 0x94, + /* (2^217)P */ 0x30, 0xbd, 0x90, 0x75, 0xd3, 0xbd, 0x3b, 0x58, 0x27, 0x14, 0x9f, 0x6b, 0xd4, 0x31, 0x99, 0xcd, 0xde, 0x3a, 0x21, 0x1e, 0xb4, 0x02, 0xe4, 0x33, 0x04, 0x02, 0xb0, 0x50, 0x66, 0x68, 0x90, 0xdd, 0x7b, 0x69, 0x31, 0xd9, 0xcf, 0x68, 0x73, 0xf1, 0x60, 0xdd, 0xc8, 0x1d, 0x5d, 0xe3, 0xd6, 0x5b, 0x2a, 0xa4, 0xea, 0xc4, 0x3f, 0x08, 0xcd, 0x9c, + /* (2^218)P */ 0x6b, 0x1a, 0xbf, 0x55, 0xc1, 0x1b, 0x0c, 0x05, 0x09, 0xdf, 0xf5, 0x5e, 0xa3, 0x77, 0x95, 0xe9, 0xdf, 0x19, 0xdd, 0xc7, 0x94, 0xcb, 0x06, 0x73, 0xd0, 0x88, 0x02, 0x33, 0x94, 0xca, 0x7a, 0x2f, 0x8e, 0x3d, 0x72, 0x61, 0x2d, 0x4d, 0xa6, 0x61, 0x1f, 0x32, 0x5e, 0x87, 0x53, 0x36, 0x11, 0x15, 0x20, 0xb3, 0x5a, 0x57, 0x51, 0x93, 0x20, 0xd8, + /* (2^219)P */ 0xb7, 0x56, 0xf4, 0xab, 0x7d, 0x0c, 0xfb, 0x99, 0x1a, 0x30, 0x29, 0xb0, 0x75, 0x2a, 0xf8, 0x53, 0x71, 0x23, 0xbd, 0xa7, 0xd8, 0x0a, 0xe2, 0x27, 0x65, 0xe9, 0x74, 0x26, 0x98, 0x4a, 0x69, 0x19, 0xb2, 0x4d, 0x0a, 0x17, 0x98, 0xb2, 0xa9, 0x57, 0x4e, 0xf6, 0x86, 0xc8, 0x01, 0xa4, 0xc6, 0x98, 0xad, 0x5a, 0x90, 0x2c, 0x05, 0x46, 0x64, 0xb7, + /* (2^220)P */ 0x7b, 0x91, 0xdf, 0xfc, 0xf8, 0x1c, 0x8c, 0x15, 0x9e, 0xf7, 0xd5, 0xa8, 0xe8, 0xe7, 0xe3, 0xa3, 0xb0, 0x04, 0x74, 0xfa, 0x78, 0xfb, 0x26, 0xbf, 0x67, 0x42, 0xf9, 0x8c, 0x9b, 0xb4, 0x69, 0x5b, 0x02, 0x13, 0x6d, 0x09, 0x6c, 0xd6, 0x99, 0x61, 0x7b, 0x89, 0x4a, 0x67, 0x75, 0xa3, 0x98, 0x13, 0x23, 0x1d, 0x18, 0x24, 0x0e, 0xef, 0x41, 0x79, + /* (2^221)P */ 0x86, 0x33, 0xab, 0x08, 0xcb, 0xbf, 0x1e, 0x76, 0x3c, 0x0b, 0xbd, 0x30, 0xdb, 0xe9, 0xa3, 0x35, 0x87, 0x1b, 0xe9, 0x07, 0x00, 0x66, 0x7f, 0x3b, 0x35, 0x0c, 0x8a, 0x3f, 0x61, 0xbc, 0xe0, 0xae, 0xf6, 0xcc, 0x54, 0xe1, 0x72, 0x36, 0x2d, 0xee, 0x93, 0x24, 0xf8, 0xd7, 0xc5, 0xf9, 0xcb, 0xb0, 0xe5, 0x88, 0x0d, 0x23, 0x4b, 0x76, 0x15, 0xa2, + /* (2^222)P */ 0x37, 0xdb, 0x83, 0xd5, 0x6d, 0x06, 0x24, 0x37, 0x1b, 0x15, 0x85, 0x15, 0xe2, 0xc0, 0x4e, 0x02, 0xa9, 0x6d, 0x0a, 0x3a, 0x94, 0x4a, 0x6f, 0x49, 0x00, 0x01, 0x72, 0xbb, 0x60, 0x14, 0x35, 0xae, 0xb4, 0xc6, 0x01, 0x0a, 0x00, 0x9e, 0xc3, 0x58, 0xc5, 0xd1, 0x5e, 0x30, 0x73, 0x96, 0x24, 0x85, 0x9d, 0xf0, 0xf9, 0xec, 0x09, 0xd3, 0xe7, 0x70, + /* (2^223)P */ 0xf3, 0xbd, 0x96, 0x87, 0xe9, 0x71, 0xbd, 0xd6, 0xa2, 0x45, 0xeb, 0x0a, 0xcd, 0x2c, 0xf1, 0x72, 0xa6, 0x31, 0xa9, 0x6f, 0x09, 0xa1, 0x5e, 0xdd, 0xc8, 0x8d, 0x0d, 0xbc, 0x5a, 0x8d, 0xb1, 0x2c, 0x9a, 0xcc, 0x37, 0x74, 0xc2, 0xa9, 0x4e, 0xd6, 0xc0, 0x3c, 0xa0, 0x23, 0xb0, 0xa0, 0x77, 0x14, 0x80, 0x45, 0x71, 0x6a, 0x2d, 0x41, 0xc3, 0x82, + /* (2^224)P */ 0x37, 0x44, 0xec, 0x8a, 0x3e, 0xc1, 0x0c, 0xa9, 0x12, 0x9c, 0x08, 0x88, 0xcb, 0xd9, 0xf8, 0xba, 0x00, 0xd6, 0xc3, 0xdf, 0xef, 0x7a, 0x44, 0x7e, 0x25, 0x69, 0xc9, 0xc1, 0x46, 0xe5, 0x20, 0x9e, 0xcc, 0x0b, 0x05, 0x3e, 0xf4, 0x78, 0x43, 0x0c, 0xa6, 0x2f, 0xc1, 0xfa, 0x70, 0xb2, 0x3c, 0x31, 0x7a, 0x63, 0x58, 0xab, 0x17, 0xcf, 0x4c, 0x4f, + /* (2^225)P */ 0x2b, 0x08, 0x31, 0x59, 0x75, 0x8b, 0xec, 0x0a, 0xa9, 0x79, 0x70, 0xdd, 0xf1, 0x11, 0xc3, 0x11, 0x1f, 0xab, 0x37, 0xaa, 0x26, 0xea, 0x53, 0xc4, 0x79, 0xa7, 0x91, 0x00, 0xaa, 0x08, 0x42, 0xeb, 0x8b, 0x8b, 0xe8, 0xc3, 0x2f, 0xb8, 0x78, 0x90, 0x38, 0x0e, 0x8a, 0x42, 0x0c, 0x0f, 0xbf, 0x3e, 0xf8, 0xd8, 0x07, 0xcf, 0x6a, 0x34, 0xc9, 0xfa, + /* (2^226)P */ 0x11, 0xe0, 0x76, 0x4d, 0x23, 0xc5, 0xa6, 0xcc, 0x9f, 0x9a, 0x2a, 0xde, 0x3a, 0xb5, 0x92, 0x39, 0x19, 0x8a, 0xf1, 0x8d, 0xf9, 0x4d, 0xc9, 0xb4, 0x39, 0x9f, 0x57, 0xd8, 0x72, 0xab, 0x1d, 0x61, 0x6a, 0xb2, 0xff, 0x52, 0xba, 0x54, 0x0e, 0xfb, 0x83, 0x30, 0x8a, 0xf7, 0x3b, 0xf4, 0xd8, 0xae, 0x1a, 0x94, 0x3a, 0xec, 0x63, 0xfe, 0x6e, 0x7c, + /* (2^227)P */ 0xdc, 0x70, 0x8e, 0x55, 0x44, 0xbf, 0xd2, 0x6a, 0xa0, 0x14, 0x61, 0x89, 0xd5, 0x55, 0x45, 0x3c, 0xf6, 0x40, 0x0d, 0x83, 0x85, 0x44, 0xb4, 0x62, 0x56, 0xfe, 0x60, 0xd7, 0x07, 0x1d, 0x47, 0x30, 0x3b, 0x73, 0xa4, 0xb5, 0xb7, 0xea, 0xac, 0xda, 0xf1, 0x17, 0xaa, 0x60, 0xdf, 0xe9, 0x84, 0xda, 0x31, 0x32, 0x61, 0xbf, 0xd0, 0x7e, 0x8a, 0x02, + /* (2^228)P */ 0xb9, 0x51, 0xb3, 0x89, 0x21, 0x5d, 0xa2, 0xfe, 0x79, 0x2a, 0xb3, 0x2a, 0x3b, 0xe6, 0x6f, 0x2b, 0x22, 0x03, 0xea, 0x7b, 0x1f, 0xaf, 0x85, 0xc3, 0x38, 0x55, 0x5b, 0x8e, 0xb4, 0xaa, 0x77, 0xfe, 0x03, 0x6e, 0xda, 0x91, 0x24, 0x0c, 0x48, 0x39, 0x27, 0x43, 0x16, 0xd2, 0x0a, 0x0d, 0x43, 0xa3, 0x0e, 0xca, 0x45, 0xd1, 0x7f, 0xf5, 0xd3, 0x16, + /* (2^229)P */ 0x3d, 0x32, 0x9b, 0x38, 0xf8, 0x06, 0x93, 0x78, 0x5b, 0x50, 0x2b, 0x06, 0xd8, 0x66, 0xfe, 0xab, 0x9b, 0x58, 0xc7, 0xd1, 0x4d, 0xd5, 0xf8, 0x3b, 0x10, 0x7e, 0x85, 0xde, 0x58, 0x4e, 0xdf, 0x53, 0xd9, 0x58, 0xe0, 0x15, 0x81, 0x9f, 0x1a, 0x78, 0xfc, 0x9f, 0x10, 0xc2, 0x23, 0xd6, 0x78, 0xd1, 0x9d, 0xd2, 0xd5, 0x1c, 0x53, 0xe2, 0xc9, 0x76, + /* (2^230)P */ 0x98, 0x1e, 0x38, 0x7b, 0x71, 0x18, 0x4b, 0x15, 0xaf, 0xa1, 0xa6, 0x98, 0xcb, 0x26, 0xa3, 0xc8, 0x07, 0x46, 0xda, 0x3b, 0x70, 0x65, 0xec, 0x7a, 0x2b, 0x34, 0x94, 0xa8, 0xb6, 0x14, 0xf8, 0x1a, 0xce, 0xf7, 0xc8, 0x60, 0xf3, 0x88, 0xf4, 0x33, 0x60, 0x7b, 0xd1, 0x02, 0xe7, 0xda, 0x00, 0x4a, 0xea, 0xd2, 0xfd, 0x88, 0xd2, 0x99, 0x28, 0xf3, + /* (2^231)P */ 0x28, 0x24, 0x1d, 0x26, 0xc2, 0xeb, 0x8b, 0x3b, 0xb4, 0x6b, 0xbe, 0x6b, 0x77, 0xff, 0xf3, 0x21, 0x3b, 0x26, 0x6a, 0x8c, 0x8e, 0x2a, 0x44, 0xa8, 0x01, 0x2b, 0x71, 0xea, 0x64, 0x30, 0xfd, 0xfd, 0x95, 0xcb, 0x39, 0x38, 0x48, 0xfa, 0x96, 0x97, 0x8c, 0x2f, 0x33, 0xca, 0x03, 0xe6, 0xd7, 0x94, 0x55, 0x6c, 0xc3, 0xb3, 0xa8, 0xf7, 0xae, 0x8c, + /* (2^232)P */ 0xea, 0x62, 0x8a, 0xb4, 0xeb, 0x74, 0xf7, 0xb8, 0xae, 0xc5, 0x20, 0x71, 0x06, 0xd6, 0x7c, 0x62, 0x9b, 0x69, 0x74, 0xef, 0xa7, 0x6d, 0xd6, 0x8c, 0x37, 0xb9, 0xbf, 0xcf, 0xeb, 0xe4, 0x2f, 0x04, 0x02, 0x21, 0x7d, 0x75, 0x6b, 0x92, 0x48, 0xf8, 0x70, 0xad, 0x69, 0xe2, 0xea, 0x0e, 0x88, 0x67, 0x72, 0xcc, 0x2d, 0x10, 0xce, 0x2d, 0xcf, 0x65, + /* (2^233)P */ 0x49, 0xf3, 0x57, 0x64, 0xe5, 0x5c, 0xc5, 0x65, 0x49, 0x97, 0xc4, 0x8a, 0xcc, 0xa9, 0xca, 0x94, 0x7b, 0x86, 0x88, 0xb6, 0x51, 0x27, 0x69, 0xa5, 0x0f, 0x8b, 0x06, 0x59, 0xa0, 0x94, 0xef, 0x63, 0x1a, 0x01, 0x9e, 0x4f, 0xd2, 0x5a, 0x93, 0xc0, 0x7c, 0xe6, 0x61, 0x77, 0xb6, 0xf5, 0x40, 0xd9, 0x98, 0x43, 0x5b, 0x56, 0x68, 0xe9, 0x37, 0x8f, + /* (2^234)P */ 0xee, 0x87, 0xd2, 0x05, 0x1b, 0x39, 0x89, 0x10, 0x07, 0x6d, 0xe8, 0xfd, 0x8b, 0x4d, 0xb2, 0xa7, 0x7b, 0x1e, 0xa0, 0x6c, 0x0d, 0x3d, 0x3d, 0x49, 0xba, 0x61, 0x36, 0x1f, 0xc2, 0x84, 0x4a, 0xcc, 0x87, 0xa9, 0x1b, 0x23, 0x04, 0xe2, 0x3e, 0x97, 0xe1, 0xdb, 0xd5, 0x5a, 0xe8, 0x41, 0x6b, 0xe5, 0x5a, 0xa1, 0x99, 0xe5, 0x7b, 0xa7, 0xe0, 0x3b, + /* (2^235)P */ 0xea, 0xa3, 0x6a, 0xdd, 0x77, 0x7f, 0x77, 0x41, 0xc5, 0x6a, 0xe4, 0xaf, 0x11, 0x5f, 0x88, 0xa5, 0x10, 0xee, 0xd0, 0x8c, 0x0c, 0xb4, 0xa5, 0x2a, 0xd0, 0xd8, 0x1d, 0x47, 0x06, 0xc0, 0xd5, 0xce, 0x51, 0x54, 0x9b, 0x2b, 0xe6, 0x2f, 0xe7, 0xe7, 0x31, 0x5f, 0x5c, 0x23, 0x81, 0x3e, 0x03, 0x93, 0xaa, 0x2d, 0x71, 0x84, 0xa0, 0x89, 0x32, 0xa6, + /* (2^236)P */ 0x55, 0xa3, 0x13, 0x92, 0x4e, 0x93, 0x7d, 0xec, 0xca, 0x57, 0xfb, 0x37, 0xae, 0xd2, 0x18, 0x2e, 0x54, 0x05, 0x6c, 0xd1, 0x28, 0xca, 0x90, 0x40, 0x82, 0x2e, 0x79, 0xc6, 0x5a, 0xc7, 0xdd, 0x84, 0x93, 0xdf, 0x15, 0xb8, 0x1f, 0xb1, 0xf9, 0xaf, 0x2c, 0xe5, 0x32, 0xcd, 0xc2, 0x99, 0x6d, 0xac, 0x85, 0x5c, 0x63, 0xd3, 0xe2, 0xff, 0x24, 0xda, + /* (2^237)P */ 0x2d, 0x8d, 0xfd, 0x65, 0xcc, 0xe5, 0x02, 0xa0, 0xe5, 0xb9, 0xec, 0x59, 0x09, 0x50, 0x27, 0xb7, 0x3d, 0x2a, 0x79, 0xb2, 0x76, 0x5d, 0x64, 0x95, 0xf8, 0xc5, 0xaf, 0x8a, 0x62, 0x11, 0x5c, 0x56, 0x1c, 0x05, 0x64, 0x9e, 0x5e, 0xbd, 0x54, 0x04, 0xe6, 0x9e, 0xab, 0xe6, 0x22, 0x7e, 0x42, 0x54, 0xb5, 0xa5, 0xd0, 0x8d, 0x28, 0x6b, 0x0f, 0x0b, + /* (2^238)P */ 0x2d, 0xb2, 0x8c, 0x59, 0x10, 0x37, 0x84, 0x3b, 0x9b, 0x65, 0x1b, 0x0f, 0x10, 0xf9, 0xea, 0x60, 0x1b, 0x02, 0xf5, 0xee, 0x8b, 0xe6, 0x32, 0x7d, 0x10, 0x7f, 0x5f, 0x8c, 0x72, 0x09, 0x4e, 0x1f, 0x29, 0xff, 0x65, 0xcb, 0x3e, 0x3a, 0xd2, 0x96, 0x50, 0x1e, 0xea, 0x64, 0x99, 0xb5, 0x4c, 0x7a, 0x69, 0xb8, 0x95, 0xae, 0x48, 0xc0, 0x7c, 0xb1, + /* (2^239)P */ 0xcd, 0x7c, 0x4f, 0x3e, 0xea, 0xf3, 0x90, 0xcb, 0x12, 0x76, 0xd1, 0x17, 0xdc, 0x0d, 0x13, 0x0f, 0xfd, 0x4d, 0xb5, 0x1f, 0xe4, 0xdd, 0xf2, 0x4d, 0x58, 0xea, 0xa5, 0x66, 0x92, 0xcf, 0xe5, 0x54, 0xea, 0x9b, 0x35, 0x83, 0x1a, 0x44, 0x8e, 0x62, 0x73, 0x45, 0x98, 0xa3, 0x89, 0x95, 0x52, 0x93, 0x1a, 0x8d, 0x63, 0x0f, 0xc2, 0x57, 0x3c, 0xb1, + /* (2^240)P */ 0x72, 0xb4, 0xdf, 0x51, 0xb7, 0xf6, 0x52, 0xa2, 0x14, 0x56, 0xe5, 0x0a, 0x2e, 0x75, 0x81, 0x02, 0xee, 0x93, 0x48, 0x0a, 0x92, 0x4e, 0x0c, 0x0f, 0xdf, 0x09, 0x89, 0x99, 0xf6, 0xf9, 0x22, 0xa2, 0x32, 0xf8, 0xb0, 0x76, 0x0c, 0xb2, 0x4d, 0x6e, 0xbe, 0x83, 0x35, 0x61, 0x44, 0xd2, 0x58, 0xc7, 0xdd, 0x14, 0xcf, 0xc3, 0x4b, 0x7c, 0x07, 0xee, + /* (2^241)P */ 0x8b, 0x03, 0xee, 0xcb, 0xa7, 0x2e, 0x28, 0xbd, 0x97, 0xd1, 0x4c, 0x2b, 0xd1, 0x92, 0x67, 0x5b, 0x5a, 0x12, 0xbf, 0x29, 0x17, 0xfc, 0x50, 0x09, 0x74, 0x76, 0xa2, 0xd4, 0x82, 0xfd, 0x2c, 0x0c, 0x90, 0xf7, 0xe7, 0xe5, 0x9a, 0x2c, 0x16, 0x40, 0xb9, 0x6c, 0xd9, 0xe0, 0x22, 0x9e, 0xf8, 0xdd, 0x73, 0xe4, 0x7b, 0x9e, 0xbe, 0x4f, 0x66, 0x22, + /* (2^242)P */ 0xa4, 0x10, 0xbe, 0xb8, 0x83, 0x3a, 0x77, 0x8e, 0xea, 0x0a, 0xc4, 0x97, 0x3e, 0xb6, 0x6c, 0x81, 0xd7, 0x65, 0xd9, 0xf7, 0xae, 0xe6, 0xbe, 0xab, 0x59, 0x81, 0x29, 0x4b, 0xff, 0xe1, 0x0f, 0xc3, 0x2b, 0xad, 0x4b, 0xef, 0xc4, 0x50, 0x9f, 0x88, 0x31, 0xf2, 0xde, 0x80, 0xd6, 0xf4, 0x20, 0x9c, 0x77, 0x9b, 0xbe, 0xbe, 0x08, 0xf5, 0xf0, 0x95, + /* (2^243)P */ 0x0e, 0x7c, 0x7b, 0x7c, 0xb3, 0xd8, 0x83, 0xfc, 0x8c, 0x75, 0x51, 0x74, 0x1b, 0xe1, 0x6d, 0x11, 0x05, 0x46, 0x24, 0x0d, 0xa4, 0x2b, 0x32, 0xfd, 0x2c, 0x4e, 0x21, 0xdf, 0x39, 0x6b, 0x96, 0xfc, 0xff, 0x92, 0xfc, 0x35, 0x0d, 0x9a, 0x4b, 0xc0, 0x70, 0x46, 0x32, 0x7d, 0xc0, 0xc4, 0x04, 0xe0, 0x2d, 0x83, 0xa7, 0x00, 0xc7, 0xcb, 0xb4, 0x8f, + /* (2^244)P */ 0xa9, 0x5a, 0x7f, 0x0e, 0xdd, 0x2c, 0x85, 0xaa, 0x4d, 0xac, 0xde, 0xb3, 0xb6, 0xaf, 0xe6, 0xd1, 0x06, 0x7b, 0x2c, 0xa4, 0x01, 0x19, 0x22, 0x7d, 0x78, 0xf0, 0x3a, 0xea, 0x89, 0xfe, 0x21, 0x61, 0x6d, 0xb8, 0xfe, 0xa5, 0x2a, 0xab, 0x0d, 0x7b, 0x51, 0x39, 0xb6, 0xde, 0xbc, 0xf0, 0xc5, 0x48, 0xd7, 0x09, 0x82, 0x6e, 0x66, 0x75, 0xc5, 0xcd, + /* (2^245)P */ 0xee, 0xdf, 0x2b, 0x6c, 0xa8, 0xde, 0x61, 0xe1, 0x27, 0xfa, 0x2a, 0x0f, 0x68, 0xe7, 0x7a, 0x9b, 0x13, 0xe9, 0x56, 0xd2, 0x1c, 0x3d, 0x2f, 0x3c, 0x7a, 0xf6, 0x6f, 0x45, 0xee, 0xe8, 0xf4, 0xa0, 0xa6, 0xe8, 0xa5, 0x27, 0xee, 0xf2, 0x85, 0xa9, 0xd5, 0x0e, 0xa9, 0x26, 0x60, 0xfe, 0xee, 0xc7, 0x59, 0x99, 0x5e, 0xa3, 0xdf, 0x23, 0x36, 0xd5, + /* (2^246)P */ 0x15, 0x66, 0x6f, 0xd5, 0x78, 0xa4, 0x0a, 0xf7, 0xb1, 0xe8, 0x75, 0x6b, 0x48, 0x7d, 0xa6, 0x4d, 0x3d, 0x36, 0x9b, 0xc7, 0xcc, 0x68, 0x9a, 0xfe, 0x2f, 0x39, 0x2a, 0x51, 0x31, 0x39, 0x7d, 0x73, 0x6f, 0xc8, 0x74, 0x72, 0x6f, 0x6e, 0xda, 0x5f, 0xad, 0x48, 0xc8, 0x40, 0xe1, 0x06, 0x01, 0x36, 0xa1, 0x88, 0xc8, 0x99, 0x9c, 0xd1, 0x11, 0x8f, + /* (2^247)P */ 0xab, 0xc5, 0xcb, 0xcf, 0xbd, 0x73, 0x21, 0xd0, 0x82, 0xb1, 0x2e, 0x2d, 0xd4, 0x36, 0x1b, 0xed, 0xa9, 0x8a, 0x26, 0x79, 0xc4, 0x17, 0xae, 0xe5, 0x09, 0x0a, 0x0c, 0xa4, 0x21, 0xa0, 0x6e, 0xdd, 0x62, 0x8e, 0x44, 0x62, 0xcc, 0x50, 0xff, 0x93, 0xb3, 0x9a, 0x72, 0x8c, 0x3f, 0xa1, 0xa6, 0x4d, 0x87, 0xd5, 0x1c, 0x5a, 0xc0, 0x0b, 0x1a, 0xd6, + /* (2^248)P */ 0x67, 0x36, 0x6a, 0x1f, 0x96, 0xe5, 0x80, 0x20, 0xa9, 0xe8, 0x0b, 0x0e, 0x21, 0x29, 0x3f, 0xc8, 0x0a, 0x6d, 0x27, 0x47, 0xca, 0xd9, 0x05, 0x55, 0xbf, 0x11, 0xcf, 0x31, 0x7a, 0x37, 0xc7, 0x90, 0xa9, 0xf4, 0x07, 0x5e, 0xd5, 0xc3, 0x92, 0xaa, 0x95, 0xc8, 0x23, 0x2a, 0x53, 0x45, 0xe3, 0x3a, 0x24, 0xe9, 0x67, 0x97, 0x3a, 0x82, 0xf9, 0xa6, + /* (2^249)P */ 0x92, 0x9e, 0x6d, 0x82, 0x67, 0xe9, 0xf9, 0x17, 0x96, 0x2c, 0xa7, 0xd3, 0x89, 0xf9, 0xdb, 0xd8, 0x20, 0xc6, 0x2e, 0xec, 0x4a, 0x76, 0x64, 0xbf, 0x27, 0x40, 0xe2, 0xb4, 0xdf, 0x1f, 0xa0, 0xef, 0x07, 0x80, 0xfb, 0x8e, 0x12, 0xf8, 0xb8, 0xe1, 0xc6, 0xdf, 0x7c, 0x69, 0x35, 0x5a, 0xe1, 0x8e, 0x5d, 0x69, 0x84, 0x56, 0xb6, 0x31, 0x1c, 0x0b, + /* (2^250)P */ 0xd6, 0x94, 0x5c, 0xef, 0xbb, 0x46, 0x45, 0x44, 0x5b, 0xa1, 0xae, 0x03, 0x65, 0xdd, 0xb5, 0x66, 0x88, 0x35, 0x29, 0x95, 0x16, 0x54, 0xa6, 0xf5, 0xc9, 0x78, 0x34, 0xe6, 0x0f, 0xc4, 0x2b, 0x5b, 0x79, 0x51, 0x68, 0x48, 0x3a, 0x26, 0x87, 0x05, 0x70, 0xaf, 0x8b, 0xa6, 0xc7, 0x2e, 0xb3, 0xa9, 0x10, 0x01, 0xb0, 0xb9, 0x31, 0xfd, 0xdc, 0x80, + /* (2^251)P */ 0x25, 0xf2, 0xad, 0xd6, 0x75, 0xa3, 0x04, 0x05, 0x64, 0x8a, 0x97, 0x60, 0x27, 0x2a, 0xe5, 0x6d, 0xb0, 0x73, 0xf4, 0x07, 0x2a, 0x9d, 0xe9, 0x46, 0xb4, 0x1c, 0x51, 0xf8, 0x63, 0x98, 0x7e, 0xe5, 0x13, 0x51, 0xed, 0x98, 0x65, 0x98, 0x4f, 0x8f, 0xe7, 0x7e, 0x72, 0xd7, 0x64, 0x11, 0x2f, 0xcd, 0x12, 0xf8, 0xc4, 0x63, 0x52, 0x0f, 0x7f, 0xc4, + /* (2^252)P */ 0x5c, 0xd9, 0x85, 0x63, 0xc7, 0x8a, 0x65, 0x9a, 0x25, 0x83, 0x31, 0x73, 0x49, 0xf0, 0x93, 0x96, 0x70, 0x67, 0x6d, 0xb1, 0xff, 0x95, 0x54, 0xe4, 0xf8, 0x15, 0x6c, 0x5f, 0xbd, 0xf6, 0x0f, 0x38, 0x7b, 0x68, 0x7d, 0xd9, 0x3d, 0xf0, 0xa9, 0xa0, 0xe4, 0xd1, 0xb6, 0x34, 0x6d, 0x14, 0x16, 0xc2, 0x4c, 0x30, 0x0e, 0x67, 0xd3, 0xbe, 0x2e, 0xc0, + /* (2^253)P */ 0x06, 0x6b, 0x52, 0xc8, 0x14, 0xcd, 0xae, 0x03, 0x93, 0xea, 0xc1, 0xf2, 0xf6, 0x8b, 0xc5, 0xb6, 0xdc, 0x82, 0x42, 0x29, 0x94, 0xe0, 0x25, 0x6c, 0x3f, 0x9f, 0x5d, 0xe4, 0x96, 0xf6, 0x8e, 0x3f, 0xf9, 0x72, 0xc4, 0x77, 0x60, 0x8b, 0xa4, 0xf9, 0xa8, 0xc3, 0x0a, 0x81, 0xb1, 0x97, 0x70, 0x18, 0xab, 0xea, 0x37, 0x8a, 0x08, 0xc7, 0xe2, 0x95, + /* (2^254)P */ 0x94, 0x49, 0xd9, 0x5f, 0x76, 0x72, 0x82, 0xad, 0x2d, 0x50, 0x1a, 0x7a, 0x5b, 0xe6, 0x95, 0x1e, 0x95, 0x65, 0x87, 0x1c, 0x52, 0xd7, 0x44, 0xe6, 0x9b, 0x56, 0xcd, 0x6f, 0x05, 0xff, 0x67, 0xc5, 0xdb, 0xa2, 0xac, 0xe4, 0xa2, 0x28, 0x63, 0x5f, 0xfb, 0x0c, 0x3b, 0xf1, 0x87, 0xc3, 0x36, 0x78, 0x3f, 0x77, 0xfa, 0x50, 0x85, 0xf9, 0xd7, 0x82, + /* (2^255)P */ 0x64, 0xc0, 0xe0, 0xd8, 0x2d, 0xed, 0xcb, 0x6a, 0xfd, 0xcd, 0xbc, 0x7e, 0x9f, 0xc8, 0x85, 0xe9, 0xc1, 0x7c, 0x0f, 0xe5, 0x18, 0xea, 0xd4, 0x51, 0xad, 0x59, 0x13, 0x75, 0xd9, 0x3d, 0xd4, 0x8a, 0xb2, 0xbe, 0x78, 0x52, 0x2b, 0x52, 0x94, 0x37, 0x41, 0xd6, 0xb4, 0xb6, 0x45, 0x20, 0x76, 0xe0, 0x1f, 0x31, 0xdb, 0xb1, 0xa1, 0x43, 0xf0, 0x18, + /* (2^256)P */ 0x74, 0xa9, 0xa4, 0xa9, 0xdd, 0x6e, 0x3e, 0x68, 0xe5, 0xc3, 0x2e, 0x92, 0x17, 0xa4, 0xcb, 0x80, 0xb1, 0xf0, 0x06, 0x93, 0xef, 0xe6, 0x00, 0xe6, 0x3b, 0xb1, 0x32, 0x65, 0x7b, 0x83, 0xb6, 0x8a, 0x49, 0x1b, 0x14, 0x89, 0xee, 0xba, 0xf5, 0x6a, 0x8d, 0x36, 0xef, 0xb0, 0xd8, 0xb2, 0x16, 0x99, 0x17, 0x35, 0x02, 0x16, 0x55, 0x58, 0xdd, 0x82, + /* (2^257)P */ 0x36, 0x95, 0xe8, 0xf4, 0x36, 0x42, 0xbb, 0xc5, 0x3e, 0xfa, 0x30, 0x84, 0x9e, 0x59, 0xfd, 0xd2, 0x95, 0x42, 0xf8, 0x64, 0xd9, 0xb9, 0x0e, 0x9f, 0xfa, 0xd0, 0x7b, 0x20, 0x31, 0x77, 0x48, 0x29, 0x4d, 0xd0, 0x32, 0x57, 0x56, 0x30, 0xa6, 0x17, 0x53, 0x04, 0xbf, 0x08, 0x28, 0xec, 0xb8, 0x46, 0xc1, 0x03, 0x89, 0xdc, 0xed, 0xa0, 0x35, 0x53, + /* (2^258)P */ 0xc5, 0x7f, 0x9e, 0xd8, 0xc5, 0xba, 0x5f, 0x68, 0xc8, 0x23, 0x75, 0xea, 0x0d, 0xd9, 0x5a, 0xfd, 0x61, 0x1a, 0xa3, 0x2e, 0x45, 0x63, 0x14, 0x55, 0x86, 0x21, 0x29, 0xbe, 0xef, 0x5e, 0x50, 0xe5, 0x18, 0x59, 0xe7, 0xe3, 0xce, 0x4d, 0x8c, 0x15, 0x8f, 0x89, 0x66, 0x44, 0x52, 0x3d, 0xfa, 0xc7, 0x9a, 0x59, 0x90, 0x8e, 0xc0, 0x06, 0x3f, 0xc9, + /* (2^259)P */ 0x8e, 0x04, 0xd9, 0x16, 0x50, 0x1d, 0x8c, 0x9f, 0xd5, 0xe3, 0xce, 0xfd, 0x47, 0x04, 0x27, 0x4d, 0xc2, 0xfa, 0x71, 0xd9, 0x0b, 0xb8, 0x65, 0xf4, 0x11, 0xf3, 0x08, 0xee, 0x81, 0xc8, 0x67, 0x99, 0x0b, 0x8d, 0x77, 0xa3, 0x4f, 0xb5, 0x9b, 0xdb, 0x26, 0xf1, 0x97, 0xeb, 0x04, 0x54, 0xeb, 0x80, 0x08, 0x1d, 0x1d, 0xf6, 0x3d, 0x1f, 0x5a, 0xb8, + /* (2^260)P */ 0xb7, 0x9c, 0x9d, 0xee, 0xb9, 0x5c, 0xad, 0x0d, 0x9e, 0xfd, 0x60, 0x3c, 0x27, 0x4e, 0xa2, 0x95, 0xfb, 0x64, 0x7e, 0x79, 0x64, 0x87, 0x10, 0xb4, 0x73, 0xe0, 0x9d, 0x46, 0x4d, 0x3d, 0xee, 0x83, 0xe4, 0x16, 0x88, 0x97, 0xe6, 0x4d, 0xba, 0x70, 0xb6, 0x96, 0x7b, 0xff, 0x4b, 0xc8, 0xcf, 0x72, 0x83, 0x3e, 0x5b, 0x24, 0x2e, 0x57, 0xf1, 0x82, + /* (2^261)P */ 0x30, 0x71, 0x40, 0x51, 0x4f, 0x44, 0xbb, 0xc7, 0xf0, 0x54, 0x6e, 0x9d, 0xeb, 0x15, 0xad, 0xf8, 0x61, 0x43, 0x5a, 0xef, 0xc0, 0xb1, 0x57, 0xae, 0x03, 0x40, 0xe8, 0x68, 0x6f, 0x03, 0x20, 0x4f, 0x8a, 0x51, 0x2a, 0x9e, 0xd2, 0x45, 0xaf, 0xb4, 0xf5, 0xd4, 0x95, 0x7f, 0x3d, 0x3d, 0xb7, 0xb6, 0x28, 0xc5, 0x08, 0x8b, 0x44, 0xd6, 0x3f, 0xe7, + /* (2^262)P */ 0xa9, 0x52, 0x04, 0x67, 0xcb, 0x20, 0x63, 0xf8, 0x18, 0x01, 0x44, 0x21, 0x6a, 0x8a, 0x83, 0x48, 0xd4, 0xaf, 0x23, 0x0f, 0x35, 0x8d, 0xe5, 0x5a, 0xc4, 0x7c, 0x55, 0x46, 0x19, 0x5f, 0x35, 0xe0, 0x5d, 0x97, 0x4c, 0x2d, 0x04, 0xed, 0x59, 0xd4, 0xb0, 0xb2, 0xc6, 0xe3, 0x51, 0xe1, 0x38, 0xc6, 0x30, 0x49, 0x8f, 0xae, 0x61, 0x64, 0xce, 0xa8, + /* (2^263)P */ 0x9b, 0x64, 0x83, 0x3c, 0xd3, 0xdf, 0xb9, 0x27, 0xe7, 0x5b, 0x7f, 0xeb, 0xf3, 0x26, 0xcf, 0xb1, 0x8f, 0xaf, 0x26, 0xc8, 0x48, 0xce, 0xa1, 0xac, 0x7d, 0x10, 0x34, 0x28, 0xe1, 0x1f, 0x69, 0x03, 0x64, 0x77, 0x61, 0xdd, 0x4a, 0x9b, 0x18, 0x47, 0xf8, 0xca, 0x63, 0xc9, 0x03, 0x2d, 0x20, 0x2a, 0x69, 0x6e, 0x42, 0xd0, 0xe7, 0xaa, 0xb5, 0xf3, + /* (2^264)P */ 0xea, 0x31, 0x0c, 0x57, 0x0f, 0x3e, 0xe3, 0x35, 0xd8, 0x30, 0xa5, 0x6f, 0xdd, 0x95, 0x43, 0xc6, 0x66, 0x07, 0x4f, 0x34, 0xc3, 0x7e, 0x04, 0x10, 0x2d, 0xc4, 0x1c, 0x94, 0x52, 0x2e, 0x5b, 0x9a, 0x65, 0x2f, 0x91, 0xaa, 0x4f, 0x3c, 0xdc, 0x23, 0x18, 0xe1, 0x4f, 0x85, 0xcd, 0xf4, 0x8c, 0x51, 0xf7, 0xab, 0x4f, 0xdc, 0x15, 0x5c, 0x9e, 0xc5, + /* (2^265)P */ 0x54, 0x57, 0x23, 0x17, 0xe7, 0x82, 0x2f, 0x04, 0x7d, 0xfe, 0xe7, 0x1f, 0xa2, 0x57, 0x79, 0xe9, 0x58, 0x9b, 0xbe, 0xc6, 0x16, 0x4a, 0x17, 0x50, 0x90, 0x4a, 0x34, 0x70, 0x87, 0x37, 0x01, 0x26, 0xd8, 0xa3, 0x5f, 0x07, 0x7c, 0xd0, 0x7d, 0x05, 0x8a, 0x93, 0x51, 0x2f, 0x99, 0xea, 0xcf, 0x00, 0xd8, 0xc7, 0xe6, 0x9b, 0x8c, 0x62, 0x45, 0x87, + /* (2^266)P */ 0xc3, 0xfd, 0x29, 0x66, 0xe7, 0x30, 0x29, 0x77, 0xe0, 0x0d, 0x63, 0x5b, 0xe6, 0x90, 0x1a, 0x1e, 0x99, 0xc2, 0xa7, 0xab, 0xff, 0xa7, 0xbd, 0x79, 0x01, 0x97, 0xfd, 0x27, 0x1b, 0x43, 0x2b, 0xe6, 0xfe, 0x5e, 0xf1, 0xb9, 0x35, 0x38, 0x08, 0x25, 0x55, 0x90, 0x68, 0x2e, 0xc3, 0x67, 0x39, 0x9f, 0x2b, 0x2c, 0x70, 0x48, 0x8c, 0x47, 0xee, 0x56, + /* (2^267)P */ 0xf7, 0x32, 0x70, 0xb5, 0xe6, 0x42, 0xfd, 0x0a, 0x39, 0x9b, 0x07, 0xfe, 0x0e, 0xf4, 0x47, 0xba, 0x6a, 0x3f, 0xf5, 0x2c, 0x15, 0xf3, 0x60, 0x3f, 0xb1, 0x83, 0x7b, 0x2e, 0x34, 0x58, 0x1a, 0x6e, 0x4a, 0x49, 0x05, 0x45, 0xca, 0xdb, 0x00, 0x01, 0x0c, 0x42, 0x5e, 0x60, 0x40, 0x5f, 0xd9, 0xc7, 0x3a, 0x9e, 0x1c, 0x8d, 0xab, 0x11, 0x55, 0x65, + /* (2^268)P */ 0x87, 0x40, 0xb7, 0x0d, 0xaa, 0x34, 0x89, 0x90, 0x75, 0x6d, 0xa2, 0xfe, 0x3b, 0x6d, 0x5c, 0x39, 0x98, 0x10, 0x9e, 0x15, 0xc5, 0x35, 0xa2, 0x27, 0x23, 0x0a, 0x2d, 0x60, 0xe2, 0xa8, 0x7f, 0x3e, 0x77, 0x8f, 0xcc, 0x44, 0xcc, 0x30, 0x28, 0xe2, 0xf0, 0x04, 0x8c, 0xee, 0xe4, 0x5f, 0x68, 0x8c, 0xdf, 0x70, 0xbf, 0x31, 0xee, 0x2a, 0xfc, 0xce, + /* (2^269)P */ 0x92, 0xf2, 0xa0, 0xd9, 0x58, 0x3b, 0x7c, 0x1a, 0x99, 0x46, 0x59, 0x54, 0x60, 0x06, 0x8d, 0x5e, 0xf0, 0x22, 0xa1, 0xed, 0x92, 0x8a, 0x4d, 0x76, 0x95, 0x05, 0x0b, 0xff, 0xfc, 0x9a, 0xd1, 0xcc, 0x05, 0xb9, 0x5e, 0x99, 0xe8, 0x2a, 0x76, 0x7b, 0xfd, 0xa6, 0xe2, 0xd1, 0x1a, 0xd6, 0x76, 0x9f, 0x2f, 0x0e, 0xd1, 0xa8, 0x77, 0x5a, 0x40, 0x5a, + /* (2^270)P */ 0xff, 0xf9, 0x3f, 0xa9, 0xa6, 0x6c, 0x6d, 0x03, 0x8b, 0xa7, 0x10, 0x5d, 0x3f, 0xec, 0x3e, 0x1c, 0x0b, 0x6b, 0xa2, 0x6a, 0x22, 0xa9, 0x28, 0xd0, 0x66, 0xc9, 0xc2, 0x3d, 0x47, 0x20, 0x7d, 0xa6, 0x1d, 0xd8, 0x25, 0xb5, 0xf2, 0xf9, 0x70, 0x19, 0x6b, 0xf8, 0x43, 0x36, 0xc5, 0x1f, 0xe4, 0x5a, 0x4c, 0x13, 0xe4, 0x6d, 0x08, 0x0b, 0x1d, 0xb1, + /* (2^271)P */ 0x3f, 0x20, 0x9b, 0xfb, 0xec, 0x7d, 0x31, 0xc5, 0xfc, 0x88, 0x0b, 0x30, 0xed, 0x36, 0xc0, 0x63, 0xb1, 0x7d, 0x10, 0xda, 0xb6, 0x2e, 0xad, 0xf3, 0xec, 0x94, 0xe7, 0xec, 0xb5, 0x9c, 0xfe, 0xf5, 0x35, 0xf0, 0xa2, 0x2d, 0x7f, 0xca, 0x6b, 0x67, 0x1a, 0xf6, 0xb3, 0xda, 0x09, 0x2a, 0xaa, 0xdf, 0xb1, 0xca, 0x9b, 0xfb, 0xeb, 0xb3, 0xcd, 0xc0, + /* (2^272)P */ 0xcd, 0x4d, 0x89, 0x00, 0xa4, 0x3b, 0x48, 0xf0, 0x76, 0x91, 0x35, 0xa5, 0xf8, 0xc9, 0xb6, 0x46, 0xbc, 0xf6, 0x9a, 0x45, 0x47, 0x17, 0x96, 0x80, 0x5b, 0x3a, 0x28, 0x33, 0xf9, 0x5a, 0xef, 0x43, 0x07, 0xfe, 0x3b, 0xf4, 0x8e, 0x19, 0xce, 0xd2, 0x94, 0x4b, 0x6d, 0x8e, 0x67, 0x20, 0xc7, 0x4f, 0x2f, 0x59, 0x8e, 0xe1, 0xa1, 0xa9, 0xf9, 0x0e, + /* (2^273)P */ 0xdc, 0x7b, 0xb5, 0x50, 0x2e, 0xe9, 0x7e, 0x8b, 0x78, 0xa1, 0x38, 0x96, 0x22, 0xc3, 0x61, 0x67, 0x6d, 0xc8, 0x58, 0xed, 0x41, 0x1d, 0x5d, 0x86, 0x98, 0x7f, 0x2f, 0x1b, 0x8d, 0x3e, 0xaa, 0xc1, 0xd2, 0x0a, 0xf3, 0xbf, 0x95, 0x04, 0xf3, 0x10, 0x3c, 0x2b, 0x7f, 0x90, 0x46, 0x04, 0xaa, 0x6a, 0xa9, 0x35, 0x76, 0xac, 0x49, 0xb5, 0x00, 0x45, + /* (2^274)P */ 0xb1, 0x93, 0x79, 0x84, 0x4a, 0x2a, 0x30, 0x78, 0x16, 0xaa, 0xc5, 0x74, 0x06, 0xce, 0xa5, 0xa7, 0x32, 0x86, 0xe0, 0xf9, 0x10, 0xd2, 0x58, 0x76, 0xfb, 0x66, 0x49, 0x76, 0x3a, 0x90, 0xba, 0xb5, 0xcc, 0x99, 0xcd, 0x09, 0xc1, 0x9a, 0x74, 0x23, 0xdf, 0x0c, 0xfe, 0x99, 0x52, 0x80, 0xa3, 0x7c, 0x1c, 0x71, 0x5f, 0x2c, 0x49, 0x57, 0xf4, 0xf9, + /* (2^275)P */ 0x6d, 0xbf, 0x52, 0xe6, 0x25, 0x98, 0xed, 0xcf, 0xe3, 0xbc, 0x08, 0xa2, 0x1a, 0x90, 0xae, 0xa0, 0xbf, 0x07, 0x15, 0xad, 0x0a, 0x9f, 0x3e, 0x47, 0x44, 0xc2, 0x10, 0x46, 0xa6, 0x7a, 0x9e, 0x2f, 0x57, 0xbc, 0xe2, 0xf0, 0x1d, 0xd6, 0x9a, 0x06, 0xed, 0xfc, 0x54, 0x95, 0x92, 0x15, 0xa2, 0xf7, 0x8d, 0x6b, 0xef, 0xb2, 0x05, 0xed, 0x5c, 0x63, + /* (2^276)P */ 0xbc, 0x0b, 0x27, 0x3a, 0x3a, 0xf8, 0xe1, 0x48, 0x02, 0x7e, 0x27, 0xe6, 0x81, 0x62, 0x07, 0x73, 0x74, 0xe5, 0x52, 0xd7, 0xf8, 0x26, 0xca, 0x93, 0x4d, 0x3e, 0x9b, 0x55, 0x09, 0x8e, 0xe3, 0xd7, 0xa6, 0xe3, 0xb6, 0x2a, 0xa9, 0xb3, 0xb0, 0xa0, 0x8c, 0x01, 0xbb, 0x07, 0x90, 0x78, 0x6d, 0x6d, 0xe9, 0xf0, 0x7a, 0x90, 0xbd, 0xdc, 0x0c, 0x36, + /* (2^277)P */ 0x7f, 0x20, 0x12, 0x0f, 0x40, 0x00, 0x53, 0xd8, 0x0c, 0x27, 0x47, 0x47, 0x22, 0x80, 0xfb, 0x62, 0xe4, 0xa7, 0xf7, 0xbd, 0x42, 0xa5, 0xc3, 0x2b, 0xb2, 0x7f, 0x50, 0xcc, 0xe2, 0xfb, 0xd5, 0xc0, 0x63, 0xdd, 0x24, 0x5f, 0x7c, 0x08, 0x91, 0xbf, 0x6e, 0x47, 0x44, 0xd4, 0x6a, 0xc0, 0xc3, 0x09, 0x39, 0x27, 0xdd, 0xc7, 0xca, 0x06, 0x29, 0x55, + /* (2^278)P */ 0x76, 0x28, 0x58, 0xb0, 0xd2, 0xf3, 0x0f, 0x04, 0xe9, 0xc9, 0xab, 0x66, 0x5b, 0x75, 0x51, 0xdc, 0xe5, 0x8f, 0xe8, 0x1f, 0xdb, 0x03, 0x0f, 0xb0, 0x7d, 0xf9, 0x20, 0x64, 0x89, 0xe9, 0xdc, 0xe6, 0x24, 0xc3, 0xd5, 0xd2, 0x41, 0xa6, 0xe4, 0xe3, 0xc4, 0x79, 0x7c, 0x0f, 0xa1, 0x61, 0x2f, 0xda, 0xa4, 0xc9, 0xfd, 0xad, 0x5c, 0x65, 0x6a, 0xf3, + /* (2^279)P */ 0xd5, 0xab, 0x72, 0x7a, 0x3b, 0x59, 0xea, 0xcf, 0xd5, 0x17, 0xd2, 0xb2, 0x5f, 0x2d, 0xab, 0xad, 0x9e, 0x88, 0x64, 0x55, 0x96, 0x6e, 0xf3, 0x44, 0xa9, 0x11, 0xf5, 0xf8, 0x3a, 0xf1, 0xcd, 0x79, 0x4c, 0x99, 0x6d, 0x23, 0x6a, 0xa0, 0xc2, 0x1a, 0x19, 0x45, 0xb5, 0xd8, 0x95, 0x2f, 0x49, 0xe9, 0x46, 0x39, 0x26, 0x60, 0x04, 0x15, 0x8b, 0xcc, + /* (2^280)P */ 0x66, 0x0c, 0xf0, 0x54, 0x41, 0x02, 0x91, 0xab, 0xe5, 0x85, 0x8a, 0x44, 0xa6, 0x34, 0x96, 0x32, 0xc0, 0xdf, 0x6c, 0x41, 0x39, 0xd4, 0xc6, 0xe1, 0xe3, 0x81, 0xb0, 0x4c, 0x34, 0x4f, 0xe5, 0xf4, 0x35, 0x46, 0x1f, 0xeb, 0x75, 0xfd, 0x43, 0x37, 0x50, 0x99, 0xab, 0xad, 0xb7, 0x8c, 0xa1, 0x57, 0xcb, 0xe6, 0xce, 0x16, 0x2e, 0x85, 0xcc, 0xf9, + /* (2^281)P */ 0x63, 0xd1, 0x3f, 0x9e, 0xa2, 0x17, 0x2e, 0x1d, 0x3e, 0xce, 0x48, 0x2d, 0xbb, 0x8f, 0x69, 0xc9, 0xa6, 0x3d, 0x4e, 0xfe, 0x09, 0x56, 0xb3, 0x02, 0x5f, 0x99, 0x97, 0x0c, 0x54, 0xda, 0x32, 0x97, 0x9b, 0xf4, 0x95, 0xf1, 0xad, 0xe3, 0x2b, 0x04, 0xa7, 0x9b, 0x3f, 0xbb, 0xe7, 0x87, 0x2e, 0x1f, 0x8b, 0x4b, 0x7a, 0xa4, 0x43, 0x0c, 0x0f, 0x35, + /* (2^282)P */ 0x05, 0xdc, 0xe0, 0x2c, 0xa1, 0xc1, 0xd0, 0xf1, 0x1f, 0x4e, 0xc0, 0x6c, 0x35, 0x7b, 0xca, 0x8f, 0x8b, 0x02, 0xb1, 0xf7, 0xd6, 0x2e, 0xe7, 0x93, 0x80, 0x85, 0x18, 0x88, 0x19, 0xb9, 0xb4, 0x4a, 0xbc, 0xeb, 0x5a, 0x78, 0x38, 0xed, 0xc6, 0x27, 0x2a, 0x74, 0x76, 0xf0, 0x1b, 0x79, 0x92, 0x2f, 0xd2, 0x81, 0x98, 0xdf, 0xa9, 0x50, 0x19, 0xeb, + /* (2^283)P */ 0xb5, 0xe7, 0xb4, 0x11, 0x3a, 0x81, 0xb6, 0xb4, 0xf8, 0xa2, 0xb3, 0x6c, 0xfc, 0x9d, 0xe0, 0xc0, 0xe0, 0x59, 0x7f, 0x05, 0x37, 0xef, 0x2c, 0xa9, 0x3a, 0x24, 0xac, 0x7b, 0x25, 0xa0, 0x55, 0xd2, 0x44, 0x82, 0x82, 0x6e, 0x64, 0xa3, 0x58, 0xc8, 0x67, 0xae, 0x26, 0xa7, 0x0f, 0x42, 0x63, 0xe1, 0x93, 0x01, 0x52, 0x19, 0xaf, 0x49, 0x3e, 0x33, + /* (2^284)P */ 0x05, 0x85, 0xe6, 0x66, 0xaf, 0x5f, 0xdf, 0xbf, 0x9d, 0x24, 0x62, 0x60, 0x90, 0xe2, 0x4c, 0x7d, 0x4e, 0xc3, 0x74, 0x5d, 0x4f, 0x53, 0xf3, 0x63, 0x13, 0xf4, 0x74, 0x28, 0x6b, 0x7d, 0x57, 0x0c, 0x9d, 0x84, 0xa7, 0x1a, 0xff, 0xa0, 0x79, 0xdf, 0xfc, 0x65, 0x98, 0x8e, 0x22, 0x0d, 0x62, 0x7e, 0xf2, 0x34, 0x60, 0x83, 0x05, 0x14, 0xb1, 0xc1, + /* (2^285)P */ 0x64, 0x22, 0xcc, 0xdf, 0x5c, 0xbc, 0x88, 0x68, 0x4c, 0xd9, 0xbc, 0x0e, 0xc9, 0x8b, 0xb4, 0x23, 0x52, 0xad, 0xb0, 0xb3, 0xf1, 0x17, 0xd8, 0x15, 0x04, 0x6b, 0x99, 0xf0, 0xc4, 0x7d, 0x48, 0x22, 0x4a, 0xf8, 0x6f, 0xaa, 0x88, 0x0d, 0xc5, 0x5e, 0xa9, 0x1c, 0x61, 0x3d, 0x95, 0xa9, 0x7b, 0x6a, 0x79, 0x33, 0x0a, 0x2b, 0x99, 0xe3, 0x4e, 0x48, + /* (2^286)P */ 0x6b, 0x9b, 0x6a, 0x2a, 0xf1, 0x60, 0x31, 0xb4, 0x73, 0xd1, 0x87, 0x45, 0x9c, 0x15, 0x58, 0x4b, 0x91, 0x6d, 0x94, 0x1c, 0x41, 0x11, 0x4a, 0x83, 0xec, 0xaf, 0x65, 0xbc, 0x34, 0xaa, 0x26, 0xe2, 0xaf, 0xed, 0x46, 0x05, 0x4e, 0xdb, 0xc6, 0x4e, 0x10, 0x28, 0x4e, 0x72, 0xe5, 0x31, 0xa3, 0x20, 0xd7, 0xb1, 0x96, 0x64, 0xf6, 0xce, 0x08, 0x08, + /* (2^287)P */ 0x16, 0xa9, 0x5c, 0x9f, 0x9a, 0xb4, 0xb8, 0xc8, 0x32, 0x78, 0xc0, 0x3a, 0xd9, 0x5f, 0x94, 0xac, 0x3a, 0x42, 0x1f, 0x43, 0xd6, 0x80, 0x47, 0x2c, 0xdc, 0x76, 0x27, 0xfa, 0x50, 0xe5, 0xa1, 0xe4, 0xc3, 0xcb, 0x61, 0x31, 0xe1, 0x2e, 0xde, 0x81, 0x3b, 0x77, 0x1c, 0x39, 0x3c, 0xdb, 0xda, 0x87, 0x4b, 0x84, 0x12, 0xeb, 0xdd, 0x54, 0xbf, 0xe7, + /* (2^288)P */ 0xbf, 0xcb, 0x73, 0x21, 0x3d, 0x7e, 0x13, 0x8c, 0xa6, 0x34, 0x21, 0x2b, 0xa5, 0xe4, 0x9f, 0x8e, 0x9c, 0x01, 0x9c, 0x43, 0xd9, 0xc7, 0xb9, 0xf1, 0xbe, 0x7f, 0x45, 0x51, 0x97, 0xa1, 0x8e, 0x01, 0xf8, 0xbd, 0xd2, 0xbf, 0x81, 0x3a, 0x8b, 0xab, 0xe4, 0x89, 0xb7, 0xbd, 0xf2, 0xcd, 0xa9, 0x8a, 0x8a, 0xde, 0xfb, 0x8a, 0x55, 0x12, 0x7b, 0x17, + /* (2^289)P */ 0x1b, 0x95, 0x58, 0x4d, 0xe6, 0x51, 0x31, 0x52, 0x1c, 0xd8, 0x15, 0x84, 0xb1, 0x0d, 0x36, 0x25, 0x88, 0x91, 0x46, 0x71, 0x42, 0x56, 0xe2, 0x90, 0x08, 0x9e, 0x77, 0x1b, 0xee, 0x22, 0x3f, 0xec, 0xee, 0x8c, 0x7b, 0x2e, 0x79, 0xc4, 0x6c, 0x07, 0xa1, 0x7e, 0x52, 0xf5, 0x26, 0x5c, 0x84, 0x2a, 0x50, 0x6e, 0x82, 0xb3, 0x76, 0xda, 0x35, 0x16, + /* (2^290)P */ 0x0a, 0x6f, 0x99, 0x87, 0xc0, 0x7d, 0x8a, 0xb2, 0xca, 0xae, 0xe8, 0x65, 0x98, 0x0f, 0xb3, 0x44, 0xe1, 0xdc, 0x52, 0x79, 0x75, 0xec, 0x8f, 0x95, 0x87, 0x45, 0xd1, 0x32, 0x18, 0x55, 0x15, 0xce, 0x64, 0x9b, 0x08, 0x4f, 0x2c, 0xea, 0xba, 0x1c, 0x57, 0x06, 0x63, 0xc8, 0xb1, 0xfd, 0xc5, 0x67, 0xe7, 0x1f, 0x87, 0x9e, 0xde, 0x72, 0x7d, 0xec, + /* (2^291)P */ 0x36, 0x8b, 0x4d, 0x2c, 0xc2, 0x46, 0xe8, 0x96, 0xac, 0x0b, 0x8c, 0xc5, 0x09, 0x10, 0xfc, 0xf2, 0xda, 0xea, 0x22, 0xb2, 0xd3, 0x89, 0xeb, 0xb2, 0x85, 0x0f, 0xff, 0x59, 0x50, 0x2c, 0x99, 0x5a, 0x1f, 0xec, 0x2a, 0x6f, 0xec, 0xcf, 0xe9, 0xce, 0x12, 0x6b, 0x19, 0xd8, 0xde, 0x9b, 0xce, 0x0e, 0x6a, 0xaa, 0xe1, 0x32, 0xea, 0x4c, 0xfe, 0x92, + /* (2^292)P */ 0x5f, 0x17, 0x70, 0x53, 0x26, 0x03, 0x0b, 0xab, 0xd1, 0xc1, 0x42, 0x0b, 0xab, 0x2b, 0x3d, 0x31, 0xa4, 0xd5, 0x2b, 0x5e, 0x00, 0xd5, 0x9a, 0x22, 0x34, 0xe0, 0x53, 0x3f, 0x59, 0x7f, 0x2c, 0x6d, 0x72, 0x9a, 0xa4, 0xbe, 0x3d, 0x42, 0x05, 0x1b, 0xf2, 0x7f, 0x88, 0x56, 0xd1, 0x7c, 0x7d, 0x6b, 0x9f, 0x43, 0xfe, 0x65, 0x19, 0xae, 0x9c, 0x4c, + /* (2^293)P */ 0xf3, 0x7c, 0x20, 0xa9, 0xfc, 0xf2, 0xf2, 0x3b, 0x3c, 0x57, 0x41, 0x94, 0xe5, 0xcc, 0x6a, 0x37, 0x5d, 0x09, 0xf2, 0xab, 0xc2, 0xca, 0x60, 0x38, 0x6b, 0x7a, 0xe1, 0x78, 0x2b, 0xc1, 0x1d, 0xe8, 0xfd, 0xbc, 0x3d, 0x5c, 0xa2, 0xdb, 0x49, 0x20, 0x79, 0xe6, 0x1b, 0x9b, 0x65, 0xd9, 0x6d, 0xec, 0x57, 0x1d, 0xd2, 0xe9, 0x90, 0xeb, 0x43, 0x7b, + /* (2^294)P */ 0x2a, 0x8b, 0x2e, 0x19, 0x18, 0x10, 0xb8, 0x83, 0xe7, 0x7d, 0x2d, 0x9a, 0x3a, 0xe5, 0xd1, 0xe4, 0x7c, 0x38, 0xe5, 0x59, 0x2a, 0x6e, 0xd9, 0x01, 0x29, 0x3d, 0x23, 0xf7, 0x52, 0xba, 0x61, 0x04, 0x9a, 0xde, 0xc4, 0x31, 0x50, 0xeb, 0x1b, 0xaa, 0xde, 0x39, 0x58, 0xd8, 0x1b, 0x1e, 0xfc, 0x57, 0x9a, 0x28, 0x43, 0x9e, 0x97, 0x5e, 0xaa, 0xa3, + /* (2^295)P */ 0x97, 0x0a, 0x74, 0xc4, 0x39, 0x99, 0x6b, 0x40, 0xc7, 0x3e, 0x8c, 0xa7, 0xb1, 0x4e, 0x9a, 0x59, 0x6e, 0x1c, 0xfe, 0xfc, 0x2a, 0x5e, 0x73, 0x2b, 0x8c, 0xa9, 0x71, 0xf5, 0xda, 0x6b, 0x15, 0xab, 0xf7, 0xbe, 0x2a, 0x44, 0x5f, 0xba, 0xae, 0x67, 0x93, 0xc5, 0x86, 0xc1, 0xb8, 0xdf, 0xdc, 0xcb, 0xd7, 0xff, 0xb1, 0x71, 0x7c, 0x6f, 0x88, 0xf8, + /* (2^296)P */ 0x3f, 0x89, 0xb1, 0xbf, 0x24, 0x16, 0xac, 0x56, 0xfe, 0xdf, 0x94, 0x71, 0xbf, 0xd6, 0x57, 0x0c, 0xb4, 0x77, 0x37, 0xaa, 0x2a, 0x70, 0x76, 0x49, 0xaf, 0x0c, 0x97, 0x8e, 0x78, 0x2a, 0x67, 0xc9, 0x3b, 0x3d, 0x5b, 0x01, 0x2f, 0xda, 0xd5, 0xa8, 0xde, 0x02, 0xa9, 0xac, 0x76, 0x00, 0x0b, 0x46, 0xc6, 0x2d, 0xdc, 0x08, 0xf4, 0x10, 0x2c, 0xbe, + /* (2^297)P */ 0xcb, 0x07, 0xf9, 0x91, 0xc6, 0xd5, 0x3e, 0x54, 0x63, 0xae, 0xfc, 0x10, 0xbe, 0x3a, 0x20, 0x73, 0x4e, 0x65, 0x0e, 0x2d, 0x86, 0x77, 0x83, 0x9d, 0xe2, 0x0a, 0xe9, 0xac, 0x22, 0x52, 0x76, 0xd4, 0x6e, 0xfa, 0xe0, 0x09, 0xef, 0x78, 0x82, 0x9f, 0x26, 0xf9, 0x06, 0xb5, 0xe7, 0x05, 0x0e, 0xf2, 0x46, 0x72, 0x93, 0xd3, 0x24, 0xbd, 0x87, 0x60, + /* (2^298)P */ 0x14, 0x55, 0x84, 0x7b, 0x6c, 0x60, 0x80, 0x73, 0x8c, 0xbe, 0x2d, 0xd6, 0x69, 0xd6, 0x17, 0x26, 0x44, 0x9f, 0x88, 0xa2, 0x39, 0x7c, 0x89, 0xbc, 0x6d, 0x9e, 0x46, 0xb6, 0x68, 0x66, 0xea, 0xdc, 0x31, 0xd6, 0x21, 0x51, 0x9f, 0x28, 0x28, 0xaf, 0x9e, 0x47, 0x2c, 0x4c, 0x8f, 0xf3, 0xaf, 0x1f, 0xe4, 0xab, 0xac, 0xe9, 0x0c, 0x91, 0x3a, 0x61, + /* (2^299)P */ 0xb0, 0x37, 0x55, 0x4b, 0xe9, 0xc3, 0xb1, 0xce, 0x42, 0xe6, 0xc5, 0x11, 0x7f, 0x2c, 0x11, 0xfc, 0x4e, 0x71, 0x17, 0x00, 0x74, 0x7f, 0xbf, 0x07, 0x4d, 0xfd, 0x40, 0xb2, 0x87, 0xb0, 0xef, 0x1f, 0x35, 0x2c, 0x2d, 0xd7, 0xe1, 0xe4, 0xad, 0x0e, 0x7f, 0x63, 0x66, 0x62, 0x23, 0x41, 0xf6, 0xc1, 0x14, 0xa6, 0xd7, 0xa9, 0x11, 0x56, 0x9d, 0x1b, + /* (2^300)P */ 0x02, 0x82, 0x42, 0x18, 0x4f, 0x1b, 0xc9, 0x5d, 0x78, 0x5f, 0xee, 0xed, 0x01, 0x49, 0x8f, 0xf2, 0xa0, 0xe2, 0x6e, 0xbb, 0x6b, 0x04, 0x8d, 0xb2, 0x41, 0xae, 0xc8, 0x1b, 0x59, 0x34, 0xb8, 0x2a, 0xdb, 0x1f, 0xd2, 0x52, 0xdf, 0x3f, 0x35, 0x00, 0x8b, 0x61, 0xbc, 0x97, 0xa0, 0xc4, 0x77, 0xd1, 0xe4, 0x2c, 0x59, 0x68, 0xff, 0x30, 0xf2, 0xe2, + /* (2^301)P */ 0x79, 0x08, 0xb1, 0xdb, 0x55, 0xae, 0xd0, 0xed, 0xda, 0xa0, 0xec, 0x6c, 0xae, 0x68, 0xf2, 0x0b, 0x61, 0xb3, 0xf5, 0x21, 0x69, 0x87, 0x0b, 0x03, 0xea, 0x8a, 0x15, 0xd9, 0x7e, 0xca, 0xf7, 0xcd, 0xf3, 0x33, 0xb3, 0x4c, 0x5b, 0x23, 0x4e, 0x6f, 0x90, 0xad, 0x91, 0x4b, 0x4f, 0x46, 0x37, 0xe5, 0xe8, 0xb7, 0xeb, 0xd5, 0xca, 0x34, 0x4e, 0x23, + /* (2^302)P */ 0x09, 0x02, 0xdd, 0xfd, 0x70, 0xac, 0x56, 0x80, 0x36, 0x5e, 0x49, 0xd0, 0x3f, 0xc2, 0xe0, 0xba, 0x46, 0x7f, 0x5c, 0xf7, 0xc5, 0xbd, 0xd5, 0x55, 0x7d, 0x3f, 0xd5, 0x7d, 0x06, 0xdf, 0x27, 0x20, 0x4f, 0xe9, 0x30, 0xec, 0x1b, 0xa0, 0x0c, 0xd4, 0x2c, 0xe1, 0x2b, 0x65, 0x73, 0xea, 0x75, 0x35, 0xe8, 0xe6, 0x56, 0xd6, 0x07, 0x15, 0x99, 0xdf, + /* (2^303)P */ 0x4e, 0x10, 0xb7, 0xd0, 0x63, 0x8c, 0xcf, 0x16, 0x00, 0x7c, 0x58, 0xdf, 0x86, 0xdc, 0x4e, 0xca, 0x9c, 0x40, 0x5a, 0x42, 0xfd, 0xec, 0x98, 0xa4, 0x42, 0x53, 0xae, 0x16, 0x9d, 0xfd, 0x75, 0x5a, 0x12, 0x56, 0x1e, 0xc6, 0x57, 0xcc, 0x79, 0x27, 0x96, 0x00, 0xcf, 0x80, 0x4f, 0x8a, 0x36, 0x5c, 0xbb, 0xe9, 0x12, 0xdb, 0xb6, 0x2b, 0xad, 0x96, + /* (2^304)P */ 0x92, 0x32, 0x1f, 0xfd, 0xc6, 0x02, 0x94, 0x08, 0x1b, 0x60, 0x6a, 0x9f, 0x8b, 0xd6, 0xc8, 0xad, 0xd5, 0x1b, 0x27, 0x4e, 0xa4, 0x4d, 0x4a, 0x00, 0x10, 0x5f, 0x86, 0x11, 0xf5, 0xe3, 0x14, 0x32, 0x43, 0xee, 0xb9, 0xc7, 0xab, 0xf4, 0x6f, 0xe5, 0x66, 0x0c, 0x06, 0x0d, 0x96, 0x79, 0x28, 0xaf, 0x45, 0x2b, 0x56, 0xbe, 0xe4, 0x4a, 0x52, 0xd6, + /* (2^305)P */ 0x15, 0x16, 0x69, 0xef, 0x60, 0xca, 0x82, 0x25, 0x0f, 0xc6, 0x30, 0xa0, 0x0a, 0xd1, 0x83, 0x29, 0xcd, 0xb6, 0x89, 0x6c, 0xf5, 0xb2, 0x08, 0x38, 0xe6, 0xca, 0x6b, 0x19, 0x93, 0xc6, 0x5f, 0x75, 0x8e, 0x60, 0x34, 0x23, 0xc4, 0x13, 0x17, 0x69, 0x55, 0xcc, 0x72, 0x9c, 0x2b, 0x6c, 0x80, 0xf4, 0x4b, 0x8b, 0xb6, 0x97, 0x65, 0x07, 0xb6, 0xfb, + /* (2^306)P */ 0x01, 0x99, 0x74, 0x28, 0xa6, 0x67, 0xa3, 0xe5, 0x25, 0xfb, 0xdf, 0x82, 0x93, 0xe7, 0x35, 0x74, 0xce, 0xe3, 0x15, 0x1c, 0x1d, 0x79, 0x52, 0x84, 0x08, 0x04, 0x2f, 0x5c, 0xb8, 0xcd, 0x7f, 0x89, 0xb0, 0x39, 0x93, 0x63, 0xc9, 0x5d, 0x06, 0x01, 0x59, 0xf7, 0x7e, 0xf1, 0x4c, 0x3d, 0x12, 0x8d, 0x69, 0x1d, 0xb7, 0x21, 0x5e, 0x88, 0x82, 0xa2, + /* (2^307)P */ 0x8e, 0x69, 0xaf, 0x9a, 0x41, 0x0d, 0x9d, 0xcf, 0x8e, 0x8d, 0x5c, 0x51, 0x6e, 0xde, 0x0e, 0x48, 0x23, 0x89, 0xe5, 0x37, 0x80, 0xd6, 0x9d, 0x72, 0x32, 0x26, 0x38, 0x2d, 0x63, 0xa0, 0xfa, 0xd3, 0x40, 0xc0, 0x8c, 0x68, 0x6f, 0x2b, 0x1e, 0x9a, 0x39, 0x51, 0x78, 0x74, 0x9a, 0x7b, 0x4a, 0x8f, 0x0c, 0xa0, 0x88, 0x60, 0xa5, 0x21, 0xcd, 0xc7, + /* (2^308)P */ 0x3a, 0x7f, 0x73, 0x14, 0xbf, 0x89, 0x6a, 0x4c, 0x09, 0x5d, 0xf2, 0x93, 0x20, 0x2d, 0xc4, 0x29, 0x86, 0x06, 0x95, 0xab, 0x22, 0x76, 0x4c, 0x54, 0xe1, 0x7e, 0x80, 0x6d, 0xab, 0x29, 0x61, 0x87, 0x77, 0xf6, 0xc0, 0x3e, 0xda, 0xab, 0x65, 0x7e, 0x39, 0x12, 0xa1, 0x6b, 0x42, 0xf7, 0xc5, 0x97, 0x77, 0xec, 0x6f, 0x22, 0xbe, 0x44, 0xc7, 0x03, + /* (2^309)P */ 0xa5, 0x23, 0x90, 0x41, 0xa3, 0xc5, 0x3e, 0xe0, 0xa5, 0x32, 0x49, 0x1f, 0x39, 0x78, 0xb1, 0xd8, 0x24, 0xea, 0xd4, 0x87, 0x53, 0x42, 0x51, 0xf4, 0xd9, 0x46, 0x25, 0x2f, 0x62, 0xa9, 0x90, 0x9a, 0x4a, 0x25, 0x8a, 0xd2, 0x10, 0xe7, 0x3c, 0xbc, 0x58, 0x8d, 0x16, 0x14, 0x96, 0xa4, 0x6f, 0xf8, 0x12, 0x69, 0x91, 0x73, 0xe2, 0xfa, 0xf4, 0x57, + /* (2^310)P */ 0x51, 0x45, 0x3f, 0x96, 0xdc, 0x97, 0x38, 0xa6, 0x01, 0x63, 0x09, 0xea, 0xc2, 0x13, 0x30, 0xb0, 0x00, 0xb8, 0x0a, 0xce, 0xd1, 0x8f, 0x3e, 0x69, 0x62, 0x46, 0x33, 0x9c, 0xbf, 0x4b, 0xcb, 0x0c, 0x90, 0x1c, 0x45, 0xcf, 0x37, 0x5b, 0xf7, 0x4b, 0x5e, 0x95, 0xc3, 0x28, 0x9f, 0x08, 0x83, 0x53, 0x74, 0xab, 0x0c, 0xb4, 0xc0, 0xa1, 0xbc, 0x89, + /* (2^311)P */ 0x06, 0xb1, 0x51, 0x15, 0x65, 0x60, 0x21, 0x17, 0x7a, 0x20, 0x65, 0xee, 0x12, 0x35, 0x4d, 0x46, 0xf4, 0xf8, 0xd0, 0xb1, 0xca, 0x09, 0x30, 0x08, 0x89, 0x23, 0x3b, 0xe7, 0xab, 0x8b, 0x77, 0xa6, 0xad, 0x25, 0xdd, 0xea, 0x3c, 0x7d, 0xa5, 0x24, 0xb3, 0xe8, 0xfa, 0xfb, 0xc9, 0xf2, 0x71, 0xe9, 0xfa, 0xf2, 0xdc, 0x54, 0xdd, 0x55, 0x2e, 0x2f, + /* (2^312)P */ 0x7f, 0x96, 0x96, 0xfb, 0x52, 0x86, 0xcf, 0xea, 0x62, 0x18, 0xf1, 0x53, 0x1f, 0x61, 0x2a, 0x9f, 0x8c, 0x51, 0xca, 0x2c, 0xde, 0x6d, 0xce, 0xab, 0x58, 0x32, 0x0b, 0x33, 0x9b, 0x99, 0xb4, 0x5c, 0x88, 0x2a, 0x76, 0xcc, 0x3e, 0x54, 0x1e, 0x9d, 0xa2, 0x89, 0xe4, 0x19, 0xba, 0x80, 0xc8, 0x39, 0x32, 0x7f, 0x0f, 0xc7, 0x84, 0xbb, 0x43, 0x56, + /* (2^313)P */ 0x9b, 0x07, 0xb4, 0x42, 0xa9, 0xa0, 0x78, 0x4f, 0x28, 0x70, 0x2b, 0x7e, 0x61, 0xe0, 0xdd, 0x02, 0x98, 0xfc, 0xed, 0x31, 0x80, 0xf1, 0x15, 0x52, 0x89, 0x23, 0xcd, 0x5d, 0x2b, 0xc5, 0x19, 0x32, 0xfb, 0x70, 0x50, 0x7a, 0x97, 0x6b, 0x42, 0xdb, 0xca, 0xdb, 0xc4, 0x59, 0x99, 0xe0, 0x12, 0x1f, 0x17, 0xba, 0x8b, 0xf0, 0xc4, 0x38, 0x5d, 0x27, + /* (2^314)P */ 0x29, 0x1d, 0xdc, 0x2b, 0xf6, 0x5b, 0x04, 0x61, 0x36, 0x76, 0xa0, 0x56, 0x36, 0x6e, 0xd7, 0x24, 0x4d, 0xe7, 0xef, 0x44, 0xd2, 0xd5, 0x07, 0xcd, 0xc4, 0x9d, 0x80, 0x48, 0xc3, 0x38, 0xcf, 0xd8, 0xa3, 0xdd, 0xb2, 0x5e, 0xb5, 0x70, 0x15, 0xbb, 0x36, 0x85, 0x8a, 0xd7, 0xfb, 0x56, 0x94, 0x73, 0x9c, 0x81, 0xbe, 0xb1, 0x44, 0x28, 0xf1, 0x37, + /* (2^315)P */ 0xbf, 0xcf, 0x5c, 0xd2, 0xe2, 0xea, 0xc2, 0xcd, 0x70, 0x7a, 0x9d, 0xcb, 0x81, 0xc1, 0xe9, 0xf1, 0x56, 0x71, 0x52, 0xf7, 0x1b, 0x87, 0xc6, 0xd8, 0xcc, 0xb2, 0x69, 0xf3, 0xb0, 0xbd, 0xba, 0x83, 0x12, 0x26, 0xc4, 0xce, 0x72, 0xde, 0x3b, 0x21, 0x28, 0x9e, 0x5a, 0x94, 0xf5, 0x04, 0xa3, 0xc8, 0x0f, 0x5e, 0xbc, 0x71, 0xf9, 0x0d, 0xce, 0xf5, + /* (2^316)P */ 0x93, 0x97, 0x00, 0x85, 0xf4, 0xb4, 0x40, 0xec, 0xd9, 0x2b, 0x6c, 0xd6, 0x63, 0x9e, 0x93, 0x0a, 0x5a, 0xf4, 0xa7, 0x9a, 0xe3, 0x3c, 0xf0, 0x55, 0xd1, 0x96, 0x6c, 0xf5, 0x2a, 0xce, 0xd7, 0x95, 0x72, 0xbf, 0xc5, 0x0c, 0xce, 0x79, 0xa2, 0x0a, 0x78, 0xe0, 0x72, 0xd0, 0x66, 0x28, 0x05, 0x75, 0xd3, 0x23, 0x09, 0x91, 0xed, 0x7e, 0xc4, 0xbc, + /* (2^317)P */ 0x77, 0xc2, 0x9a, 0xf7, 0xa6, 0xe6, 0x18, 0xb4, 0xe7, 0xf6, 0xda, 0xec, 0x44, 0x6d, 0xfb, 0x08, 0xee, 0x65, 0xa8, 0x92, 0x85, 0x1f, 0xba, 0x38, 0x93, 0x20, 0x5c, 0x4d, 0xd2, 0x18, 0x0f, 0x24, 0xbe, 0x1a, 0x96, 0x44, 0x7d, 0xeb, 0xb3, 0xda, 0x95, 0xf4, 0xaf, 0x6c, 0x06, 0x0f, 0x47, 0x37, 0xc8, 0x77, 0x63, 0xe1, 0x29, 0xef, 0xff, 0xa5, + /* (2^318)P */ 0x16, 0x12, 0xd9, 0x47, 0x90, 0x22, 0x9b, 0x05, 0xf2, 0xa5, 0x9a, 0xae, 0x83, 0x98, 0xb5, 0xac, 0xab, 0x29, 0xaa, 0xdc, 0x5f, 0xde, 0xcd, 0xf7, 0x42, 0xad, 0x3b, 0x96, 0xd6, 0x3e, 0x6e, 0x52, 0x47, 0xb1, 0xab, 0x51, 0xde, 0x49, 0x7c, 0x87, 0x8d, 0x86, 0xe2, 0x70, 0x13, 0x21, 0x51, 0x1c, 0x0c, 0x25, 0xc1, 0xb0, 0xe6, 0x19, 0xcf, 0x12, + /* (2^319)P */ 0xf0, 0xbc, 0x97, 0x8f, 0x4b, 0x2f, 0xd1, 0x1f, 0x8c, 0x57, 0xed, 0x3c, 0xf4, 0x26, 0x19, 0xbb, 0x60, 0xca, 0x24, 0xc5, 0xd9, 0x97, 0xe2, 0x5f, 0x76, 0x49, 0x39, 0x7e, 0x2d, 0x12, 0x21, 0x98, 0xda, 0xe6, 0xdb, 0xd2, 0xd8, 0x9f, 0x18, 0xd8, 0x83, 0x6c, 0xba, 0x89, 0x8d, 0x29, 0xfa, 0x46, 0x33, 0x8c, 0x28, 0xdf, 0x6a, 0xb3, 0x69, 0x28, + /* (2^320)P */ 0x86, 0x17, 0xbc, 0xd6, 0x7c, 0xba, 0x1e, 0x83, 0xbb, 0x84, 0xb5, 0x8c, 0xad, 0xdf, 0xa1, 0x24, 0x81, 0x70, 0x40, 0x0f, 0xad, 0xad, 0x3b, 0x23, 0xd0, 0x93, 0xa0, 0x49, 0x5c, 0x4b, 0x51, 0xbe, 0x20, 0x49, 0x4e, 0xda, 0x2d, 0xd3, 0xad, 0x1b, 0x74, 0x08, 0x41, 0xf0, 0xef, 0x19, 0xe9, 0x45, 0x5d, 0x02, 0xae, 0x26, 0x25, 0xd9, 0xd1, 0xc2, + /* (2^321)P */ 0x48, 0x81, 0x3e, 0xb2, 0x83, 0xf8, 0x4d, 0xb3, 0xd0, 0x4c, 0x75, 0xb3, 0xa0, 0x52, 0x26, 0xf2, 0xaf, 0x5d, 0x36, 0x70, 0x72, 0xd6, 0xb7, 0x88, 0x08, 0x69, 0xbd, 0x15, 0x25, 0xb1, 0x45, 0x1b, 0xb7, 0x0b, 0x5f, 0x71, 0x5d, 0x83, 0x49, 0xb9, 0x84, 0x3b, 0x7c, 0xc1, 0x50, 0x93, 0x05, 0x53, 0xe0, 0x61, 0xea, 0xc1, 0xef, 0xdb, 0x82, 0x97, + /* (2^322)P */ 0x00, 0xd5, 0xc3, 0x3a, 0x4d, 0x8a, 0x23, 0x7a, 0xef, 0xff, 0x37, 0xef, 0xf3, 0xbc, 0xa9, 0xb6, 0xae, 0xd7, 0x3a, 0x7b, 0xfd, 0x3e, 0x8e, 0x9b, 0xab, 0x44, 0x54, 0x60, 0x28, 0x6c, 0xbf, 0x15, 0x24, 0x4a, 0x56, 0x60, 0x7f, 0xa9, 0x7a, 0x28, 0x59, 0x2c, 0x8a, 0xd1, 0x7d, 0x6b, 0x00, 0xfd, 0xa5, 0xad, 0xbc, 0x19, 0x3f, 0xcb, 0x73, 0xe0, + /* (2^323)P */ 0xcf, 0x9e, 0x66, 0x06, 0x4d, 0x2b, 0xf5, 0x9c, 0xc2, 0x9d, 0x9e, 0xed, 0x5a, 0x5c, 0x2d, 0x00, 0xbf, 0x29, 0x90, 0x88, 0xe4, 0x5d, 0xfd, 0xe2, 0xf0, 0x38, 0xec, 0x4d, 0x26, 0xea, 0x54, 0xf0, 0x3c, 0x84, 0x10, 0x6a, 0xf9, 0x66, 0x9c, 0xe7, 0x21, 0xfd, 0x0f, 0xc7, 0x13, 0x50, 0x81, 0xb6, 0x50, 0xf9, 0x04, 0x7f, 0xa4, 0x37, 0x85, 0x14, + /* (2^324)P */ 0xdb, 0x87, 0x49, 0xc7, 0xa8, 0x39, 0x0c, 0x32, 0x98, 0x0c, 0xb9, 0x1a, 0x1b, 0x4d, 0xe0, 0x8a, 0x9a, 0x8e, 0x8f, 0xab, 0x5a, 0x17, 0x3d, 0x04, 0x21, 0xce, 0x3e, 0x2c, 0xf9, 0xa3, 0x97, 0xe4, 0x77, 0x95, 0x0e, 0xb6, 0xa5, 0x15, 0xad, 0x3a, 0x1e, 0x46, 0x53, 0x17, 0x09, 0x83, 0x71, 0x4e, 0x86, 0x38, 0xd5, 0x23, 0x44, 0x16, 0x8d, 0xc8, + /* (2^325)P */ 0x05, 0x5e, 0x99, 0x08, 0xbb, 0xc3, 0xc0, 0xb7, 0x6c, 0x12, 0xf2, 0xf3, 0xf4, 0x7c, 0x6a, 0x4d, 0x9e, 0xeb, 0x3d, 0xb9, 0x63, 0x94, 0xce, 0x81, 0xd8, 0x11, 0xcb, 0x55, 0x69, 0x4a, 0x20, 0x0b, 0x4c, 0x2e, 0x14, 0xb8, 0xd4, 0x6a, 0x7c, 0xf0, 0xed, 0xfc, 0x8f, 0xef, 0xa0, 0xeb, 0x6c, 0x01, 0xe2, 0xdc, 0x10, 0x22, 0xa2, 0x01, 0x85, 0x64, + /* (2^326)P */ 0x58, 0xe1, 0x9c, 0x27, 0x55, 0xc6, 0x25, 0xa6, 0x7d, 0x67, 0x88, 0x65, 0x99, 0x6c, 0xcb, 0xdb, 0x27, 0x4f, 0x44, 0x29, 0xf5, 0x4a, 0x23, 0x10, 0xbc, 0x03, 0x3f, 0x36, 0x1e, 0xef, 0xb0, 0xba, 0x75, 0xe8, 0x74, 0x5f, 0x69, 0x3e, 0x26, 0x40, 0xb4, 0x2f, 0xdc, 0x43, 0xbf, 0xa1, 0x8b, 0xbd, 0xca, 0x6e, 0xc1, 0x6e, 0x21, 0x79, 0xa0, 0xd0, + /* (2^327)P */ 0x78, 0x93, 0x4a, 0x2d, 0x22, 0x6e, 0x6e, 0x7d, 0x74, 0xd2, 0x66, 0x58, 0xce, 0x7b, 0x1d, 0x97, 0xb1, 0xf2, 0xda, 0x1c, 0x79, 0xfb, 0xba, 0xd1, 0xc0, 0xc5, 0x6e, 0xc9, 0x11, 0x89, 0xd2, 0x41, 0x8d, 0x70, 0xb9, 0xcc, 0xea, 0x6a, 0xb3, 0x45, 0xb6, 0x05, 0x2e, 0xf2, 0x17, 0xf1, 0x27, 0xb8, 0xed, 0x06, 0x1f, 0xdb, 0x9d, 0x1f, 0x69, 0x28, + /* (2^328)P */ 0x93, 0x12, 0xa8, 0x11, 0xe1, 0x92, 0x30, 0x8d, 0xac, 0xe1, 0x1c, 0x60, 0x7c, 0xed, 0x2d, 0x2e, 0xd3, 0x03, 0x5c, 0x9c, 0xc5, 0xbd, 0x64, 0x4a, 0x8c, 0xba, 0x76, 0xfe, 0xc6, 0xc1, 0xea, 0xc2, 0x4f, 0xbe, 0x70, 0x3d, 0x64, 0xcf, 0x8e, 0x18, 0xcb, 0xcd, 0x57, 0xa7, 0xf7, 0x36, 0xa9, 0x6b, 0x3e, 0xb8, 0x69, 0xee, 0x47, 0xa2, 0x7e, 0xb2, + /* (2^329)P */ 0x96, 0xaf, 0x3a, 0xf5, 0xed, 0xcd, 0xaf, 0xf7, 0x82, 0xaf, 0x59, 0x62, 0x0b, 0x36, 0x85, 0xf9, 0xaf, 0xd6, 0x38, 0xff, 0x87, 0x2e, 0x1d, 0x6c, 0x8b, 0xaf, 0x3b, 0xdf, 0x28, 0xa2, 0xd6, 0x4d, 0x80, 0x92, 0xc3, 0x0f, 0x34, 0xa8, 0xae, 0x69, 0x5d, 0x7b, 0x9d, 0xbc, 0xf5, 0xfd, 0x1d, 0xb1, 0x96, 0x55, 0x86, 0xe1, 0x5c, 0xb6, 0xac, 0xb9, + /* (2^330)P */ 0x50, 0x9e, 0x37, 0x28, 0x7d, 0xa8, 0x33, 0x63, 0xda, 0x3f, 0x20, 0x98, 0x0e, 0x09, 0xa8, 0x77, 0x3b, 0x7a, 0xfc, 0x16, 0x85, 0x44, 0x64, 0x77, 0x65, 0x68, 0x92, 0x41, 0xc6, 0x1f, 0xdf, 0x27, 0xf9, 0xec, 0xa0, 0x61, 0x22, 0xea, 0x19, 0xe7, 0x75, 0x8b, 0x4e, 0xe5, 0x0f, 0xb7, 0xf7, 0xd2, 0x53, 0xf4, 0xdd, 0x4a, 0xaa, 0x78, 0x40, 0xb7, + /* (2^331)P */ 0xd4, 0x89, 0xe3, 0x79, 0xba, 0xb6, 0xc3, 0xda, 0xe6, 0x78, 0x65, 0x7d, 0x6e, 0x22, 0x62, 0xb1, 0x3d, 0xea, 0x90, 0x84, 0x30, 0x5e, 0xd4, 0x39, 0x84, 0x78, 0xd9, 0x75, 0xd6, 0xce, 0x2a, 0x11, 0x29, 0x69, 0xa4, 0x5e, 0xaa, 0x2a, 0x98, 0x5a, 0xe5, 0x91, 0x8f, 0xb2, 0xfb, 0xda, 0x97, 0xe8, 0x83, 0x6f, 0x04, 0xb9, 0x5d, 0xaf, 0xe1, 0x9b, + /* (2^332)P */ 0x8b, 0xe4, 0xe1, 0x48, 0x9c, 0xc4, 0x83, 0x89, 0xdf, 0x65, 0xd3, 0x35, 0x55, 0x13, 0xf4, 0x1f, 0x36, 0x92, 0x33, 0x38, 0xcb, 0xed, 0x15, 0xe6, 0x60, 0x2d, 0x25, 0xf5, 0x36, 0x60, 0x3a, 0x37, 0x9b, 0x71, 0x9d, 0x42, 0xb0, 0x14, 0xc8, 0xba, 0x62, 0xa3, 0x49, 0xb0, 0x88, 0xc1, 0x72, 0x73, 0xdd, 0x62, 0x40, 0xa9, 0x62, 0x88, 0x99, 0xca, + /* (2^333)P */ 0x47, 0x7b, 0xea, 0xda, 0x46, 0x2f, 0x45, 0xc6, 0xe3, 0xb4, 0x4d, 0x8d, 0xac, 0x0b, 0x54, 0x22, 0x06, 0x31, 0x16, 0x66, 0x3e, 0xe4, 0x38, 0x12, 0xcd, 0xf3, 0xe7, 0x99, 0x37, 0xd9, 0x62, 0x24, 0x4b, 0x05, 0xf2, 0x58, 0xe6, 0x29, 0x4b, 0x0d, 0xf6, 0xc1, 0xba, 0xa0, 0x1e, 0x0f, 0xcb, 0x1f, 0xc6, 0x2b, 0x19, 0xfc, 0x82, 0x01, 0xd0, 0x86, + /* (2^334)P */ 0xa2, 0xae, 0x77, 0x20, 0xfb, 0xa8, 0x18, 0xb4, 0x61, 0xef, 0xe8, 0x52, 0x79, 0xbb, 0x86, 0x90, 0x5d, 0x2e, 0x76, 0xed, 0x66, 0x60, 0x5d, 0x00, 0xb5, 0xa4, 0x00, 0x40, 0x89, 0xec, 0xd1, 0xd2, 0x0d, 0x26, 0xb9, 0x30, 0xb2, 0xd2, 0xb8, 0xe8, 0x0e, 0x56, 0xf9, 0x67, 0x94, 0x2e, 0x62, 0xe1, 0x79, 0x48, 0x2b, 0xa9, 0xfa, 0xea, 0xdb, 0x28, + /* (2^335)P */ 0x35, 0xf1, 0xb0, 0x43, 0xbd, 0x27, 0xef, 0x18, 0x44, 0xa2, 0x04, 0xb4, 0x69, 0xa1, 0x97, 0x1f, 0x8c, 0x04, 0x82, 0x9b, 0x00, 0x6d, 0xf8, 0xbf, 0x7d, 0xc1, 0x5b, 0xab, 0xe8, 0xb2, 0x34, 0xbd, 0xaf, 0x7f, 0xb2, 0x0d, 0xf3, 0xed, 0xfc, 0x5b, 0x50, 0xee, 0xe7, 0x4a, 0x20, 0xd9, 0xf5, 0xc6, 0x9a, 0x97, 0x6d, 0x07, 0x2f, 0xb9, 0x31, 0x02, + /* (2^336)P */ 0xf9, 0x54, 0x4a, 0xc5, 0x61, 0x7e, 0x1d, 0xa6, 0x0e, 0x1a, 0xa8, 0xd3, 0x8c, 0x36, 0x7d, 0xf1, 0x06, 0xb1, 0xac, 0x93, 0xcd, 0xe9, 0x8f, 0x61, 0x6c, 0x5d, 0x03, 0x23, 0xdf, 0x85, 0x53, 0x39, 0x63, 0x5e, 0xeb, 0xf3, 0xd3, 0xd3, 0x75, 0x97, 0x9b, 0x62, 0x9b, 0x01, 0xb3, 0x19, 0xd8, 0x2b, 0x36, 0xf2, 0x2c, 0x2c, 0x6f, 0x36, 0xc6, 0x3c, + /* (2^337)P */ 0x05, 0x74, 0x43, 0x10, 0xb6, 0xb0, 0xf8, 0xbf, 0x02, 0x46, 0x9a, 0xee, 0xc1, 0xaf, 0xc1, 0xe5, 0x5a, 0x2e, 0xbb, 0xe1, 0xdc, 0xc6, 0xce, 0x51, 0x29, 0x50, 0xbf, 0x1b, 0xde, 0xff, 0xba, 0x4d, 0x8d, 0x8b, 0x7e, 0xe7, 0xbd, 0x5b, 0x8f, 0xbe, 0xe3, 0x75, 0x71, 0xff, 0x37, 0x05, 0x5a, 0x10, 0xeb, 0x54, 0x7e, 0x44, 0x72, 0x2c, 0xd4, 0xfc, + /* (2^338)P */ 0x03, 0x12, 0x1c, 0xb2, 0x08, 0x90, 0xa1, 0x2d, 0x50, 0xa0, 0xad, 0x7f, 0x8d, 0xa6, 0x97, 0xc1, 0xbd, 0xdc, 0xc3, 0xa7, 0xad, 0x31, 0xdf, 0xb8, 0x03, 0x84, 0xc3, 0xb9, 0x29, 0x3d, 0x92, 0x2e, 0xc3, 0x90, 0x07, 0xe8, 0xa7, 0xc7, 0xbc, 0x61, 0xe9, 0x3e, 0xa0, 0x35, 0xda, 0x1d, 0xab, 0x48, 0xfe, 0x50, 0xc9, 0x25, 0x59, 0x23, 0x69, 0x3f, + /* (2^339)P */ 0x8e, 0x91, 0xab, 0x6b, 0x91, 0x4f, 0x89, 0x76, 0x67, 0xad, 0xb2, 0x65, 0x9d, 0xad, 0x02, 0x36, 0xdc, 0xac, 0x96, 0x93, 0x97, 0x21, 0x14, 0xd0, 0xe8, 0x11, 0x60, 0x1e, 0xeb, 0x96, 0x06, 0xf2, 0x53, 0xf2, 0x6d, 0xb7, 0x93, 0x6f, 0x26, 0x91, 0x23, 0xe3, 0x34, 0x04, 0x92, 0x91, 0x37, 0x08, 0x50, 0xd6, 0x28, 0x09, 0x27, 0xa1, 0x0c, 0x00, + /* (2^340)P */ 0x1f, 0xbb, 0x21, 0x26, 0x33, 0xcb, 0xa4, 0xd1, 0xee, 0x85, 0xf9, 0xd9, 0x3c, 0x90, 0xc3, 0xd1, 0x26, 0xa2, 0x25, 0x93, 0x43, 0x61, 0xed, 0x91, 0x6e, 0x54, 0x03, 0x2e, 0x42, 0x9d, 0xf7, 0xa6, 0x02, 0x0f, 0x2f, 0x9c, 0x7a, 0x8d, 0x12, 0xc2, 0x18, 0xfc, 0x41, 0xff, 0x85, 0x26, 0x1a, 0x44, 0x55, 0x0b, 0x89, 0xab, 0x6f, 0x62, 0x33, 0x8c, + /* (2^341)P */ 0xe0, 0x3c, 0x5d, 0x70, 0x64, 0x87, 0x81, 0x35, 0xf2, 0x37, 0xa6, 0x24, 0x3e, 0xe0, 0x62, 0xd5, 0x71, 0xe7, 0x93, 0xfb, 0xac, 0xc3, 0xe7, 0xc7, 0x04, 0xe2, 0x70, 0xd3, 0x29, 0x5b, 0x21, 0xbf, 0xf4, 0x26, 0x5d, 0xf3, 0x95, 0xb4, 0x2a, 0x6a, 0x07, 0x55, 0xa6, 0x4b, 0x3b, 0x15, 0xf2, 0x25, 0x8a, 0x95, 0x3f, 0x63, 0x2f, 0x7a, 0x23, 0x96, + /* (2^342)P */ 0x0d, 0x3d, 0xd9, 0x13, 0xa7, 0xb3, 0x5e, 0x67, 0xf7, 0x02, 0x23, 0xee, 0x84, 0xff, 0x99, 0xda, 0xb9, 0x53, 0xf8, 0xf0, 0x0e, 0x39, 0x2f, 0x3c, 0x64, 0x34, 0xe3, 0x09, 0xfd, 0x2b, 0x33, 0xc7, 0xfe, 0x62, 0x2b, 0x84, 0xdf, 0x2b, 0xd2, 0x7c, 0x26, 0x01, 0x70, 0x66, 0x5b, 0x85, 0xc2, 0xbe, 0x88, 0x37, 0xf1, 0x30, 0xac, 0xb8, 0x76, 0xa3, + /* (2^343)P */ 0x6e, 0x01, 0xf0, 0x55, 0x35, 0xe4, 0xbd, 0x43, 0x62, 0x9d, 0xd6, 0x11, 0xef, 0x6f, 0xb8, 0x8c, 0xaa, 0x98, 0x87, 0xc6, 0x6d, 0xc4, 0xcc, 0x74, 0x92, 0x53, 0x4a, 0xdf, 0xe4, 0x08, 0x89, 0x17, 0xd0, 0x0f, 0xf4, 0x00, 0x60, 0x78, 0x08, 0x44, 0xb5, 0xda, 0x18, 0xed, 0x98, 0xc8, 0x61, 0x3d, 0x39, 0xdb, 0xcf, 0x1d, 0x49, 0x40, 0x65, 0x75, + /* (2^344)P */ 0x8e, 0x10, 0xae, 0x5f, 0x06, 0xd2, 0x95, 0xfd, 0x20, 0x16, 0x49, 0x5b, 0x57, 0xbe, 0x22, 0x8b, 0x43, 0xfb, 0xe6, 0xcc, 0x26, 0xa5, 0x5d, 0xd3, 0x68, 0xc5, 0xf9, 0x5a, 0x86, 0x24, 0x87, 0x27, 0x05, 0xfd, 0xe2, 0xff, 0xb3, 0xa3, 0x7b, 0x37, 0x59, 0xc5, 0x4e, 0x14, 0x94, 0xf9, 0x3b, 0xcb, 0x7c, 0xed, 0xca, 0x1d, 0xb2, 0xac, 0x05, 0x4a, + /* (2^345)P */ 0xf4, 0xd1, 0x81, 0xeb, 0x89, 0xbf, 0xfe, 0x1e, 0x41, 0x92, 0x29, 0xee, 0xe1, 0x43, 0xf5, 0x86, 0x1d, 0x2f, 0xbb, 0x1e, 0x84, 0x5d, 0x7b, 0x8d, 0xd5, 0xda, 0xee, 0x1e, 0x8a, 0xd0, 0x27, 0xf2, 0x60, 0x51, 0x59, 0x82, 0xf4, 0x84, 0x2b, 0x5b, 0x14, 0x2d, 0x81, 0x82, 0x3e, 0x2b, 0xb4, 0x6d, 0x51, 0x4f, 0xc5, 0xcb, 0xbf, 0x74, 0xe3, 0xb4, + /* (2^346)P */ 0x19, 0x2f, 0x22, 0xb3, 0x04, 0x5f, 0x81, 0xca, 0x05, 0x60, 0xb9, 0xaa, 0xee, 0x0e, 0x2f, 0x48, 0x38, 0xf9, 0x91, 0xb4, 0x66, 0xe4, 0x57, 0x28, 0x54, 0x10, 0xe9, 0x61, 0x9d, 0xd4, 0x90, 0x75, 0xb1, 0x39, 0x23, 0xb6, 0xfc, 0x82, 0xe0, 0xfa, 0xbb, 0x5c, 0x6e, 0xc3, 0x44, 0x13, 0x00, 0x83, 0x55, 0x9e, 0x8e, 0x10, 0x61, 0x81, 0x91, 0x04, + /* (2^347)P */ 0x5f, 0x2a, 0xd7, 0x81, 0xd9, 0x9c, 0xbb, 0x79, 0xbc, 0x62, 0x56, 0x98, 0x03, 0x5a, 0x18, 0x85, 0x2a, 0x9c, 0xd0, 0xfb, 0xd2, 0xb1, 0xaf, 0xef, 0x0d, 0x24, 0xc5, 0xfa, 0x39, 0xbb, 0x6b, 0xed, 0xa4, 0xdf, 0xe4, 0x87, 0xcd, 0x41, 0xd3, 0x72, 0x32, 0xc6, 0x28, 0x21, 0xb1, 0xba, 0x8b, 0xa3, 0x91, 0x79, 0x76, 0x22, 0x25, 0x10, 0x61, 0xd1, + /* (2^348)P */ 0x73, 0xb5, 0x32, 0x97, 0xdd, 0xeb, 0xdd, 0x22, 0x22, 0xf1, 0x33, 0x3c, 0x77, 0x56, 0x7d, 0x6b, 0x48, 0x2b, 0x05, 0x81, 0x03, 0x03, 0x91, 0x9a, 0xe3, 0x5e, 0xd4, 0xee, 0x3f, 0xf8, 0xbb, 0x50, 0x21, 0x32, 0x4c, 0x4a, 0x58, 0x49, 0xde, 0x0c, 0xde, 0x30, 0x82, 0x3d, 0x92, 0xf0, 0x6c, 0xcc, 0x32, 0x3e, 0xd2, 0x78, 0x8a, 0x6e, 0x2c, 0xd0, + /* (2^349)P */ 0xf0, 0xf7, 0xa1, 0x0b, 0xc1, 0x74, 0x85, 0xa8, 0xe9, 0xdd, 0x48, 0xa1, 0xc0, 0x16, 0xd8, 0x2b, 0x61, 0x08, 0xc2, 0x2b, 0x30, 0x26, 0x79, 0xce, 0x9e, 0xfd, 0x39, 0xd7, 0x81, 0xa4, 0x63, 0x8c, 0xd5, 0x74, 0xa0, 0x88, 0xfa, 0x03, 0x30, 0xe9, 0x7f, 0x2b, 0xc6, 0x02, 0xc9, 0x5e, 0xe4, 0xd5, 0x4d, 0x92, 0xd0, 0xf6, 0xf2, 0x5b, 0x79, 0x08, + /* (2^350)P */ 0x34, 0x89, 0x81, 0x43, 0xd1, 0x94, 0x2c, 0x10, 0x54, 0x9b, 0xa0, 0xe5, 0x44, 0xe8, 0xc2, 0x2f, 0x3e, 0x0e, 0x74, 0xae, 0xba, 0xe2, 0xac, 0x85, 0x6b, 0xd3, 0x5c, 0x97, 0xf7, 0x90, 0xf1, 0x12, 0xc0, 0x03, 0xc8, 0x1f, 0x37, 0x72, 0x8c, 0x9b, 0x9c, 0x17, 0x96, 0x9d, 0xc7, 0xbf, 0xa3, 0x3f, 0x44, 0x3d, 0x87, 0x81, 0xbd, 0x81, 0xa6, 0x5f, + /* (2^351)P */ 0xe4, 0xff, 0x78, 0x62, 0x82, 0x5b, 0x76, 0x58, 0xf5, 0x5b, 0xa6, 0xc4, 0x53, 0x11, 0x3b, 0x7b, 0xaa, 0x67, 0xf8, 0xea, 0x3b, 0x5d, 0x9a, 0x2e, 0x04, 0xeb, 0x4a, 0x24, 0xfb, 0x56, 0xf0, 0xa8, 0xd4, 0x14, 0xed, 0x0f, 0xfd, 0xc5, 0x26, 0x17, 0x2a, 0xf0, 0xb9, 0x13, 0x8c, 0xbd, 0x65, 0x14, 0x24, 0x95, 0x27, 0x12, 0x63, 0x2a, 0x09, 0x18, + /* (2^352)P */ 0xe1, 0x5c, 0xe7, 0xe0, 0x00, 0x6a, 0x96, 0xf2, 0x49, 0x6a, 0x39, 0xa5, 0xe0, 0x17, 0x79, 0x4a, 0x63, 0x07, 0x62, 0x09, 0x61, 0x1b, 0x6e, 0xa9, 0xb5, 0x62, 0xb7, 0xde, 0xdf, 0x80, 0x4c, 0x5a, 0x99, 0x73, 0x59, 0x9d, 0xfb, 0xb1, 0x5e, 0xbe, 0xb8, 0xb7, 0x63, 0x93, 0xe8, 0xad, 0x5e, 0x1f, 0xae, 0x59, 0x1c, 0xcd, 0xb4, 0xc2, 0xb3, 0x8a, + /* (2^353)P */ 0x78, 0x53, 0xa1, 0x4c, 0x70, 0x9c, 0x63, 0x7e, 0xb3, 0x12, 0x40, 0x5f, 0xbb, 0x23, 0xa7, 0xf7, 0x77, 0x96, 0x5b, 0x4d, 0x91, 0x10, 0x52, 0x85, 0x9e, 0xa5, 0x38, 0x0b, 0xfd, 0x25, 0x01, 0x4b, 0xfa, 0x4d, 0xd3, 0x3f, 0x78, 0x74, 0x42, 0xff, 0x62, 0x2d, 0x27, 0xdc, 0x9d, 0xd1, 0x29, 0x76, 0x2e, 0x78, 0xb3, 0x35, 0xfa, 0x15, 0xd5, 0x38, + /* (2^354)P */ 0x8b, 0xc7, 0x43, 0xce, 0xf0, 0x5e, 0xf1, 0x0d, 0x02, 0x38, 0xe8, 0x82, 0xc9, 0x25, 0xad, 0x2d, 0x27, 0xa4, 0x54, 0x18, 0xb2, 0x30, 0x73, 0xa4, 0x41, 0x08, 0xe4, 0x86, 0xe6, 0x8c, 0xe9, 0x2a, 0x34, 0xb3, 0xd6, 0x61, 0x8f, 0x66, 0x26, 0x08, 0xb6, 0x06, 0x33, 0xaa, 0x12, 0xac, 0x72, 0xec, 0x2e, 0x52, 0xa3, 0x25, 0x3e, 0xd7, 0x62, 0xe8, + /* (2^355)P */ 0xc4, 0xbb, 0x89, 0xc8, 0x40, 0xcc, 0x84, 0xec, 0x4a, 0xd9, 0xc4, 0x55, 0x78, 0x00, 0xcf, 0xd8, 0xe9, 0x24, 0x59, 0xdc, 0x5e, 0xf0, 0x66, 0xa1, 0x83, 0xae, 0x97, 0x18, 0xc5, 0x54, 0x27, 0xa2, 0x21, 0x52, 0x03, 0x31, 0x5b, 0x11, 0x67, 0xf6, 0x12, 0x00, 0x87, 0x2f, 0xff, 0x59, 0x70, 0x8f, 0x6d, 0x71, 0xab, 0xab, 0x24, 0xb8, 0xba, 0x35, + /* (2^356)P */ 0x69, 0x43, 0xa7, 0x14, 0x06, 0x96, 0xe9, 0xc2, 0xe3, 0x2b, 0x45, 0x22, 0xc0, 0xd0, 0x2f, 0x34, 0xd1, 0x01, 0x99, 0xfc, 0x99, 0x38, 0xa1, 0x25, 0x2e, 0x59, 0x6c, 0x27, 0xc9, 0xeb, 0x7b, 0xdc, 0x4e, 0x26, 0x68, 0xba, 0xfa, 0xec, 0x02, 0x05, 0x64, 0x80, 0x30, 0x20, 0x5c, 0x26, 0x7f, 0xaf, 0x95, 0x17, 0x3d, 0x5c, 0x9e, 0x96, 0x96, 0xaf, + /* (2^357)P */ 0xa6, 0xba, 0x21, 0x29, 0x32, 0xe2, 0x98, 0xde, 0x9b, 0x6d, 0x0b, 0x44, 0x91, 0xa8, 0x3e, 0xd4, 0xb8, 0x04, 0x6c, 0xf6, 0x04, 0x39, 0xbd, 0x52, 0x05, 0x15, 0x27, 0x78, 0x8e, 0x55, 0xac, 0x79, 0xc5, 0xe6, 0x00, 0x7f, 0x90, 0xa2, 0xdd, 0x07, 0x13, 0xe0, 0x24, 0x70, 0x5c, 0x0f, 0x4d, 0xa9, 0xf9, 0xae, 0xcb, 0x34, 0x10, 0x9d, 0x89, 0x9d, + /* (2^358)P */ 0x12, 0xe0, 0xb3, 0x9f, 0xc4, 0x96, 0x1d, 0xcf, 0xed, 0x99, 0x64, 0x28, 0x8d, 0xc7, 0x31, 0x82, 0xee, 0x5e, 0x75, 0x48, 0xff, 0x3a, 0xf2, 0x09, 0x34, 0x03, 0x93, 0x52, 0x19, 0xb2, 0xc5, 0x81, 0x93, 0x45, 0x5e, 0x59, 0x21, 0x2b, 0xec, 0x89, 0xba, 0x36, 0x6e, 0xf9, 0x82, 0x75, 0x7e, 0x82, 0x3f, 0xaa, 0xe2, 0xe3, 0x3b, 0x94, 0xfd, 0x98, + /* (2^359)P */ 0x7c, 0xdb, 0x75, 0x31, 0x61, 0xfb, 0x15, 0x28, 0x94, 0xd7, 0xc3, 0x5a, 0xa9, 0xa1, 0x0a, 0x66, 0x0f, 0x2b, 0x13, 0x3e, 0x42, 0xb5, 0x28, 0x3a, 0xca, 0x83, 0xf3, 0x61, 0x22, 0xf4, 0x40, 0xc5, 0xdf, 0xe7, 0x31, 0x9f, 0x7e, 0x51, 0x75, 0x06, 0x9d, 0x51, 0xc8, 0xe7, 0x9f, 0xc3, 0x71, 0x4f, 0x3d, 0x5b, 0xfb, 0xe9, 0x8e, 0x08, 0x40, 0x8e, + /* (2^360)P */ 0xf7, 0x31, 0xad, 0x50, 0x5d, 0x25, 0x93, 0x73, 0x68, 0xf6, 0x7c, 0x89, 0x5a, 0x3d, 0x9f, 0x9b, 0x05, 0x82, 0xe7, 0x70, 0x4b, 0x19, 0xaa, 0xcf, 0xff, 0xde, 0x50, 0x8f, 0x2f, 0x69, 0xd3, 0xf0, 0x99, 0x51, 0x6b, 0x9d, 0xb6, 0x56, 0x6f, 0xf8, 0x4c, 0x74, 0x8b, 0x4c, 0x91, 0xf9, 0xa9, 0xb1, 0x3e, 0x07, 0xdf, 0x0b, 0x27, 0x8a, 0xb1, 0xed, + /* (2^361)P */ 0xfb, 0x67, 0xd9, 0x48, 0xd2, 0xe4, 0x44, 0x9b, 0x43, 0x15, 0x8a, 0xeb, 0x00, 0x53, 0xad, 0x25, 0xc7, 0x7e, 0x19, 0x30, 0x87, 0xb7, 0xd5, 0x5f, 0x04, 0xf8, 0xaa, 0xdd, 0x57, 0xae, 0x34, 0x75, 0xe2, 0x84, 0x4b, 0x54, 0x60, 0x37, 0x95, 0xe4, 0xd3, 0xec, 0xac, 0xef, 0x47, 0x31, 0xa3, 0xc8, 0x31, 0x22, 0xdb, 0x26, 0xe7, 0x6a, 0xb5, 0xad, + /* (2^362)P */ 0x44, 0x09, 0x5c, 0x95, 0xe4, 0x72, 0x3c, 0x1a, 0xd1, 0xac, 0x42, 0x51, 0x99, 0x6f, 0xfa, 0x1f, 0xf2, 0x22, 0xbe, 0xff, 0x7b, 0x66, 0xf5, 0x6c, 0xb3, 0x66, 0xc7, 0x4d, 0x78, 0x31, 0x83, 0x80, 0xf5, 0x41, 0xe9, 0x7f, 0xbe, 0xf7, 0x23, 0x49, 0x6b, 0x84, 0x4e, 0x7e, 0x47, 0x07, 0x6e, 0x74, 0xdf, 0xe5, 0x9d, 0x9e, 0x56, 0x2a, 0xc0, 0xbc, + /* (2^363)P */ 0xac, 0x10, 0x80, 0x8c, 0x7c, 0xfa, 0x83, 0xdf, 0xb3, 0xd0, 0xc4, 0xbe, 0xfb, 0x9f, 0xac, 0xc9, 0xc3, 0x40, 0x95, 0x0b, 0x09, 0x23, 0xda, 0x63, 0x67, 0xcf, 0xe7, 0x9f, 0x7d, 0x7b, 0x6b, 0xe2, 0xe6, 0x6d, 0xdb, 0x87, 0x9e, 0xa6, 0xff, 0x6d, 0xab, 0xbd, 0xfb, 0x54, 0x84, 0x68, 0xcf, 0x89, 0xf1, 0xd0, 0xe2, 0x85, 0x61, 0xdc, 0x22, 0xd1, + /* (2^364)P */ 0xa8, 0x48, 0xfb, 0x8c, 0x6a, 0x63, 0x01, 0x72, 0x43, 0x43, 0xeb, 0x21, 0xa3, 0x00, 0x8a, 0xc0, 0x87, 0x51, 0x9e, 0x86, 0x75, 0x16, 0x79, 0xf9, 0x6b, 0x11, 0x80, 0x62, 0xc2, 0x9d, 0xb8, 0x8c, 0x30, 0x8e, 0x8d, 0x03, 0x52, 0x7e, 0x31, 0x59, 0x38, 0xf9, 0x25, 0xc7, 0x0f, 0xc7, 0xa8, 0x2b, 0x5c, 0x80, 0xfa, 0x90, 0xa2, 0x63, 0xca, 0xe7, + /* (2^365)P */ 0xf1, 0x5d, 0xb5, 0xd9, 0x20, 0x10, 0x7d, 0x0f, 0xc5, 0x50, 0x46, 0x07, 0xff, 0x02, 0x75, 0x2b, 0x4a, 0xf3, 0x39, 0x91, 0x72, 0xb7, 0xd5, 0xcc, 0x38, 0xb8, 0xe7, 0x36, 0x26, 0x5e, 0x11, 0x97, 0x25, 0xfb, 0x49, 0x68, 0xdc, 0xb4, 0x46, 0x87, 0x5c, 0xc2, 0x7f, 0xaa, 0x7d, 0x36, 0x23, 0xa6, 0xc6, 0x53, 0xec, 0xbc, 0x57, 0x47, 0xc1, 0x2b, + /* (2^366)P */ 0x25, 0x5d, 0x7d, 0x95, 0xda, 0x0b, 0x8f, 0x78, 0x1e, 0x19, 0x09, 0xfa, 0x67, 0xe0, 0xa0, 0x17, 0x24, 0x76, 0x6c, 0x30, 0x1f, 0x62, 0x3d, 0xbe, 0x45, 0x70, 0xcc, 0xb6, 0x1e, 0x68, 0x06, 0x25, 0x68, 0x16, 0x1a, 0x33, 0x3f, 0x90, 0xc7, 0x78, 0x2d, 0x98, 0x3c, 0x2f, 0xb9, 0x2d, 0x94, 0x0b, 0xfb, 0x49, 0x56, 0x30, 0xd7, 0xc1, 0xe6, 0x48, + /* (2^367)P */ 0x7a, 0xd1, 0xe0, 0x8e, 0x67, 0xfc, 0x0b, 0x50, 0x1f, 0x84, 0x98, 0xfa, 0xaf, 0xae, 0x2e, 0x31, 0x27, 0xcf, 0x3f, 0xf2, 0x6e, 0x8d, 0x81, 0x8f, 0xd2, 0x5f, 0xde, 0xd3, 0x5e, 0xe9, 0xe7, 0x13, 0x48, 0x83, 0x5a, 0x4e, 0x84, 0xd1, 0x58, 0xcf, 0x6b, 0x84, 0xdf, 0x13, 0x1d, 0x91, 0x85, 0xe8, 0xcb, 0x29, 0x79, 0xd2, 0xca, 0xac, 0x6a, 0x93, + /* (2^368)P */ 0x53, 0x82, 0xce, 0x61, 0x96, 0x88, 0x6f, 0xe1, 0x4a, 0x4c, 0x1e, 0x30, 0x73, 0xe8, 0x74, 0xde, 0x40, 0x2b, 0xe0, 0xc4, 0xb5, 0xd8, 0x7c, 0x15, 0xe7, 0xe1, 0xb1, 0xe0, 0xd6, 0x88, 0xb1, 0x6a, 0x57, 0x19, 0x6a, 0x22, 0x66, 0x57, 0xf6, 0x8d, 0xfd, 0xc0, 0xf2, 0xa3, 0x03, 0x56, 0xfb, 0x2e, 0x75, 0x5e, 0xc7, 0x8e, 0x22, 0x96, 0x5c, 0x06, + /* (2^369)P */ 0x98, 0x7e, 0xbf, 0x3e, 0xbf, 0x24, 0x9d, 0x15, 0xd3, 0xf6, 0xd3, 0xd2, 0xf0, 0x11, 0xf2, 0xdb, 0x36, 0x23, 0x38, 0xf7, 0x1d, 0x71, 0x20, 0xd2, 0x54, 0x7f, 0x1e, 0x24, 0x8f, 0xe2, 0xaa, 0xf7, 0x3f, 0x6b, 0x41, 0x4e, 0xdc, 0x0e, 0xec, 0xe8, 0x35, 0x0a, 0x08, 0x6d, 0x89, 0x5b, 0x32, 0x91, 0x01, 0xb6, 0xe0, 0x2c, 0xc6, 0xa1, 0xbe, 0xb4, + /* (2^370)P */ 0x29, 0xf2, 0x1e, 0x1c, 0xdc, 0x68, 0x8a, 0x43, 0x87, 0x2c, 0x48, 0xb3, 0x9e, 0xed, 0xd2, 0x82, 0x46, 0xac, 0x2f, 0xef, 0x93, 0x34, 0x37, 0xca, 0x64, 0x8d, 0xc9, 0x06, 0x90, 0xbb, 0x78, 0x0a, 0x3c, 0x4c, 0xcf, 0x35, 0x7a, 0x0f, 0xf7, 0xa7, 0xf4, 0x2f, 0x45, 0x69, 0x3f, 0xa9, 0x5d, 0xce, 0x7b, 0x8a, 0x84, 0xc3, 0xae, 0xf4, 0xda, 0xd5, + /* (2^371)P */ 0xca, 0xba, 0x95, 0x43, 0x05, 0x7b, 0x06, 0xd9, 0x5c, 0x0a, 0x18, 0x5f, 0x6a, 0x6a, 0xce, 0xc0, 0x3d, 0x95, 0x51, 0x0e, 0x1a, 0xbe, 0x85, 0x7a, 0xf2, 0x69, 0xec, 0xc0, 0x8c, 0xca, 0xa3, 0x32, 0x0a, 0x76, 0x50, 0xc6, 0x76, 0x61, 0x00, 0x89, 0xbf, 0x6e, 0x0f, 0x48, 0x90, 0x31, 0x93, 0xec, 0x34, 0x70, 0xf0, 0xc3, 0x8d, 0xf0, 0x0f, 0xb5, + /* (2^372)P */ 0xbe, 0x23, 0xe2, 0x18, 0x99, 0xf1, 0xed, 0x8a, 0xf6, 0xc9, 0xac, 0xb8, 0x1e, 0x9a, 0x3c, 0x15, 0xae, 0xd7, 0x6d, 0xb3, 0x04, 0xee, 0x5b, 0x0d, 0x1e, 0x79, 0xb7, 0xf9, 0xf9, 0x8d, 0xad, 0xf9, 0x8f, 0x5a, 0x6a, 0x7b, 0xd7, 0x9b, 0xca, 0x62, 0xfe, 0x9c, 0xc0, 0x6f, 0x6d, 0x9d, 0x76, 0xa3, 0x69, 0xb9, 0x4c, 0xa1, 0xc4, 0x0c, 0x76, 0xaa, + /* (2^373)P */ 0x1c, 0x06, 0xfe, 0x3f, 0x45, 0x70, 0xcd, 0x97, 0xa9, 0xa2, 0xb1, 0xd3, 0xf2, 0xa5, 0x0c, 0x49, 0x2c, 0x75, 0x73, 0x1f, 0xcf, 0x00, 0xaf, 0xd5, 0x2e, 0xde, 0x0d, 0x8f, 0x8f, 0x7c, 0xc4, 0x58, 0xce, 0xd4, 0xf6, 0x24, 0x19, 0x2e, 0xd8, 0xc5, 0x1d, 0x1a, 0x3f, 0xb8, 0x4f, 0xbc, 0x7d, 0xbd, 0x68, 0xe3, 0x81, 0x98, 0x1b, 0xa8, 0xc9, 0xd9, + /* (2^374)P */ 0x39, 0x95, 0x78, 0x24, 0x6c, 0x38, 0xe4, 0xe7, 0xd0, 0x8d, 0xb9, 0x38, 0x71, 0x5e, 0xc1, 0x62, 0x80, 0xcc, 0xcb, 0x8c, 0x97, 0xca, 0xf8, 0xb9, 0xd9, 0x9c, 0xce, 0x72, 0x7b, 0x70, 0xee, 0x5f, 0xea, 0xa2, 0xdf, 0xa9, 0x14, 0x10, 0xf9, 0x6e, 0x59, 0x9f, 0x9c, 0xe0, 0x0c, 0xb2, 0x07, 0x97, 0xcd, 0xd2, 0x89, 0x16, 0xfd, 0x9c, 0xa8, 0xa5, + /* (2^375)P */ 0x5a, 0x61, 0xf1, 0x59, 0x7c, 0x38, 0xda, 0xe2, 0x85, 0x99, 0x68, 0xe9, 0xc9, 0xf7, 0x32, 0x7e, 0xc4, 0xca, 0xb7, 0x11, 0x08, 0x69, 0x2b, 0x66, 0x02, 0xf7, 0x2e, 0x18, 0xc3, 0x8e, 0xe1, 0xf9, 0xc5, 0x19, 0x9a, 0x0a, 0x9c, 0x07, 0xba, 0xc7, 0x9c, 0x03, 0x34, 0x89, 0x99, 0x67, 0x0b, 0x16, 0x4b, 0x07, 0x36, 0x16, 0x36, 0x2c, 0xe2, 0xa1, + /* (2^376)P */ 0x70, 0x10, 0x91, 0x27, 0xa8, 0x24, 0x8e, 0x29, 0x04, 0x6f, 0x79, 0x1f, 0xd3, 0xa5, 0x68, 0xd3, 0x0b, 0x7d, 0x56, 0x4d, 0x14, 0x57, 0x7b, 0x2e, 0x00, 0x9f, 0x9a, 0xfd, 0x6c, 0x63, 0x18, 0x81, 0xdb, 0x9d, 0xb7, 0xd7, 0xa4, 0x1e, 0xe8, 0x40, 0xf1, 0x4c, 0xa3, 0x01, 0xd5, 0x4b, 0x75, 0xea, 0xdd, 0x97, 0xfd, 0x5b, 0xb2, 0x66, 0x6a, 0x24, + /* (2^377)P */ 0x72, 0x11, 0xfe, 0x73, 0x1b, 0xd3, 0xea, 0x7f, 0x93, 0x15, 0x15, 0x05, 0xfe, 0x40, 0xe8, 0x28, 0xd8, 0x50, 0x47, 0x66, 0xfa, 0xb7, 0xb5, 0x04, 0xba, 0x35, 0x1e, 0x32, 0x9f, 0x5f, 0x32, 0xba, 0x3d, 0xd1, 0xed, 0x9a, 0x76, 0xca, 0xa3, 0x3e, 0x77, 0xd8, 0xd8, 0x7c, 0x5f, 0x68, 0x42, 0xb5, 0x86, 0x7f, 0x3b, 0xc9, 0xc1, 0x89, 0x64, 0xda, + /* (2^378)P */ 0xd5, 0xd4, 0x17, 0x31, 0xfc, 0x6a, 0xfd, 0xb8, 0xe8, 0xe5, 0x3e, 0x39, 0x06, 0xe4, 0xd1, 0x90, 0x2a, 0xca, 0xf6, 0x54, 0x6c, 0x1b, 0x2f, 0x49, 0x97, 0xb1, 0x2a, 0x82, 0x43, 0x3d, 0x1f, 0x8b, 0xe2, 0x47, 0xc5, 0x24, 0xa8, 0xd5, 0x53, 0x29, 0x7d, 0xc6, 0x87, 0xa6, 0x25, 0x3a, 0x64, 0xdd, 0x71, 0x08, 0x9e, 0xcd, 0xe9, 0x45, 0xc7, 0xba, + /* (2^379)P */ 0x37, 0x72, 0x6d, 0x13, 0x7a, 0x8d, 0x04, 0x31, 0xe6, 0xe3, 0x9e, 0x36, 0x71, 0x3e, 0xc0, 0x1e, 0xe3, 0x71, 0xd3, 0x49, 0x4e, 0x4a, 0x36, 0x42, 0x68, 0x68, 0x61, 0xc7, 0x3c, 0xdb, 0x81, 0x49, 0xf7, 0x91, 0x4d, 0xea, 0x4c, 0x4f, 0x98, 0xc6, 0x7e, 0x60, 0x84, 0x4b, 0x6a, 0x37, 0xbb, 0x52, 0xf7, 0xce, 0x02, 0xe4, 0xad, 0xd1, 0x3c, 0xa7, + /* (2^380)P */ 0x51, 0x06, 0x2d, 0xf8, 0x08, 0xe8, 0xf1, 0x0c, 0xe5, 0xa9, 0xac, 0x29, 0x73, 0x3b, 0xed, 0x98, 0x5f, 0x55, 0x08, 0x38, 0x51, 0x44, 0x36, 0x5d, 0xea, 0xc3, 0xb8, 0x0e, 0xa0, 0x4f, 0xd2, 0x79, 0xe9, 0x98, 0xc3, 0xf5, 0x00, 0xb9, 0x26, 0x27, 0x42, 0xa8, 0x07, 0xc1, 0x12, 0x31, 0xc1, 0xc3, 0x3c, 0x3b, 0x7a, 0x72, 0x97, 0xc2, 0x70, 0x3a, + /* (2^381)P */ 0xf4, 0xb2, 0xba, 0x32, 0xbc, 0xa9, 0x2f, 0x87, 0xc7, 0x3c, 0x45, 0xcd, 0xae, 0xe2, 0x13, 0x6d, 0x3a, 0xf2, 0xf5, 0x66, 0x97, 0x29, 0xaf, 0x53, 0x9f, 0xda, 0xea, 0x14, 0xdf, 0x04, 0x98, 0x19, 0x95, 0x9e, 0x2a, 0x00, 0x5c, 0x9d, 0x1d, 0xf0, 0x39, 0x23, 0xff, 0xfc, 0xca, 0x36, 0xb7, 0xde, 0xdf, 0x37, 0x78, 0x52, 0x21, 0xfa, 0x19, 0x10, + /* (2^382)P */ 0x50, 0x20, 0x73, 0x74, 0x62, 0x21, 0xf2, 0xf7, 0x9b, 0x66, 0x85, 0x34, 0x74, 0xd4, 0x9d, 0x60, 0xd7, 0xbc, 0xc8, 0x46, 0x3b, 0xb8, 0x80, 0x42, 0x15, 0x0a, 0x6c, 0x35, 0x1a, 0x69, 0xf0, 0x1d, 0x4b, 0x29, 0x54, 0x5a, 0x9a, 0x48, 0xec, 0x9f, 0x37, 0x74, 0x91, 0xd0, 0xd1, 0x9e, 0x00, 0xc2, 0x76, 0x56, 0xd6, 0xa0, 0x15, 0x14, 0x83, 0x59, + /* (2^383)P */ 0xc2, 0xf8, 0x22, 0x20, 0x23, 0x07, 0xbd, 0x1d, 0x6f, 0x1e, 0x8c, 0x56, 0x06, 0x6a, 0x4b, 0x9f, 0xe2, 0xa9, 0x92, 0x46, 0x4b, 0x46, 0x59, 0xd7, 0xe1, 0xda, 0x14, 0x98, 0x07, 0x65, 0x7e, 0x28, 0x20, 0xf2, 0x9d, 0x4f, 0x36, 0x5c, 0x92, 0xe0, 0x9d, 0xfe, 0x3e, 0xda, 0xe4, 0x47, 0x19, 0x3c, 0x00, 0x7f, 0x22, 0xf2, 0x9e, 0x51, 0xae, 0x4d, + /* (2^384)P */ 0xbe, 0x8c, 0x1b, 0x10, 0xb6, 0xad, 0xcc, 0xcc, 0xd8, 0x5e, 0x21, 0xa6, 0xfb, 0xf1, 0xf6, 0xbd, 0x0a, 0x24, 0x67, 0xb4, 0x57, 0x7a, 0xbc, 0xe8, 0xe9, 0xff, 0xee, 0x0a, 0x1f, 0xee, 0xbd, 0xc8, 0x44, 0xed, 0x2b, 0xbb, 0x55, 0x1f, 0xdd, 0x7c, 0xb3, 0xeb, 0x3f, 0x63, 0xa1, 0x28, 0x91, 0x21, 0xab, 0x71, 0xc6, 0x4c, 0xd0, 0xe9, 0xb0, 0x21, + /* (2^385)P */ 0xad, 0xc9, 0x77, 0x2b, 0xee, 0x89, 0xa4, 0x7b, 0xfd, 0xf9, 0xf6, 0x14, 0xe4, 0xed, 0x1a, 0x16, 0x9b, 0x78, 0x41, 0x43, 0xa8, 0x83, 0x72, 0x06, 0x2e, 0x7c, 0xdf, 0xeb, 0x7e, 0xdd, 0xd7, 0x8b, 0xea, 0x9a, 0x2b, 0x03, 0xba, 0x57, 0xf3, 0xf1, 0xd9, 0xe5, 0x09, 0xc5, 0x98, 0x61, 0x1c, 0x51, 0x6d, 0x5d, 0x6e, 0xfb, 0x5e, 0x95, 0x9f, 0xb5, + /* (2^386)P */ 0x23, 0xe2, 0x1e, 0x95, 0xa3, 0x5e, 0x42, 0x10, 0xc7, 0xc3, 0x70, 0xbf, 0x4b, 0x6b, 0x83, 0x36, 0x93, 0xb7, 0x68, 0x47, 0x88, 0x3a, 0x10, 0x88, 0x48, 0x7f, 0x8c, 0xae, 0x54, 0x10, 0x02, 0xa4, 0x52, 0x8f, 0x8d, 0xf7, 0x26, 0x4f, 0x50, 0xc3, 0x6a, 0xe2, 0x4e, 0x3b, 0x4c, 0xb9, 0x8a, 0x14, 0x15, 0x6d, 0x21, 0x29, 0xb3, 0x6e, 0x4e, 0xd0, + /* (2^387)P */ 0x4c, 0x8a, 0x18, 0x3f, 0xb7, 0x20, 0xfd, 0x3e, 0x54, 0xca, 0x68, 0x3c, 0xea, 0x6f, 0xf4, 0x6b, 0xa2, 0xbd, 0x01, 0xbd, 0xfe, 0x08, 0xa8, 0xd8, 0xc2, 0x20, 0x36, 0x05, 0xcd, 0xe9, 0xf3, 0x9e, 0xfa, 0x85, 0x66, 0x8f, 0x4b, 0x1d, 0x8c, 0x64, 0x4f, 0xb8, 0xc6, 0x0f, 0x5b, 0x57, 0xd8, 0x24, 0x19, 0x5a, 0x14, 0x4b, 0x92, 0xd3, 0x96, 0xbc, + /* (2^388)P */ 0xa9, 0x3f, 0xc9, 0x6c, 0xca, 0x64, 0x1e, 0x6f, 0xdf, 0x65, 0x7f, 0x9a, 0x47, 0x6b, 0x8a, 0x60, 0x31, 0xa6, 0x06, 0xac, 0x69, 0x30, 0xe6, 0xea, 0x63, 0x42, 0x26, 0x5f, 0xdb, 0xd0, 0xf2, 0x8e, 0x34, 0x0a, 0x3a, 0xeb, 0xf3, 0x79, 0xc8, 0xb7, 0x60, 0x56, 0x5c, 0x37, 0x95, 0x71, 0xf8, 0x7f, 0x49, 0x3e, 0x9e, 0x01, 0x26, 0x1e, 0x80, 0x9f, + /* (2^389)P */ 0xf8, 0x16, 0x9a, 0xaa, 0xb0, 0x28, 0xb5, 0x8e, 0xd0, 0x60, 0xe5, 0x26, 0xa9, 0x47, 0xc4, 0x5c, 0xa9, 0x39, 0xfe, 0x0a, 0xd8, 0x07, 0x2b, 0xb3, 0xce, 0xf1, 0xea, 0x1a, 0xf4, 0x7b, 0x98, 0x31, 0x3d, 0x13, 0x29, 0x80, 0xe8, 0x0d, 0xcf, 0x56, 0x39, 0x86, 0x50, 0x0c, 0xb3, 0x18, 0xf4, 0xc5, 0xca, 0xf2, 0x6f, 0xcd, 0x8d, 0xd5, 0x02, 0xb0, + /* (2^390)P */ 0xbf, 0x39, 0x3f, 0xac, 0x6d, 0x1a, 0x6a, 0xe4, 0x42, 0x24, 0xd6, 0x41, 0x9d, 0xb9, 0x5b, 0x46, 0x73, 0x93, 0x76, 0xaa, 0xb7, 0x37, 0x36, 0xa6, 0x09, 0xe5, 0x04, 0x3b, 0x66, 0xc4, 0x29, 0x3e, 0x41, 0xc2, 0xcb, 0xe5, 0x17, 0xd7, 0x34, 0x67, 0x1d, 0x2c, 0x12, 0xec, 0x24, 0x7a, 0x40, 0xa2, 0x45, 0x41, 0xf0, 0x75, 0xed, 0x43, 0x30, 0xc9, + /* (2^391)P */ 0x80, 0xf6, 0x47, 0x5b, 0xad, 0x54, 0x02, 0xbc, 0xdd, 0xa4, 0xb2, 0xd7, 0x42, 0x95, 0xf2, 0x0d, 0x1b, 0xef, 0x37, 0xa7, 0xb4, 0x34, 0x04, 0x08, 0x71, 0x1b, 0xd3, 0xdf, 0xa1, 0xf0, 0x2b, 0xfa, 0xc0, 0x1f, 0xf3, 0x44, 0xb5, 0xc6, 0x47, 0x3d, 0x65, 0x67, 0x45, 0x4d, 0x2f, 0xde, 0x52, 0x73, 0xfc, 0x30, 0x01, 0x6b, 0xc1, 0x03, 0xd8, 0xd7, + /* (2^392)P */ 0x1c, 0x67, 0x55, 0x3e, 0x01, 0x17, 0x0f, 0x3e, 0xe5, 0x34, 0x58, 0xfc, 0xcb, 0x71, 0x24, 0x74, 0x5d, 0x36, 0x1e, 0x89, 0x2a, 0x63, 0xf8, 0xf8, 0x9f, 0x50, 0x9f, 0x32, 0x92, 0x29, 0xd8, 0x1a, 0xec, 0x76, 0x57, 0x6c, 0x67, 0x12, 0x6a, 0x6e, 0xef, 0x97, 0x1f, 0xc3, 0x77, 0x60, 0x3c, 0x22, 0xcb, 0xc7, 0x04, 0x1a, 0x89, 0x2d, 0x10, 0xa6, + /* (2^393)P */ 0x12, 0xf5, 0xa9, 0x26, 0x16, 0xd9, 0x3c, 0x65, 0x5d, 0x83, 0xab, 0xd1, 0x70, 0x6b, 0x1c, 0xdb, 0xe7, 0x86, 0x0d, 0xfb, 0xe7, 0xf8, 0x2a, 0x58, 0x6e, 0x7a, 0x66, 0x13, 0x53, 0x3a, 0x6f, 0x8d, 0x43, 0x5f, 0x14, 0x23, 0x14, 0xff, 0x3d, 0x52, 0x7f, 0xee, 0xbd, 0x7a, 0x34, 0x8b, 0x35, 0x24, 0xc3, 0x7a, 0xdb, 0xcf, 0x22, 0x74, 0x9a, 0x8f, + /* (2^394)P */ 0xdb, 0x20, 0xfc, 0xe5, 0x39, 0x4e, 0x7d, 0x78, 0xee, 0x0b, 0xbf, 0x1d, 0x80, 0xd4, 0x05, 0x4f, 0xb9, 0xd7, 0x4e, 0x94, 0x88, 0x9a, 0x50, 0x78, 0x1a, 0x70, 0x8c, 0xcc, 0x25, 0xb6, 0x61, 0x09, 0xdc, 0x7b, 0xea, 0x3f, 0x7f, 0xea, 0x2a, 0x0d, 0x47, 0x1c, 0x8e, 0xa6, 0x5b, 0xd2, 0xa3, 0x61, 0x93, 0x3c, 0x68, 0x9f, 0x8b, 0xea, 0xb0, 0xcb, + /* (2^395)P */ 0xff, 0x54, 0x02, 0x19, 0xae, 0x8b, 0x4c, 0x2c, 0x3a, 0xe0, 0xe4, 0xac, 0x87, 0xf7, 0x51, 0x45, 0x41, 0x43, 0xdc, 0xaa, 0xcd, 0xcb, 0xdc, 0x40, 0xe3, 0x44, 0x3b, 0x1d, 0x9e, 0x3d, 0xb9, 0x82, 0xcc, 0x7a, 0xc5, 0x12, 0xf8, 0x1e, 0xdd, 0xdb, 0x8d, 0xb0, 0x2a, 0xe8, 0xe6, 0x6c, 0x94, 0x3b, 0xb7, 0x2d, 0xba, 0x79, 0x3b, 0xb5, 0x86, 0xfb, + /* (2^396)P */ 0x82, 0x88, 0x13, 0xdd, 0x6c, 0xcd, 0x85, 0x2b, 0x90, 0x86, 0xb7, 0xac, 0x16, 0xa6, 0x6e, 0x6a, 0x94, 0xd8, 0x1e, 0x4e, 0x41, 0x0f, 0xce, 0x81, 0x6a, 0xa8, 0x26, 0x56, 0x43, 0x52, 0x52, 0xe6, 0xff, 0x88, 0xcf, 0x47, 0x05, 0x1d, 0xff, 0xf3, 0xa0, 0x10, 0xb2, 0x97, 0x87, 0xeb, 0x47, 0xbb, 0xfa, 0x1f, 0xe8, 0x4c, 0xce, 0xc4, 0xcd, 0x93, + /* (2^397)P */ 0xf4, 0x11, 0xf5, 0x8d, 0x89, 0x29, 0x79, 0xb3, 0x59, 0x0b, 0x29, 0x7d, 0x9c, 0x12, 0x4a, 0x65, 0x72, 0x3a, 0xf9, 0xec, 0x37, 0x18, 0x86, 0xef, 0x44, 0x07, 0x25, 0x74, 0x76, 0x53, 0xed, 0x51, 0x01, 0xc6, 0x28, 0xc5, 0xc3, 0x4a, 0x0f, 0x99, 0xec, 0xc8, 0x40, 0x5a, 0x83, 0x30, 0x79, 0xa2, 0x3e, 0x63, 0x09, 0x2d, 0x6f, 0x23, 0x54, 0x1c, + /* (2^398)P */ 0x5c, 0x6f, 0x3b, 0x1c, 0x30, 0x77, 0x7e, 0x87, 0x66, 0x83, 0x2e, 0x7e, 0x85, 0x50, 0xfd, 0xa0, 0x7a, 0xc2, 0xf5, 0x0f, 0xc1, 0x64, 0xe7, 0x0b, 0xbd, 0x59, 0xa7, 0xe7, 0x65, 0x53, 0xc3, 0xf5, 0x55, 0x5b, 0xe1, 0x82, 0x30, 0x5a, 0x61, 0xcd, 0xa0, 0x89, 0x32, 0xdb, 0x87, 0xfc, 0x21, 0x8a, 0xab, 0x6d, 0x82, 0xa8, 0x42, 0x81, 0x4f, 0xf2, + /* (2^399)P */ 0xb3, 0xeb, 0x88, 0x18, 0xf6, 0x56, 0x96, 0xbf, 0xba, 0x5d, 0x71, 0xa1, 0x5a, 0xd1, 0x04, 0x7b, 0xd5, 0x46, 0x01, 0x74, 0xfe, 0x15, 0x25, 0xb7, 0xff, 0x0c, 0x24, 0x47, 0xac, 0xfd, 0xab, 0x47, 0x32, 0xe1, 0x6a, 0x4e, 0xca, 0xcf, 0x7f, 0xdd, 0xf8, 0xd2, 0x4b, 0x3b, 0xf5, 0x17, 0xba, 0xba, 0x8b, 0xa1, 0xec, 0x28, 0x3f, 0x97, 0xab, 0x2a, + /* (2^400)P */ 0x51, 0x38, 0xc9, 0x5e, 0xc6, 0xb3, 0x64, 0xf2, 0x24, 0x4d, 0x04, 0x7d, 0xc8, 0x39, 0x0c, 0x4a, 0xc9, 0x73, 0x74, 0x1b, 0x5c, 0xb2, 0xc5, 0x41, 0x62, 0xa0, 0x4c, 0x6d, 0x8d, 0x91, 0x9a, 0x7b, 0x88, 0xab, 0x9c, 0x7e, 0x23, 0xdb, 0x6f, 0xb5, 0x72, 0xd6, 0x47, 0x40, 0xef, 0x22, 0x58, 0x62, 0x19, 0x6c, 0x38, 0xba, 0x5b, 0x00, 0x30, 0x9f, + /* (2^401)P */ 0x65, 0xbb, 0x3b, 0x9b, 0xe9, 0xae, 0xbf, 0xbe, 0xe4, 0x13, 0x95, 0xf3, 0xe3, 0x77, 0xcb, 0xe4, 0x9a, 0x22, 0xb5, 0x4a, 0x08, 0x9d, 0xb3, 0x9e, 0x27, 0xe0, 0x15, 0x6c, 0x9f, 0x7e, 0x9a, 0x5e, 0x15, 0x45, 0x25, 0x8d, 0x01, 0x0a, 0xd2, 0x2b, 0xbd, 0x48, 0x06, 0x0d, 0x18, 0x97, 0x4b, 0xdc, 0xbc, 0xf0, 0xcd, 0xb2, 0x52, 0x3c, 0xac, 0xf5, + /* (2^402)P */ 0x3e, 0xed, 0x47, 0x6b, 0x5c, 0xf6, 0x76, 0xd0, 0xe9, 0x15, 0xa3, 0xcb, 0x36, 0x00, 0x21, 0xa3, 0x79, 0x20, 0xa5, 0x3e, 0x88, 0x03, 0xcb, 0x7e, 0x63, 0xbb, 0xed, 0xa9, 0x13, 0x35, 0x16, 0xaf, 0x2e, 0xb4, 0x70, 0x14, 0x93, 0xfb, 0xc4, 0x9b, 0xd8, 0xb1, 0xbe, 0x43, 0xd1, 0x85, 0xb8, 0x97, 0xef, 0xea, 0x88, 0xa1, 0x25, 0x52, 0x62, 0x75, + /* (2^403)P */ 0x8e, 0x4f, 0xaa, 0x23, 0x62, 0x7e, 0x2b, 0x37, 0x89, 0x00, 0x11, 0x30, 0xc5, 0x33, 0x4a, 0x89, 0x8a, 0xe2, 0xfc, 0x5c, 0x6a, 0x75, 0xe5, 0xf7, 0x02, 0x4a, 0x9b, 0xf7, 0xb5, 0x6a, 0x85, 0x31, 0xd3, 0x5a, 0xcf, 0xc3, 0xf8, 0xde, 0x2f, 0xcf, 0xb5, 0x24, 0xf4, 0xe3, 0xa1, 0xad, 0x42, 0xae, 0x09, 0xb9, 0x2e, 0x04, 0x2d, 0x01, 0x22, 0x3f, + /* (2^404)P */ 0x41, 0x16, 0xfb, 0x7d, 0x50, 0xfd, 0xb5, 0xba, 0x88, 0x24, 0xba, 0xfd, 0x3d, 0xb2, 0x90, 0x15, 0xb7, 0xfa, 0xa2, 0xe1, 0x4c, 0x7d, 0xb9, 0xc6, 0xff, 0x81, 0x57, 0xb6, 0xc2, 0x9e, 0xcb, 0xc4, 0x35, 0xbd, 0x01, 0xb7, 0xaa, 0xce, 0xd0, 0xe9, 0xb5, 0xd6, 0x72, 0xbf, 0xd2, 0xee, 0xc7, 0xac, 0x94, 0xff, 0x29, 0x57, 0x02, 0x49, 0x09, 0xad, + /* (2^405)P */ 0x27, 0xa5, 0x78, 0x1b, 0xbf, 0x6b, 0xaf, 0x0b, 0x8c, 0xd9, 0xa8, 0x37, 0xb0, 0x67, 0x18, 0xb6, 0xc7, 0x05, 0x8a, 0x67, 0x03, 0x30, 0x62, 0x6e, 0x56, 0x82, 0xa9, 0x54, 0x3e, 0x0c, 0x4e, 0x07, 0xe1, 0x5a, 0x38, 0xed, 0xfa, 0xc8, 0x55, 0x6b, 0x08, 0xa3, 0x6b, 0x64, 0x2a, 0x15, 0xd6, 0x39, 0x6f, 0x47, 0x99, 0x42, 0x3f, 0x33, 0x84, 0x8f, + /* (2^406)P */ 0xbc, 0x45, 0x29, 0x81, 0x0e, 0xa4, 0xc5, 0x72, 0x3a, 0x10, 0xe1, 0xc4, 0x1e, 0xda, 0xc3, 0xfe, 0xb0, 0xce, 0xd2, 0x13, 0x34, 0x67, 0x21, 0xc6, 0x7e, 0xf9, 0x8c, 0xff, 0x39, 0x50, 0xae, 0x92, 0x60, 0x35, 0x2f, 0x8b, 0x6e, 0xc9, 0xc1, 0x27, 0x3a, 0x94, 0x66, 0x3e, 0x26, 0x84, 0x93, 0xc8, 0x6c, 0xcf, 0xd2, 0x03, 0xa1, 0x10, 0xcf, 0xb7, + /* (2^407)P */ 0x64, 0xda, 0x19, 0xf6, 0xc5, 0x73, 0x17, 0x44, 0x88, 0x81, 0x07, 0x0d, 0x34, 0xb2, 0x75, 0xf9, 0xd9, 0xe2, 0xe0, 0x8b, 0x71, 0xcf, 0x72, 0x34, 0x83, 0xb4, 0xce, 0xfc, 0xd7, 0x29, 0x09, 0x5a, 0x98, 0xbf, 0x14, 0xac, 0x77, 0x55, 0x38, 0x47, 0x5b, 0x0f, 0x40, 0x24, 0xe5, 0xa5, 0xa6, 0xac, 0x2d, 0xa6, 0xff, 0x9c, 0x73, 0xfe, 0x5c, 0x7e, + /* (2^408)P */ 0x1e, 0x33, 0xcc, 0x68, 0xb2, 0xbc, 0x8c, 0x93, 0xaf, 0xcc, 0x38, 0xf8, 0xd9, 0x16, 0x72, 0x50, 0xac, 0xd9, 0xb5, 0x0b, 0x9a, 0xbe, 0x46, 0x7a, 0xf1, 0xee, 0xf1, 0xad, 0xec, 0x5b, 0x59, 0x27, 0x9c, 0x05, 0xa3, 0x87, 0xe0, 0x37, 0x2c, 0x83, 0xce, 0xb3, 0x65, 0x09, 0x8e, 0xc3, 0x9c, 0xbf, 0x6a, 0xa2, 0x00, 0xcc, 0x12, 0x36, 0xc5, 0x95, + /* (2^409)P */ 0x36, 0x11, 0x02, 0x14, 0x9c, 0x3c, 0xeb, 0x2f, 0x23, 0x5b, 0x6b, 0x2b, 0x08, 0x54, 0x53, 0xac, 0xb2, 0xa3, 0xe0, 0x26, 0x62, 0x3c, 0xe4, 0xe1, 0x81, 0xee, 0x13, 0x3e, 0xa4, 0x97, 0xef, 0xf9, 0x92, 0x27, 0x01, 0xce, 0x54, 0x8b, 0x3e, 0x31, 0xbe, 0xa7, 0x88, 0xcf, 0x47, 0x99, 0x3c, 0x10, 0x6f, 0x60, 0xb3, 0x06, 0x4e, 0xee, 0x1b, 0xf0, + /* (2^410)P */ 0x59, 0x49, 0x66, 0xcf, 0x22, 0xe6, 0xf6, 0x73, 0xfe, 0xa3, 0x1c, 0x09, 0xfa, 0x5f, 0x65, 0xa8, 0xf0, 0x82, 0xc2, 0xef, 0x16, 0x63, 0x6e, 0x79, 0x69, 0x51, 0x39, 0x07, 0x65, 0xc4, 0x81, 0xec, 0x73, 0x0f, 0x15, 0x93, 0xe1, 0x30, 0x33, 0xe9, 0x37, 0x86, 0x42, 0x4c, 0x1f, 0x9b, 0xad, 0xee, 0x3f, 0xf1, 0x2a, 0x8e, 0x6a, 0xa3, 0xc8, 0x35, + /* (2^411)P */ 0x1e, 0x49, 0xf1, 0xdd, 0xd2, 0x9c, 0x8e, 0x78, 0xb2, 0x06, 0xe4, 0x6a, 0xab, 0x3a, 0xdc, 0xcd, 0xf4, 0xeb, 0xe1, 0xe7, 0x2f, 0xaa, 0xeb, 0x40, 0x31, 0x9f, 0xb9, 0xab, 0x13, 0xa9, 0x78, 0xbf, 0x38, 0x89, 0x0e, 0x85, 0x14, 0x8b, 0x46, 0x76, 0x14, 0xda, 0xcf, 0x33, 0xc8, 0x79, 0xd3, 0xd5, 0xa3, 0x6a, 0x69, 0x45, 0x70, 0x34, 0xc3, 0xe9, + /* (2^412)P */ 0x5e, 0xe7, 0x78, 0xe9, 0x24, 0xcc, 0xe9, 0xf4, 0xc8, 0x6b, 0xe0, 0xfb, 0x3a, 0xbe, 0xcc, 0x42, 0x4a, 0x00, 0x22, 0xf8, 0xe6, 0x32, 0xbe, 0x6d, 0x18, 0x55, 0x60, 0xe9, 0x72, 0x69, 0x50, 0x56, 0xca, 0x04, 0x18, 0x38, 0xa1, 0xee, 0xd8, 0x38, 0x3c, 0xa7, 0x70, 0xe2, 0xb9, 0x4c, 0xa0, 0xc8, 0x89, 0x72, 0xcf, 0x49, 0x7f, 0xdf, 0xbc, 0x67, + /* (2^413)P */ 0x1d, 0x17, 0xcb, 0x0b, 0xbd, 0xb2, 0x36, 0xe3, 0xa8, 0x99, 0x31, 0xb6, 0x26, 0x9c, 0x0c, 0x74, 0xaf, 0x4d, 0x24, 0x61, 0xcf, 0x31, 0x7b, 0xed, 0xdd, 0xc3, 0xf6, 0x32, 0x70, 0xfe, 0x17, 0xf6, 0x51, 0x37, 0x65, 0xce, 0x5d, 0xaf, 0xa5, 0x2f, 0x2a, 0xfe, 0x00, 0x71, 0x7c, 0x50, 0xbe, 0x21, 0xc7, 0xed, 0xc6, 0xfc, 0x67, 0xcf, 0x9c, 0xdd, + /* (2^414)P */ 0x26, 0x3e, 0xf8, 0xbb, 0xd0, 0xb1, 0x01, 0xd8, 0xeb, 0x0b, 0x62, 0x87, 0x35, 0x4c, 0xde, 0xca, 0x99, 0x9c, 0x6d, 0xf7, 0xb6, 0xf0, 0x57, 0x0a, 0x52, 0x29, 0x6a, 0x3f, 0x26, 0x31, 0x04, 0x07, 0x2a, 0xc9, 0xfa, 0x9b, 0x0e, 0x62, 0x8e, 0x72, 0xf2, 0xad, 0xce, 0xb6, 0x35, 0x7a, 0xc1, 0xae, 0x35, 0xc7, 0xa3, 0x14, 0xcf, 0x0c, 0x28, 0xb7, + /* (2^415)P */ 0xa6, 0xf1, 0x32, 0x3a, 0x20, 0xd2, 0x24, 0x97, 0xcf, 0x5d, 0x37, 0x99, 0xaf, 0x33, 0x7a, 0x5b, 0x7a, 0xcc, 0x4e, 0x41, 0x38, 0xb1, 0x4e, 0xad, 0xc9, 0xd9, 0x71, 0x7e, 0xb2, 0xf5, 0xd5, 0x01, 0x6c, 0x4d, 0xfd, 0xa1, 0xda, 0x03, 0x38, 0x9b, 0x3d, 0x92, 0x92, 0xf2, 0xca, 0xbf, 0x1f, 0x24, 0xa4, 0xbb, 0x30, 0x6a, 0x74, 0x56, 0xc8, 0xce, + /* (2^416)P */ 0x27, 0xf4, 0xed, 0xc9, 0xc3, 0xb1, 0x79, 0x85, 0xbe, 0xf6, 0xeb, 0xf3, 0x55, 0xc7, 0xaa, 0xa6, 0xe9, 0x07, 0x5d, 0xf4, 0xeb, 0xa6, 0x81, 0xe3, 0x0e, 0xcf, 0xa3, 0xc1, 0xef, 0xe7, 0x34, 0xb2, 0x03, 0x73, 0x8a, 0x91, 0xf1, 0xad, 0x05, 0xc7, 0x0b, 0x43, 0x99, 0x12, 0x31, 0xc8, 0xc7, 0xc5, 0xa4, 0x3d, 0xcd, 0xe5, 0x4e, 0x6d, 0x24, 0xdd, + /* (2^417)P */ 0x61, 0x54, 0xd0, 0x95, 0x2c, 0x45, 0x75, 0xac, 0xb5, 0x1a, 0x9d, 0x11, 0xeb, 0xed, 0x6b, 0x57, 0xa3, 0xe6, 0xcd, 0x77, 0xd4, 0x83, 0x8e, 0x39, 0xf1, 0x0f, 0x98, 0xcb, 0x40, 0x02, 0x6e, 0x10, 0x82, 0x9e, 0xb4, 0x93, 0x76, 0xd7, 0x97, 0xa3, 0x53, 0x12, 0x86, 0xc6, 0x15, 0x78, 0x73, 0x93, 0xe7, 0x7f, 0xcf, 0x1f, 0xbf, 0xcd, 0xd2, 0x7a, + /* (2^418)P */ 0xc2, 0x21, 0xdc, 0xd5, 0x69, 0xff, 0xca, 0x49, 0x3a, 0xe1, 0xc3, 0x69, 0x41, 0x56, 0xc1, 0x76, 0x63, 0x24, 0xbd, 0x64, 0x1b, 0x3d, 0x92, 0xf9, 0x13, 0x04, 0x25, 0xeb, 0x27, 0xa6, 0xef, 0x39, 0x3a, 0x80, 0xe0, 0xf8, 0x27, 0xee, 0xc9, 0x49, 0x77, 0xef, 0x3f, 0x29, 0x3d, 0x5e, 0xe6, 0x66, 0x83, 0xd1, 0xf6, 0xfe, 0x9d, 0xbc, 0xf1, 0x96, + /* (2^419)P */ 0x6b, 0xc6, 0x99, 0x26, 0x3c, 0xf3, 0x63, 0xf9, 0xc7, 0x29, 0x8c, 0x52, 0x62, 0x2d, 0xdc, 0x8a, 0x66, 0xce, 0x2c, 0xa7, 0xe4, 0xf0, 0xd7, 0x37, 0x17, 0x1e, 0xe4, 0xa3, 0x53, 0x7b, 0x29, 0x8e, 0x60, 0x99, 0xf9, 0x0c, 0x7c, 0x6f, 0xa2, 0xcc, 0x9f, 0x80, 0xdd, 0x5e, 0x46, 0xaa, 0x0d, 0x6c, 0xc9, 0x6c, 0xf7, 0x78, 0x5b, 0x38, 0xe3, 0x24, + /* (2^420)P */ 0x4b, 0x75, 0x6a, 0x2f, 0x08, 0xe1, 0x72, 0x76, 0xab, 0x82, 0x96, 0xdf, 0x3b, 0x1f, 0x9b, 0xd8, 0xed, 0xdb, 0xcd, 0x15, 0x09, 0x5a, 0x1e, 0xb7, 0xc5, 0x26, 0x72, 0x07, 0x0c, 0x50, 0xcd, 0x3b, 0x4d, 0x3f, 0xa2, 0x67, 0xc2, 0x02, 0x61, 0x2e, 0x68, 0xe9, 0x6f, 0xf0, 0x21, 0x2a, 0xa7, 0x3b, 0x88, 0x04, 0x11, 0x64, 0x49, 0x0d, 0xb4, 0x46, + /* (2^421)P */ 0x63, 0x85, 0xf3, 0xc5, 0x2b, 0x5a, 0x9f, 0xf0, 0x17, 0xcb, 0x45, 0x0a, 0xf3, 0x6e, 0x7e, 0xb0, 0x7c, 0xbc, 0xf0, 0x4f, 0x3a, 0xb0, 0xbc, 0x36, 0x36, 0x52, 0x51, 0xcb, 0xfe, 0x9a, 0xcb, 0xe8, 0x7e, 0x4b, 0x06, 0x7f, 0xaa, 0x35, 0xc8, 0x0e, 0x7a, 0x30, 0xa3, 0xb1, 0x09, 0xbb, 0x86, 0x4c, 0xbe, 0xb8, 0xbd, 0xe0, 0x32, 0xa5, 0xd4, 0xf7, + /* (2^422)P */ 0x7d, 0x50, 0x37, 0x68, 0x4e, 0x22, 0xb2, 0x2c, 0xd5, 0x0f, 0x2b, 0x6d, 0xb1, 0x51, 0xf2, 0x82, 0xe9, 0x98, 0x7c, 0x50, 0xc7, 0x96, 0x7e, 0x0e, 0xdc, 0xb1, 0x0e, 0xb2, 0x63, 0x8c, 0x30, 0x37, 0x72, 0x21, 0x9c, 0x61, 0xc2, 0xa7, 0x33, 0xd9, 0xb2, 0x63, 0x93, 0xd1, 0x6b, 0x6a, 0x73, 0xa5, 0x58, 0x80, 0xff, 0x04, 0xc7, 0x83, 0x21, 0x29, + /* (2^423)P */ 0x29, 0x04, 0xbc, 0x99, 0x39, 0xc9, 0x58, 0xc9, 0x6b, 0x17, 0xe8, 0x90, 0xb3, 0xe6, 0xa9, 0xb6, 0x28, 0x9b, 0xcb, 0x3b, 0x28, 0x90, 0x68, 0x71, 0xff, 0xcf, 0x08, 0x78, 0xc9, 0x8d, 0xa8, 0x4e, 0x43, 0xd1, 0x1c, 0x9e, 0xa4, 0xe3, 0xdf, 0xbf, 0x92, 0xf4, 0xf9, 0x41, 0xba, 0x4d, 0x1c, 0xf9, 0xdd, 0x74, 0x76, 0x1c, 0x6e, 0x3e, 0x94, 0x87, + /* (2^424)P */ 0xe4, 0xda, 0xc5, 0xd7, 0xfb, 0x87, 0xc5, 0x4d, 0x6b, 0x19, 0xaa, 0xb9, 0xbc, 0x8c, 0xf2, 0x8a, 0xd8, 0x5d, 0xdb, 0x4d, 0xef, 0xa6, 0xf2, 0x65, 0xf1, 0x22, 0x9c, 0xf1, 0x46, 0x30, 0x71, 0x7c, 0xe4, 0x53, 0x8e, 0x55, 0x2e, 0x9c, 0x9a, 0x31, 0x2a, 0xc3, 0xab, 0x0f, 0xde, 0xe4, 0xbe, 0xd8, 0x96, 0x50, 0x6e, 0x0c, 0x54, 0x49, 0xe6, 0xec, + /* (2^425)P */ 0x3c, 0x1d, 0x5a, 0xa5, 0xda, 0xad, 0xdd, 0xc2, 0xae, 0xac, 0x6f, 0x86, 0x75, 0x31, 0x91, 0x64, 0x45, 0x9d, 0xa4, 0xf0, 0x81, 0xf1, 0x0e, 0xba, 0x74, 0xaf, 0x7b, 0xcd, 0x6f, 0xfe, 0xac, 0x4e, 0xdb, 0x4e, 0x45, 0x35, 0x36, 0xc5, 0xc0, 0x6c, 0x3d, 0x64, 0xf4, 0xd8, 0x07, 0x62, 0xd1, 0xec, 0xf3, 0xfc, 0x93, 0xc9, 0x28, 0x0c, 0x2c, 0xf3, + /* (2^426)P */ 0x0c, 0x69, 0x2b, 0x5c, 0xb6, 0x41, 0x69, 0xf1, 0xa4, 0xf1, 0x5b, 0x75, 0x4c, 0x42, 0x8b, 0x47, 0xeb, 0x69, 0xfb, 0xa8, 0xe6, 0xf9, 0x7b, 0x48, 0x50, 0xaf, 0xd3, 0xda, 0xb2, 0x35, 0x10, 0xb5, 0x5b, 0x40, 0x90, 0x39, 0xc9, 0x07, 0x06, 0x73, 0x26, 0x20, 0x95, 0x01, 0xa4, 0x2d, 0xf0, 0xe7, 0x2e, 0x00, 0x7d, 0x41, 0x09, 0x68, 0x13, 0xc4, + /* (2^427)P */ 0xbe, 0x38, 0x78, 0xcf, 0xc9, 0x4f, 0x36, 0xca, 0x09, 0x61, 0x31, 0x3c, 0x57, 0x2e, 0xec, 0x17, 0xa4, 0x7d, 0x19, 0x2b, 0x9b, 0x5b, 0xbe, 0x8f, 0xd6, 0xc5, 0x2f, 0x86, 0xf2, 0x64, 0x76, 0x17, 0x00, 0x6e, 0x1a, 0x8c, 0x67, 0x1b, 0x68, 0xeb, 0x15, 0xa2, 0xd6, 0x09, 0x91, 0xdd, 0x23, 0x0d, 0x98, 0xb2, 0x10, 0x19, 0x55, 0x9b, 0x63, 0xf2, + /* (2^428)P */ 0x51, 0x1f, 0x93, 0xea, 0x2a, 0x3a, 0xfa, 0x41, 0xc0, 0x57, 0xfb, 0x74, 0xa6, 0x65, 0x09, 0x56, 0x14, 0xb6, 0x12, 0xaa, 0xb3, 0x1a, 0x8d, 0x3b, 0x76, 0x91, 0x7a, 0x23, 0x56, 0x9c, 0x6a, 0xc0, 0xe0, 0x3c, 0x3f, 0xb5, 0x1a, 0xf4, 0x57, 0x71, 0x93, 0x2b, 0xb1, 0xa7, 0x70, 0x57, 0x22, 0x80, 0xf5, 0xb8, 0x07, 0x77, 0x87, 0x0c, 0xbe, 0x83, + /* (2^429)P */ 0x07, 0x9b, 0x0e, 0x52, 0x38, 0x63, 0x13, 0x86, 0x6a, 0xa6, 0xb4, 0xd2, 0x60, 0x68, 0x9a, 0x99, 0x82, 0x0a, 0x04, 0x5f, 0x89, 0x7a, 0x1a, 0x2a, 0xae, 0x2d, 0x35, 0x0c, 0x1e, 0xad, 0xef, 0x4f, 0x9a, 0xfc, 0xc8, 0xd9, 0xcf, 0x9d, 0x48, 0x71, 0xa5, 0x55, 0x79, 0x73, 0x39, 0x1b, 0xd8, 0x73, 0xec, 0x9b, 0x03, 0x16, 0xd8, 0x82, 0xf7, 0x67, + /* (2^430)P */ 0x52, 0x67, 0x42, 0x21, 0xc9, 0x40, 0x78, 0x82, 0x2b, 0x95, 0x2d, 0x20, 0x92, 0xd1, 0xe2, 0x61, 0x25, 0xb0, 0xc6, 0x9c, 0x20, 0x59, 0x8e, 0x28, 0x6f, 0xf3, 0xfd, 0xd3, 0xc1, 0x32, 0x43, 0xc9, 0xa6, 0x08, 0x7a, 0x77, 0x9c, 0x4c, 0x8c, 0x33, 0x71, 0x13, 0x69, 0xe3, 0x52, 0x30, 0xa7, 0xf5, 0x07, 0x67, 0xac, 0xad, 0x46, 0x8a, 0x26, 0x25, + /* (2^431)P */ 0xda, 0x86, 0xc4, 0xa2, 0x71, 0x56, 0xdd, 0xd2, 0x48, 0xd3, 0xde, 0x42, 0x63, 0x01, 0xa7, 0x2c, 0x92, 0x83, 0x6f, 0x2e, 0xd8, 0x1e, 0x3f, 0xc1, 0xc5, 0x42, 0x4e, 0x34, 0x19, 0x54, 0x6e, 0x35, 0x2c, 0x51, 0x2e, 0xfd, 0x0f, 0x9a, 0x45, 0x66, 0x5e, 0x4a, 0x83, 0xda, 0x0a, 0x53, 0x68, 0x63, 0xfa, 0xce, 0x47, 0x20, 0xd3, 0x34, 0xba, 0x0d, + /* (2^432)P */ 0xd0, 0xe9, 0x64, 0xa4, 0x61, 0x4b, 0x86, 0xe5, 0x93, 0x6f, 0xda, 0x0e, 0x31, 0x7e, 0x6e, 0xe3, 0xc6, 0x73, 0xd8, 0xa3, 0x08, 0x57, 0x52, 0xcd, 0x51, 0x63, 0x1d, 0x9f, 0x93, 0x00, 0x62, 0x91, 0x26, 0x21, 0xa7, 0xdd, 0x25, 0x0f, 0x09, 0x0d, 0x35, 0xad, 0xcf, 0x11, 0x8e, 0x6e, 0xe8, 0xae, 0x1d, 0x95, 0xcb, 0x88, 0xf8, 0x70, 0x7b, 0x91, + /* (2^433)P */ 0x0c, 0x19, 0x5c, 0xd9, 0x8d, 0xda, 0x9d, 0x2c, 0x90, 0x54, 0x65, 0xe8, 0xb6, 0x35, 0x50, 0xae, 0xea, 0xae, 0x43, 0xb7, 0x1e, 0x99, 0x8b, 0x4c, 0x36, 0x4e, 0xe4, 0x1e, 0xc4, 0x64, 0x43, 0xb6, 0xeb, 0xd4, 0xe9, 0x60, 0x22, 0xee, 0xcf, 0xb8, 0x52, 0x1b, 0xf0, 0x04, 0xce, 0xbc, 0x2b, 0xf0, 0xbe, 0xcd, 0x44, 0x74, 0x1e, 0x1f, 0x63, 0xf9, + /* (2^434)P */ 0xe1, 0x3f, 0x95, 0x94, 0xb2, 0xb6, 0x31, 0xa9, 0x1b, 0xdb, 0xfd, 0x0e, 0xdb, 0xdd, 0x1a, 0x22, 0x78, 0x60, 0x9f, 0x75, 0x5f, 0x93, 0x06, 0x0c, 0xd8, 0xbb, 0xa2, 0x85, 0x2b, 0x5e, 0xc0, 0x9b, 0xa8, 0x5d, 0xaf, 0x93, 0x91, 0x91, 0x47, 0x41, 0x1a, 0xfc, 0xb4, 0x51, 0x85, 0xad, 0x69, 0x4d, 0x73, 0x69, 0xd5, 0x4e, 0x82, 0xfb, 0x66, 0xcb, + /* (2^435)P */ 0x7c, 0xbe, 0xc7, 0x51, 0xc4, 0x74, 0x6e, 0xab, 0xfd, 0x41, 0x4f, 0x76, 0x4f, 0x24, 0x03, 0xd6, 0x2a, 0xb7, 0x42, 0xb4, 0xda, 0x41, 0x2c, 0x82, 0x48, 0x4c, 0x7f, 0x6f, 0x25, 0x5d, 0x36, 0xd4, 0x69, 0xf5, 0xef, 0x02, 0x81, 0xea, 0x6f, 0x19, 0x69, 0xe8, 0x6f, 0x5b, 0x2f, 0x14, 0x0e, 0x6f, 0x89, 0xb4, 0xb5, 0xd8, 0xae, 0xef, 0x7b, 0x87, + /* (2^436)P */ 0xe9, 0x91, 0xa0, 0x8b, 0xc9, 0xe0, 0x01, 0x90, 0x37, 0xc1, 0x6f, 0xdc, 0x5e, 0xf7, 0xbf, 0x43, 0x00, 0xaa, 0x10, 0x76, 0x76, 0x18, 0x6e, 0x19, 0x1e, 0x94, 0x50, 0x11, 0x0a, 0xd1, 0xe2, 0xdb, 0x08, 0x21, 0xa0, 0x1f, 0xdb, 0x54, 0xfe, 0xea, 0x6e, 0xa3, 0x68, 0x56, 0x87, 0x0b, 0x22, 0x4e, 0x66, 0xf3, 0x82, 0x82, 0x00, 0xcd, 0xd4, 0x12, + /* (2^437)P */ 0x25, 0x8e, 0x24, 0x77, 0x64, 0x4c, 0xe0, 0xf8, 0x18, 0xc0, 0xdc, 0xc7, 0x1b, 0x35, 0x65, 0xde, 0x67, 0x41, 0x5e, 0x6f, 0x90, 0x82, 0xa7, 0x2e, 0x6d, 0xf1, 0x47, 0xb4, 0x92, 0x9c, 0xfd, 0x6a, 0x9a, 0x41, 0x36, 0x20, 0x24, 0x58, 0xc3, 0x59, 0x07, 0x9a, 0xfa, 0x9f, 0x03, 0xcb, 0xc7, 0x69, 0x37, 0x60, 0xe1, 0xab, 0x13, 0x72, 0xee, 0xa2, + /* (2^438)P */ 0x74, 0x78, 0xfb, 0x13, 0xcb, 0x8e, 0x37, 0x1a, 0xf6, 0x1d, 0x17, 0x83, 0x06, 0xd4, 0x27, 0x06, 0x21, 0xe8, 0xda, 0xdf, 0x6b, 0xf3, 0x83, 0x6b, 0x34, 0x8a, 0x8c, 0xee, 0x01, 0x05, 0x5b, 0xed, 0xd3, 0x1b, 0xc9, 0x64, 0x83, 0xc9, 0x49, 0xc2, 0x57, 0x1b, 0xdd, 0xcf, 0xf1, 0x9d, 0x63, 0xee, 0x1c, 0x0d, 0xa0, 0x0a, 0x73, 0x1f, 0x5b, 0x32, + /* (2^439)P */ 0x29, 0xce, 0x1e, 0xc0, 0x6a, 0xf5, 0xeb, 0x99, 0x5a, 0x39, 0x23, 0xe9, 0xdd, 0xac, 0x44, 0x88, 0xbc, 0x80, 0x22, 0xde, 0x2c, 0xcb, 0xa8, 0x3b, 0xff, 0xf7, 0x6f, 0xc7, 0x71, 0x72, 0xa8, 0xa3, 0xf6, 0x4d, 0xc6, 0x75, 0xda, 0x80, 0xdc, 0xd9, 0x30, 0xd9, 0x07, 0x50, 0x5a, 0x54, 0x7d, 0xda, 0x39, 0x6f, 0x78, 0x94, 0xbf, 0x25, 0x98, 0xdc, + /* (2^440)P */ 0x01, 0x26, 0x62, 0x44, 0xfb, 0x0f, 0x11, 0x72, 0x73, 0x0a, 0x16, 0xc7, 0x16, 0x9c, 0x9b, 0x37, 0xd8, 0xff, 0x4f, 0xfe, 0x57, 0xdb, 0xae, 0xef, 0x7d, 0x94, 0x30, 0x04, 0x70, 0x83, 0xde, 0x3c, 0xd4, 0xb5, 0x70, 0xda, 0xa7, 0x55, 0xc8, 0x19, 0xe1, 0x36, 0x15, 0x61, 0xe7, 0x3b, 0x7d, 0x85, 0xbb, 0xf3, 0x42, 0x5a, 0x94, 0xf4, 0x53, 0x2a, + /* (2^441)P */ 0x14, 0x60, 0xa6, 0x0b, 0x83, 0xe1, 0x23, 0x77, 0xc0, 0xce, 0x50, 0xed, 0x35, 0x8d, 0x98, 0x99, 0x7d, 0xf5, 0x8d, 0xce, 0x94, 0x25, 0xc8, 0x0f, 0x6d, 0xfa, 0x4a, 0xa4, 0x3a, 0x1f, 0x66, 0xfb, 0x5a, 0x64, 0xaf, 0x8b, 0x54, 0x54, 0x44, 0x3f, 0x5b, 0x88, 0x61, 0xe4, 0x48, 0x45, 0x26, 0x20, 0xbe, 0x0d, 0x06, 0xbb, 0x65, 0x59, 0xe1, 0x36, + /* (2^442)P */ 0xb7, 0x98, 0xce, 0xa3, 0xe3, 0xee, 0x11, 0x1b, 0x9e, 0x24, 0x59, 0x75, 0x31, 0x37, 0x44, 0x6f, 0x6b, 0x9e, 0xec, 0xb7, 0x44, 0x01, 0x7e, 0xab, 0xbb, 0x69, 0x5d, 0x11, 0xb0, 0x30, 0x64, 0xea, 0x91, 0xb4, 0x7a, 0x8c, 0x02, 0x4c, 0xb9, 0x10, 0xa7, 0xc7, 0x79, 0xe6, 0xdc, 0x77, 0xe3, 0xc8, 0xef, 0x3e, 0xf9, 0x38, 0x81, 0xce, 0x9a, 0xb2, + /* (2^443)P */ 0x91, 0x12, 0x76, 0xd0, 0x10, 0xb4, 0xaf, 0xe1, 0x89, 0x3a, 0x93, 0x6b, 0x5c, 0x19, 0x5f, 0x24, 0xed, 0x04, 0x92, 0xc7, 0xf0, 0x00, 0x08, 0xc1, 0x92, 0xff, 0x90, 0xdb, 0xb2, 0xbf, 0xdf, 0x49, 0xcd, 0xbd, 0x5c, 0x6e, 0xbf, 0x16, 0xbb, 0x61, 0xf9, 0x20, 0x33, 0x35, 0x93, 0x11, 0xbc, 0x59, 0x69, 0xce, 0x18, 0x9f, 0xf8, 0x7b, 0xa1, 0x6e, + /* (2^444)P */ 0xa1, 0xf4, 0xaf, 0xad, 0xf8, 0xe6, 0x99, 0xd2, 0xa1, 0x4d, 0xde, 0x56, 0xc9, 0x7b, 0x0b, 0x11, 0x3e, 0xbf, 0x89, 0x1a, 0x9a, 0x90, 0xe5, 0xe2, 0xa6, 0x37, 0x88, 0xa1, 0x68, 0x59, 0xae, 0x8c, 0xec, 0x02, 0x14, 0x8d, 0xb7, 0x2e, 0x25, 0x75, 0x7f, 0x76, 0x1a, 0xd3, 0x4d, 0xad, 0x8a, 0x00, 0x6c, 0x96, 0x49, 0xa4, 0xc3, 0x2e, 0x5c, 0x7b, + /* (2^445)P */ 0x26, 0x53, 0xf7, 0xda, 0xa8, 0x01, 0x14, 0xb1, 0x63, 0xe3, 0xc3, 0x89, 0x88, 0xb0, 0x85, 0x40, 0x2b, 0x26, 0x9a, 0x10, 0x1a, 0x70, 0x33, 0xf4, 0x50, 0x9d, 0x4d, 0xd8, 0x64, 0xc6, 0x0f, 0xe1, 0x17, 0xc8, 0x10, 0x4b, 0xfc, 0xa0, 0xc9, 0xba, 0x2c, 0x98, 0x09, 0xf5, 0x84, 0xb6, 0x7c, 0x4e, 0xa3, 0xe3, 0x81, 0x1b, 0x32, 0x60, 0x02, 0xdd, + /* (2^446)P */ 0xa3, 0xe5, 0x86, 0xd4, 0x43, 0xa8, 0xd1, 0x98, 0x9d, 0x9d, 0xdb, 0x04, 0xcf, 0x6e, 0x35, 0x05, 0x30, 0x53, 0x3b, 0xbc, 0x90, 0x00, 0x4a, 0xc5, 0x40, 0x2a, 0x0f, 0xde, 0x1a, 0xd7, 0x36, 0x27, 0x44, 0x62, 0xa6, 0xac, 0x9d, 0xd2, 0x70, 0x69, 0x14, 0x39, 0x9b, 0xd1, 0xc3, 0x0a, 0x3a, 0x82, 0x0e, 0xf1, 0x94, 0xd7, 0x42, 0x94, 0xd5, 0x7d, + /* (2^447)P */ 0x04, 0xc0, 0x6e, 0x12, 0x90, 0x70, 0xf9, 0xdf, 0xf7, 0xc9, 0x86, 0xc0, 0xe6, 0x92, 0x8b, 0x0a, 0xa1, 0xc1, 0x3b, 0xcc, 0x33, 0xb7, 0xf0, 0xeb, 0x51, 0x50, 0x80, 0x20, 0x69, 0x1c, 0x4f, 0x89, 0x05, 0x1e, 0xe4, 0x7a, 0x0a, 0xc2, 0xf0, 0xf5, 0x78, 0x91, 0x76, 0x34, 0x45, 0xdc, 0x24, 0x53, 0x24, 0x98, 0xe2, 0x73, 0x6f, 0xe6, 0x46, 0x67, +} diff --git a/vendor/github.com/cloudflare/circl/internal/conv/conv.go b/vendor/github.com/cloudflare/circl/internal/conv/conv.go new file mode 100644 index 00000000..649a8e93 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/internal/conv/conv.go @@ -0,0 +1,140 @@ +package conv + +import ( + "encoding/binary" + "fmt" + "math/big" + "strings" +) + +// BytesLe2Hex returns an hexadecimal string of a number stored in a +// little-endian order slice x. +func BytesLe2Hex(x []byte) string { + b := &strings.Builder{} + b.Grow(2*len(x) + 2) + fmt.Fprint(b, "0x") + if len(x) == 0 { + fmt.Fprint(b, "00") + } + for i := len(x) - 1; i >= 0; i-- { + fmt.Fprintf(b, "%02x", x[i]) + } + return b.String() +} + +// BytesLe2BigInt converts a little-endian slice x into a big-endian +// math/big.Int. +func BytesLe2BigInt(x []byte) *big.Int { + n := len(x) + b := new(big.Int) + if len(x) > 0 { + y := make([]byte, n) + for i := 0; i < n; i++ { + y[n-1-i] = x[i] + } + b.SetBytes(y) + } + return b +} + +// BytesBe2Uint64Le converts a big-endian slice x to a little-endian slice of uint64. +func BytesBe2Uint64Le(x []byte) []uint64 { + l := len(x) + z := make([]uint64, (l+7)/8) + blocks := l / 8 + for i := 0; i < blocks; i++ { + z[i] = binary.BigEndian.Uint64(x[l-8*(i+1):]) + } + remBytes := l % 8 + for i := 0; i < remBytes; i++ { + z[blocks] |= uint64(x[l-1-8*blocks-i]) << uint(8*i) + } + return z +} + +// BigInt2BytesLe stores a positive big.Int number x into a little-endian slice z. +// The slice is modified if the bitlength of x <= 8*len(z) (padding with zeros). +// If x does not fit in the slice or is negative, z is not modified. +func BigInt2BytesLe(z []byte, x *big.Int) { + xLen := (x.BitLen() + 7) >> 3 + zLen := len(z) + if zLen >= xLen && x.Sign() >= 0 { + y := x.Bytes() + for i := 0; i < xLen; i++ { + z[i] = y[xLen-1-i] + } + for i := xLen; i < zLen; i++ { + z[i] = 0 + } + } +} + +// Uint64Le2BigInt converts a little-endian slice x into a big number. +func Uint64Le2BigInt(x []uint64) *big.Int { + n := len(x) + b := new(big.Int) + var bi big.Int + for i := n - 1; i >= 0; i-- { + bi.SetUint64(x[i]) + b.Lsh(b, 64) + b.Add(b, &bi) + } + return b +} + +// Uint64Le2BytesLe converts a little-endian slice x to a little-endian slice of bytes. +func Uint64Le2BytesLe(x []uint64) []byte { + b := make([]byte, 8*len(x)) + n := len(x) + for i := 0; i < n; i++ { + binary.LittleEndian.PutUint64(b[i*8:], x[i]) + } + return b +} + +// Uint64Le2BytesBe converts a little-endian slice x to a big-endian slice of bytes. +func Uint64Le2BytesBe(x []uint64) []byte { + b := make([]byte, 8*len(x)) + n := len(x) + for i := 0; i < n; i++ { + binary.BigEndian.PutUint64(b[i*8:], x[n-1-i]) + } + return b +} + +// Uint64Le2Hex returns an hexadecimal string of a number stored in a +// little-endian order slice x. +func Uint64Le2Hex(x []uint64) string { + b := new(strings.Builder) + b.Grow(16*len(x) + 2) + fmt.Fprint(b, "0x") + if len(x) == 0 { + fmt.Fprint(b, "00") + } + for i := len(x) - 1; i >= 0; i-- { + fmt.Fprintf(b, "%016x", x[i]) + } + return b.String() +} + +// BigInt2Uint64Le stores a positive big.Int number x into a little-endian slice z. +// The slice is modified if the bitlength of x <= 8*len(z) (padding with zeros). +// If x does not fit in the slice or is negative, z is not modified. +func BigInt2Uint64Le(z []uint64, x *big.Int) { + xLen := (x.BitLen() + 63) >> 6 // number of 64-bit words + zLen := len(z) + if zLen >= xLen && x.Sign() > 0 { + var y, yi big.Int + y.Set(x) + two64 := big.NewInt(1) + two64.Lsh(two64, 64).Sub(two64, big.NewInt(1)) + for i := 0; i < xLen; i++ { + yi.And(&y, two64) + z[i] = yi.Uint64() + y.Rsh(&y, 64) + } + } + for i := xLen; i < zLen; i++ { + z[i] = 0 + } +} diff --git a/vendor/github.com/cloudflare/circl/internal/sha3/doc.go b/vendor/github.com/cloudflare/circl/internal/sha3/doc.go new file mode 100644 index 00000000..7e023090 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/internal/sha3/doc.go @@ -0,0 +1,62 @@ +// Copyright 2014 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Package sha3 implements the SHA-3 fixed-output-length hash functions and +// the SHAKE variable-output-length hash functions defined by FIPS-202. +// +// Both types of hash function use the "sponge" construction and the Keccak +// permutation. For a detailed specification see http://keccak.noekeon.org/ +// +// # Guidance +// +// If you aren't sure what function you need, use SHAKE256 with at least 64 +// bytes of output. The SHAKE instances are faster than the SHA3 instances; +// the latter have to allocate memory to conform to the hash.Hash interface. +// +// If you need a secret-key MAC (message authentication code), prepend the +// secret key to the input, hash with SHAKE256 and read at least 32 bytes of +// output. +// +// # Security strengths +// +// The SHA3-x (x equals 224, 256, 384, or 512) functions have a security +// strength against preimage attacks of x bits. Since they only produce "x" +// bits of output, their collision-resistance is only "x/2" bits. +// +// The SHAKE-256 and -128 functions have a generic security strength of 256 and +// 128 bits against all attacks, provided that at least 2x bits of their output +// is used. Requesting more than 64 or 32 bytes of output, respectively, does +// not increase the collision-resistance of the SHAKE functions. +// +// # The sponge construction +// +// A sponge builds a pseudo-random function from a public pseudo-random +// permutation, by applying the permutation to a state of "rate + capacity" +// bytes, but hiding "capacity" of the bytes. +// +// A sponge starts out with a zero state. To hash an input using a sponge, up +// to "rate" bytes of the input are XORed into the sponge's state. The sponge +// is then "full" and the permutation is applied to "empty" it. This process is +// repeated until all the input has been "absorbed". The input is then padded. +// The digest is "squeezed" from the sponge in the same way, except that output +// is copied out instead of input being XORed in. +// +// A sponge is parameterized by its generic security strength, which is equal +// to half its capacity; capacity + rate is equal to the permutation's width. +// Since the KeccakF-1600 permutation is 1600 bits (200 bytes) wide, this means +// that the security strength of a sponge instance is equal to (1600 - bitrate) / 2. +// +// # Recommendations +// +// The SHAKE functions are recommended for most new uses. They can produce +// output of arbitrary length. SHAKE256, with an output length of at least +// 64 bytes, provides 256-bit security against all attacks. The Keccak team +// recommends it for most applications upgrading from SHA2-512. (NIST chose a +// much stronger, but much slower, sponge instance for SHA3-512.) +// +// The SHA-3 functions are "drop-in" replacements for the SHA-2 functions. +// They produce output of the same length, with the same security strengths +// against all attacks. This means, in particular, that SHA3-256 only has +// 128-bit collision resistance, because its output length is 32 bytes. +package sha3 diff --git a/vendor/github.com/cloudflare/circl/internal/sha3/hashes.go b/vendor/github.com/cloudflare/circl/internal/sha3/hashes.go new file mode 100644 index 00000000..7d2365a7 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/internal/sha3/hashes.go @@ -0,0 +1,69 @@ +// Copyright 2014 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package sha3 + +// This file provides functions for creating instances of the SHA-3 +// and SHAKE hash functions, as well as utility functions for hashing +// bytes. + +// New224 creates a new SHA3-224 hash. +// Its generic security strength is 224 bits against preimage attacks, +// and 112 bits against collision attacks. +func New224() State { + return State{rate: 144, outputLen: 28, dsbyte: 0x06} +} + +// New256 creates a new SHA3-256 hash. +// Its generic security strength is 256 bits against preimage attacks, +// and 128 bits against collision attacks. +func New256() State { + return State{rate: 136, outputLen: 32, dsbyte: 0x06} +} + +// New384 creates a new SHA3-384 hash. +// Its generic security strength is 384 bits against preimage attacks, +// and 192 bits against collision attacks. +func New384() State { + return State{rate: 104, outputLen: 48, dsbyte: 0x06} +} + +// New512 creates a new SHA3-512 hash. +// Its generic security strength is 512 bits against preimage attacks, +// and 256 bits against collision attacks. +func New512() State { + return State{rate: 72, outputLen: 64, dsbyte: 0x06} +} + +// Sum224 returns the SHA3-224 digest of the data. +func Sum224(data []byte) (digest [28]byte) { + h := New224() + _, _ = h.Write(data) + h.Sum(digest[:0]) + return +} + +// Sum256 returns the SHA3-256 digest of the data. +func Sum256(data []byte) (digest [32]byte) { + h := New256() + _, _ = h.Write(data) + h.Sum(digest[:0]) + return +} + +// Sum384 returns the SHA3-384 digest of the data. +func Sum384(data []byte) (digest [48]byte) { + h := New384() + _, _ = h.Write(data) + h.Sum(digest[:0]) + return +} + +// Sum512 returns the SHA3-512 digest of the data. +func Sum512(data []byte) (digest [64]byte) { + h := New512() + _, _ = h.Write(data) + h.Sum(digest[:0]) + return +} diff --git a/vendor/github.com/cloudflare/circl/internal/sha3/keccakf.go b/vendor/github.com/cloudflare/circl/internal/sha3/keccakf.go new file mode 100644 index 00000000..e606f0ca --- /dev/null +++ b/vendor/github.com/cloudflare/circl/internal/sha3/keccakf.go @@ -0,0 +1,385 @@ +// Copyright 2014 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +//go:build !amd64 || appengine || gccgo +// +build !amd64 appengine gccgo + +package sha3 + +// KeccakF1600 applies the Keccak permutation to a 1600b-wide +// state represented as a slice of 25 uint64s. +func KeccakF1600(a *[25]uint64) { + // Implementation translated from Keccak-inplace.c + // in the keccak reference code. + var t, bc0, bc1, bc2, bc3, bc4, d0, d1, d2, d3, d4 uint64 + + for i := 0; i < 24; i += 4 { + // Combines the 5 steps in each round into 2 steps. + // Unrolls 4 rounds per loop and spreads some steps across rounds. + + // Round 1 + bc0 = a[0] ^ a[5] ^ a[10] ^ a[15] ^ a[20] + bc1 = a[1] ^ a[6] ^ a[11] ^ a[16] ^ a[21] + bc2 = a[2] ^ a[7] ^ a[12] ^ a[17] ^ a[22] + bc3 = a[3] ^ a[8] ^ a[13] ^ a[18] ^ a[23] + bc4 = a[4] ^ a[9] ^ a[14] ^ a[19] ^ a[24] + d0 = bc4 ^ (bc1<<1 | bc1>>63) + d1 = bc0 ^ (bc2<<1 | bc2>>63) + d2 = bc1 ^ (bc3<<1 | bc3>>63) + d3 = bc2 ^ (bc4<<1 | bc4>>63) + d4 = bc3 ^ (bc0<<1 | bc0>>63) + + bc0 = a[0] ^ d0 + t = a[6] ^ d1 + bc1 = t<<44 | t>>(64-44) + t = a[12] ^ d2 + bc2 = t<<43 | t>>(64-43) + t = a[18] ^ d3 + bc3 = t<<21 | t>>(64-21) + t = a[24] ^ d4 + bc4 = t<<14 | t>>(64-14) + a[0] = bc0 ^ (bc2 &^ bc1) ^ RC[i] + a[6] = bc1 ^ (bc3 &^ bc2) + a[12] = bc2 ^ (bc4 &^ bc3) + a[18] = bc3 ^ (bc0 &^ bc4) + a[24] = bc4 ^ (bc1 &^ bc0) + + t = a[10] ^ d0 + bc2 = t<<3 | t>>(64-3) + t = a[16] ^ d1 + bc3 = t<<45 | t>>(64-45) + t = a[22] ^ d2 + bc4 = t<<61 | t>>(64-61) + t = a[3] ^ d3 + bc0 = t<<28 | t>>(64-28) + t = a[9] ^ d4 + bc1 = t<<20 | t>>(64-20) + a[10] = bc0 ^ (bc2 &^ bc1) + a[16] = bc1 ^ (bc3 &^ bc2) + a[22] = bc2 ^ (bc4 &^ bc3) + a[3] = bc3 ^ (bc0 &^ bc4) + a[9] = bc4 ^ (bc1 &^ bc0) + + t = a[20] ^ d0 + bc4 = t<<18 | t>>(64-18) + t = a[1] ^ d1 + bc0 = t<<1 | t>>(64-1) + t = a[7] ^ d2 + bc1 = t<<6 | t>>(64-6) + t = a[13] ^ d3 + bc2 = t<<25 | t>>(64-25) + t = a[19] ^ d4 + bc3 = t<<8 | t>>(64-8) + a[20] = bc0 ^ (bc2 &^ bc1) + a[1] = bc1 ^ (bc3 &^ bc2) + a[7] = bc2 ^ (bc4 &^ bc3) + a[13] = bc3 ^ (bc0 &^ bc4) + a[19] = bc4 ^ (bc1 &^ bc0) + + t = a[5] ^ d0 + bc1 = t<<36 | t>>(64-36) + t = a[11] ^ d1 + bc2 = t<<10 | t>>(64-10) + t = a[17] ^ d2 + bc3 = t<<15 | t>>(64-15) + t = a[23] ^ d3 + bc4 = t<<56 | t>>(64-56) + t = a[4] ^ d4 + bc0 = t<<27 | t>>(64-27) + a[5] = bc0 ^ (bc2 &^ bc1) + a[11] = bc1 ^ (bc3 &^ bc2) + a[17] = bc2 ^ (bc4 &^ bc3) + a[23] = bc3 ^ (bc0 &^ bc4) + a[4] = bc4 ^ (bc1 &^ bc0) + + t = a[15] ^ d0 + bc3 = t<<41 | t>>(64-41) + t = a[21] ^ d1 + bc4 = t<<2 | t>>(64-2) + t = a[2] ^ d2 + bc0 = t<<62 | t>>(64-62) + t = a[8] ^ d3 + bc1 = t<<55 | t>>(64-55) + t = a[14] ^ d4 + bc2 = t<<39 | t>>(64-39) + a[15] = bc0 ^ (bc2 &^ bc1) + a[21] = bc1 ^ (bc3 &^ bc2) + a[2] = bc2 ^ (bc4 &^ bc3) + a[8] = bc3 ^ (bc0 &^ bc4) + a[14] = bc4 ^ (bc1 &^ bc0) + + // Round 2 + bc0 = a[0] ^ a[5] ^ a[10] ^ a[15] ^ a[20] + bc1 = a[1] ^ a[6] ^ a[11] ^ a[16] ^ a[21] + bc2 = a[2] ^ a[7] ^ a[12] ^ a[17] ^ a[22] + bc3 = a[3] ^ a[8] ^ a[13] ^ a[18] ^ a[23] + bc4 = a[4] ^ a[9] ^ a[14] ^ a[19] ^ a[24] + d0 = bc4 ^ (bc1<<1 | bc1>>63) + d1 = bc0 ^ (bc2<<1 | bc2>>63) + d2 = bc1 ^ (bc3<<1 | bc3>>63) + d3 = bc2 ^ (bc4<<1 | bc4>>63) + d4 = bc3 ^ (bc0<<1 | bc0>>63) + + bc0 = a[0] ^ d0 + t = a[16] ^ d1 + bc1 = t<<44 | t>>(64-44) + t = a[7] ^ d2 + bc2 = t<<43 | t>>(64-43) + t = a[23] ^ d3 + bc3 = t<<21 | t>>(64-21) + t = a[14] ^ d4 + bc4 = t<<14 | t>>(64-14) + a[0] = bc0 ^ (bc2 &^ bc1) ^ RC[i+1] + a[16] = bc1 ^ (bc3 &^ bc2) + a[7] = bc2 ^ (bc4 &^ bc3) + a[23] = bc3 ^ (bc0 &^ bc4) + a[14] = bc4 ^ (bc1 &^ bc0) + + t = a[20] ^ d0 + bc2 = t<<3 | t>>(64-3) + t = a[11] ^ d1 + bc3 = t<<45 | t>>(64-45) + t = a[2] ^ d2 + bc4 = t<<61 | t>>(64-61) + t = a[18] ^ d3 + bc0 = t<<28 | t>>(64-28) + t = a[9] ^ d4 + bc1 = t<<20 | t>>(64-20) + a[20] = bc0 ^ (bc2 &^ bc1) + a[11] = bc1 ^ (bc3 &^ bc2) + a[2] = bc2 ^ (bc4 &^ bc3) + a[18] = bc3 ^ (bc0 &^ bc4) + a[9] = bc4 ^ (bc1 &^ bc0) + + t = a[15] ^ d0 + bc4 = t<<18 | t>>(64-18) + t = a[6] ^ d1 + bc0 = t<<1 | t>>(64-1) + t = a[22] ^ d2 + bc1 = t<<6 | t>>(64-6) + t = a[13] ^ d3 + bc2 = t<<25 | t>>(64-25) + t = a[4] ^ d4 + bc3 = t<<8 | t>>(64-8) + a[15] = bc0 ^ (bc2 &^ bc1) + a[6] = bc1 ^ (bc3 &^ bc2) + a[22] = bc2 ^ (bc4 &^ bc3) + a[13] = bc3 ^ (bc0 &^ bc4) + a[4] = bc4 ^ (bc1 &^ bc0) + + t = a[10] ^ d0 + bc1 = t<<36 | t>>(64-36) + t = a[1] ^ d1 + bc2 = t<<10 | t>>(64-10) + t = a[17] ^ d2 + bc3 = t<<15 | t>>(64-15) + t = a[8] ^ d3 + bc4 = t<<56 | t>>(64-56) + t = a[24] ^ d4 + bc0 = t<<27 | t>>(64-27) + a[10] = bc0 ^ (bc2 &^ bc1) + a[1] = bc1 ^ (bc3 &^ bc2) + a[17] = bc2 ^ (bc4 &^ bc3) + a[8] = bc3 ^ (bc0 &^ bc4) + a[24] = bc4 ^ (bc1 &^ bc0) + + t = a[5] ^ d0 + bc3 = t<<41 | t>>(64-41) + t = a[21] ^ d1 + bc4 = t<<2 | t>>(64-2) + t = a[12] ^ d2 + bc0 = t<<62 | t>>(64-62) + t = a[3] ^ d3 + bc1 = t<<55 | t>>(64-55) + t = a[19] ^ d4 + bc2 = t<<39 | t>>(64-39) + a[5] = bc0 ^ (bc2 &^ bc1) + a[21] = bc1 ^ (bc3 &^ bc2) + a[12] = bc2 ^ (bc4 &^ bc3) + a[3] = bc3 ^ (bc0 &^ bc4) + a[19] = bc4 ^ (bc1 &^ bc0) + + // Round 3 + bc0 = a[0] ^ a[5] ^ a[10] ^ a[15] ^ a[20] + bc1 = a[1] ^ a[6] ^ a[11] ^ a[16] ^ a[21] + bc2 = a[2] ^ a[7] ^ a[12] ^ a[17] ^ a[22] + bc3 = a[3] ^ a[8] ^ a[13] ^ a[18] ^ a[23] + bc4 = a[4] ^ a[9] ^ a[14] ^ a[19] ^ a[24] + d0 = bc4 ^ (bc1<<1 | bc1>>63) + d1 = bc0 ^ (bc2<<1 | bc2>>63) + d2 = bc1 ^ (bc3<<1 | bc3>>63) + d3 = bc2 ^ (bc4<<1 | bc4>>63) + d4 = bc3 ^ (bc0<<1 | bc0>>63) + + bc0 = a[0] ^ d0 + t = a[11] ^ d1 + bc1 = t<<44 | t>>(64-44) + t = a[22] ^ d2 + bc2 = t<<43 | t>>(64-43) + t = a[8] ^ d3 + bc3 = t<<21 | t>>(64-21) + t = a[19] ^ d4 + bc4 = t<<14 | t>>(64-14) + a[0] = bc0 ^ (bc2 &^ bc1) ^ RC[i+2] + a[11] = bc1 ^ (bc3 &^ bc2) + a[22] = bc2 ^ (bc4 &^ bc3) + a[8] = bc3 ^ (bc0 &^ bc4) + a[19] = bc4 ^ (bc1 &^ bc0) + + t = a[15] ^ d0 + bc2 = t<<3 | t>>(64-3) + t = a[1] ^ d1 + bc3 = t<<45 | t>>(64-45) + t = a[12] ^ d2 + bc4 = t<<61 | t>>(64-61) + t = a[23] ^ d3 + bc0 = t<<28 | t>>(64-28) + t = a[9] ^ d4 + bc1 = t<<20 | t>>(64-20) + a[15] = bc0 ^ (bc2 &^ bc1) + a[1] = bc1 ^ (bc3 &^ bc2) + a[12] = bc2 ^ (bc4 &^ bc3) + a[23] = bc3 ^ (bc0 &^ bc4) + a[9] = bc4 ^ (bc1 &^ bc0) + + t = a[5] ^ d0 + bc4 = t<<18 | t>>(64-18) + t = a[16] ^ d1 + bc0 = t<<1 | t>>(64-1) + t = a[2] ^ d2 + bc1 = t<<6 | t>>(64-6) + t = a[13] ^ d3 + bc2 = t<<25 | t>>(64-25) + t = a[24] ^ d4 + bc3 = t<<8 | t>>(64-8) + a[5] = bc0 ^ (bc2 &^ bc1) + a[16] = bc1 ^ (bc3 &^ bc2) + a[2] = bc2 ^ (bc4 &^ bc3) + a[13] = bc3 ^ (bc0 &^ bc4) + a[24] = bc4 ^ (bc1 &^ bc0) + + t = a[20] ^ d0 + bc1 = t<<36 | t>>(64-36) + t = a[6] ^ d1 + bc2 = t<<10 | t>>(64-10) + t = a[17] ^ d2 + bc3 = t<<15 | t>>(64-15) + t = a[3] ^ d3 + bc4 = t<<56 | t>>(64-56) + t = a[14] ^ d4 + bc0 = t<<27 | t>>(64-27) + a[20] = bc0 ^ (bc2 &^ bc1) + a[6] = bc1 ^ (bc3 &^ bc2) + a[17] = bc2 ^ (bc4 &^ bc3) + a[3] = bc3 ^ (bc0 &^ bc4) + a[14] = bc4 ^ (bc1 &^ bc0) + + t = a[10] ^ d0 + bc3 = t<<41 | t>>(64-41) + t = a[21] ^ d1 + bc4 = t<<2 | t>>(64-2) + t = a[7] ^ d2 + bc0 = t<<62 | t>>(64-62) + t = a[18] ^ d3 + bc1 = t<<55 | t>>(64-55) + t = a[4] ^ d4 + bc2 = t<<39 | t>>(64-39) + a[10] = bc0 ^ (bc2 &^ bc1) + a[21] = bc1 ^ (bc3 &^ bc2) + a[7] = bc2 ^ (bc4 &^ bc3) + a[18] = bc3 ^ (bc0 &^ bc4) + a[4] = bc4 ^ (bc1 &^ bc0) + + // Round 4 + bc0 = a[0] ^ a[5] ^ a[10] ^ a[15] ^ a[20] + bc1 = a[1] ^ a[6] ^ a[11] ^ a[16] ^ a[21] + bc2 = a[2] ^ a[7] ^ a[12] ^ a[17] ^ a[22] + bc3 = a[3] ^ a[8] ^ a[13] ^ a[18] ^ a[23] + bc4 = a[4] ^ a[9] ^ a[14] ^ a[19] ^ a[24] + d0 = bc4 ^ (bc1<<1 | bc1>>63) + d1 = bc0 ^ (bc2<<1 | bc2>>63) + d2 = bc1 ^ (bc3<<1 | bc3>>63) + d3 = bc2 ^ (bc4<<1 | bc4>>63) + d4 = bc3 ^ (bc0<<1 | bc0>>63) + + bc0 = a[0] ^ d0 + t = a[1] ^ d1 + bc1 = t<<44 | t>>(64-44) + t = a[2] ^ d2 + bc2 = t<<43 | t>>(64-43) + t = a[3] ^ d3 + bc3 = t<<21 | t>>(64-21) + t = a[4] ^ d4 + bc4 = t<<14 | t>>(64-14) + a[0] = bc0 ^ (bc2 &^ bc1) ^ RC[i+3] + a[1] = bc1 ^ (bc3 &^ bc2) + a[2] = bc2 ^ (bc4 &^ bc3) + a[3] = bc3 ^ (bc0 &^ bc4) + a[4] = bc4 ^ (bc1 &^ bc0) + + t = a[5] ^ d0 + bc2 = t<<3 | t>>(64-3) + t = a[6] ^ d1 + bc3 = t<<45 | t>>(64-45) + t = a[7] ^ d2 + bc4 = t<<61 | t>>(64-61) + t = a[8] ^ d3 + bc0 = t<<28 | t>>(64-28) + t = a[9] ^ d4 + bc1 = t<<20 | t>>(64-20) + a[5] = bc0 ^ (bc2 &^ bc1) + a[6] = bc1 ^ (bc3 &^ bc2) + a[7] = bc2 ^ (bc4 &^ bc3) + a[8] = bc3 ^ (bc0 &^ bc4) + a[9] = bc4 ^ (bc1 &^ bc0) + + t = a[10] ^ d0 + bc4 = t<<18 | t>>(64-18) + t = a[11] ^ d1 + bc0 = t<<1 | t>>(64-1) + t = a[12] ^ d2 + bc1 = t<<6 | t>>(64-6) + t = a[13] ^ d3 + bc2 = t<<25 | t>>(64-25) + t = a[14] ^ d4 + bc3 = t<<8 | t>>(64-8) + a[10] = bc0 ^ (bc2 &^ bc1) + a[11] = bc1 ^ (bc3 &^ bc2) + a[12] = bc2 ^ (bc4 &^ bc3) + a[13] = bc3 ^ (bc0 &^ bc4) + a[14] = bc4 ^ (bc1 &^ bc0) + + t = a[15] ^ d0 + bc1 = t<<36 | t>>(64-36) + t = a[16] ^ d1 + bc2 = t<<10 | t>>(64-10) + t = a[17] ^ d2 + bc3 = t<<15 | t>>(64-15) + t = a[18] ^ d3 + bc4 = t<<56 | t>>(64-56) + t = a[19] ^ d4 + bc0 = t<<27 | t>>(64-27) + a[15] = bc0 ^ (bc2 &^ bc1) + a[16] = bc1 ^ (bc3 &^ bc2) + a[17] = bc2 ^ (bc4 &^ bc3) + a[18] = bc3 ^ (bc0 &^ bc4) + a[19] = bc4 ^ (bc1 &^ bc0) + + t = a[20] ^ d0 + bc3 = t<<41 | t>>(64-41) + t = a[21] ^ d1 + bc4 = t<<2 | t>>(64-2) + t = a[22] ^ d2 + bc0 = t<<62 | t>>(64-62) + t = a[23] ^ d3 + bc1 = t<<55 | t>>(64-55) + t = a[24] ^ d4 + bc2 = t<<39 | t>>(64-39) + a[20] = bc0 ^ (bc2 &^ bc1) + a[21] = bc1 ^ (bc3 &^ bc2) + a[22] = bc2 ^ (bc4 &^ bc3) + a[23] = bc3 ^ (bc0 &^ bc4) + a[24] = bc4 ^ (bc1 &^ bc0) + } +} diff --git a/vendor/github.com/cloudflare/circl/internal/sha3/keccakf_amd64.go b/vendor/github.com/cloudflare/circl/internal/sha3/keccakf_amd64.go new file mode 100644 index 00000000..e7364eb0 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/internal/sha3/keccakf_amd64.go @@ -0,0 +1,14 @@ +// Copyright 2015 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +//go:build amd64 && !appengine && !gccgo +// +build amd64,!appengine,!gccgo + +package sha3 + +// This function is implemented in keccakf_amd64.s. + +//go:noescape + +func KeccakF1600(state *[25]uint64) diff --git a/vendor/github.com/cloudflare/circl/internal/sha3/keccakf_amd64.s b/vendor/github.com/cloudflare/circl/internal/sha3/keccakf_amd64.s new file mode 100644 index 00000000..8589363a --- /dev/null +++ b/vendor/github.com/cloudflare/circl/internal/sha3/keccakf_amd64.s @@ -0,0 +1,390 @@ +// Copyright 2015 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// +build amd64,!appengine,!gccgo + +// This code was translated into a form compatible with 6a from the public +// domain sources at https://github.com/gvanas/KeccakCodePackage + +// Offsets in state +#define _ba (0*8) +#define _be (1*8) +#define _bi (2*8) +#define _bo (3*8) +#define _bu (4*8) +#define _ga (5*8) +#define _ge (6*8) +#define _gi (7*8) +#define _go (8*8) +#define _gu (9*8) +#define _ka (10*8) +#define _ke (11*8) +#define _ki (12*8) +#define _ko (13*8) +#define _ku (14*8) +#define _ma (15*8) +#define _me (16*8) +#define _mi (17*8) +#define _mo (18*8) +#define _mu (19*8) +#define _sa (20*8) +#define _se (21*8) +#define _si (22*8) +#define _so (23*8) +#define _su (24*8) + +// Temporary registers +#define rT1 AX + +// Round vars +#define rpState DI +#define rpStack SP + +#define rDa BX +#define rDe CX +#define rDi DX +#define rDo R8 +#define rDu R9 + +#define rBa R10 +#define rBe R11 +#define rBi R12 +#define rBo R13 +#define rBu R14 + +#define rCa SI +#define rCe BP +#define rCi rBi +#define rCo rBo +#define rCu R15 + +#define MOVQ_RBI_RCE MOVQ rBi, rCe +#define XORQ_RT1_RCA XORQ rT1, rCa +#define XORQ_RT1_RCE XORQ rT1, rCe +#define XORQ_RBA_RCU XORQ rBa, rCu +#define XORQ_RBE_RCU XORQ rBe, rCu +#define XORQ_RDU_RCU XORQ rDu, rCu +#define XORQ_RDA_RCA XORQ rDa, rCa +#define XORQ_RDE_RCE XORQ rDe, rCe + +#define mKeccakRound(iState, oState, rc, B_RBI_RCE, G_RT1_RCA, G_RT1_RCE, G_RBA_RCU, K_RT1_RCA, K_RT1_RCE, K_RBA_RCU, M_RT1_RCA, M_RT1_RCE, M_RBE_RCU, S_RDU_RCU, S_RDA_RCA, S_RDE_RCE) \ + /* Prepare round */ \ + MOVQ rCe, rDa; \ + ROLQ $1, rDa; \ + \ + MOVQ _bi(iState), rCi; \ + XORQ _gi(iState), rDi; \ + XORQ rCu, rDa; \ + XORQ _ki(iState), rCi; \ + XORQ _mi(iState), rDi; \ + XORQ rDi, rCi; \ + \ + MOVQ rCi, rDe; \ + ROLQ $1, rDe; \ + \ + MOVQ _bo(iState), rCo; \ + XORQ _go(iState), rDo; \ + XORQ rCa, rDe; \ + XORQ _ko(iState), rCo; \ + XORQ _mo(iState), rDo; \ + XORQ rDo, rCo; \ + \ + MOVQ rCo, rDi; \ + ROLQ $1, rDi; \ + \ + MOVQ rCu, rDo; \ + XORQ rCe, rDi; \ + ROLQ $1, rDo; \ + \ + MOVQ rCa, rDu; \ + XORQ rCi, rDo; \ + ROLQ $1, rDu; \ + \ + /* Result b */ \ + MOVQ _ba(iState), rBa; \ + MOVQ _ge(iState), rBe; \ + XORQ rCo, rDu; \ + MOVQ _ki(iState), rBi; \ + MOVQ _mo(iState), rBo; \ + MOVQ _su(iState), rBu; \ + XORQ rDe, rBe; \ + ROLQ $44, rBe; \ + XORQ rDi, rBi; \ + XORQ rDa, rBa; \ + ROLQ $43, rBi; \ + \ + MOVQ rBe, rCa; \ + MOVQ rc, rT1; \ + ORQ rBi, rCa; \ + XORQ rBa, rT1; \ + XORQ rT1, rCa; \ + MOVQ rCa, _ba(oState); \ + \ + XORQ rDu, rBu; \ + ROLQ $14, rBu; \ + MOVQ rBa, rCu; \ + ANDQ rBe, rCu; \ + XORQ rBu, rCu; \ + MOVQ rCu, _bu(oState); \ + \ + XORQ rDo, rBo; \ + ROLQ $21, rBo; \ + MOVQ rBo, rT1; \ + ANDQ rBu, rT1; \ + XORQ rBi, rT1; \ + MOVQ rT1, _bi(oState); \ + \ + NOTQ rBi; \ + ORQ rBa, rBu; \ + ORQ rBo, rBi; \ + XORQ rBo, rBu; \ + XORQ rBe, rBi; \ + MOVQ rBu, _bo(oState); \ + MOVQ rBi, _be(oState); \ + B_RBI_RCE; \ + \ + /* Result g */ \ + MOVQ _gu(iState), rBe; \ + XORQ rDu, rBe; \ + MOVQ _ka(iState), rBi; \ + ROLQ $20, rBe; \ + XORQ rDa, rBi; \ + ROLQ $3, rBi; \ + MOVQ _bo(iState), rBa; \ + MOVQ rBe, rT1; \ + ORQ rBi, rT1; \ + XORQ rDo, rBa; \ + MOVQ _me(iState), rBo; \ + MOVQ _si(iState), rBu; \ + ROLQ $28, rBa; \ + XORQ rBa, rT1; \ + MOVQ rT1, _ga(oState); \ + G_RT1_RCA; \ + \ + XORQ rDe, rBo; \ + ROLQ $45, rBo; \ + MOVQ rBi, rT1; \ + ANDQ rBo, rT1; \ + XORQ rBe, rT1; \ + MOVQ rT1, _ge(oState); \ + G_RT1_RCE; \ + \ + XORQ rDi, rBu; \ + ROLQ $61, rBu; \ + MOVQ rBu, rT1; \ + ORQ rBa, rT1; \ + XORQ rBo, rT1; \ + MOVQ rT1, _go(oState); \ + \ + ANDQ rBe, rBa; \ + XORQ rBu, rBa; \ + MOVQ rBa, _gu(oState); \ + NOTQ rBu; \ + G_RBA_RCU; \ + \ + ORQ rBu, rBo; \ + XORQ rBi, rBo; \ + MOVQ rBo, _gi(oState); \ + \ + /* Result k */ \ + MOVQ _be(iState), rBa; \ + MOVQ _gi(iState), rBe; \ + MOVQ _ko(iState), rBi; \ + MOVQ _mu(iState), rBo; \ + MOVQ _sa(iState), rBu; \ + XORQ rDi, rBe; \ + ROLQ $6, rBe; \ + XORQ rDo, rBi; \ + ROLQ $25, rBi; \ + MOVQ rBe, rT1; \ + ORQ rBi, rT1; \ + XORQ rDe, rBa; \ + ROLQ $1, rBa; \ + XORQ rBa, rT1; \ + MOVQ rT1, _ka(oState); \ + K_RT1_RCA; \ + \ + XORQ rDu, rBo; \ + ROLQ $8, rBo; \ + MOVQ rBi, rT1; \ + ANDQ rBo, rT1; \ + XORQ rBe, rT1; \ + MOVQ rT1, _ke(oState); \ + K_RT1_RCE; \ + \ + XORQ rDa, rBu; \ + ROLQ $18, rBu; \ + NOTQ rBo; \ + MOVQ rBo, rT1; \ + ANDQ rBu, rT1; \ + XORQ rBi, rT1; \ + MOVQ rT1, _ki(oState); \ + \ + MOVQ rBu, rT1; \ + ORQ rBa, rT1; \ + XORQ rBo, rT1; \ + MOVQ rT1, _ko(oState); \ + \ + ANDQ rBe, rBa; \ + XORQ rBu, rBa; \ + MOVQ rBa, _ku(oState); \ + K_RBA_RCU; \ + \ + /* Result m */ \ + MOVQ _ga(iState), rBe; \ + XORQ rDa, rBe; \ + MOVQ _ke(iState), rBi; \ + ROLQ $36, rBe; \ + XORQ rDe, rBi; \ + MOVQ _bu(iState), rBa; \ + ROLQ $10, rBi; \ + MOVQ rBe, rT1; \ + MOVQ _mi(iState), rBo; \ + ANDQ rBi, rT1; \ + XORQ rDu, rBa; \ + MOVQ _so(iState), rBu; \ + ROLQ $27, rBa; \ + XORQ rBa, rT1; \ + MOVQ rT1, _ma(oState); \ + M_RT1_RCA; \ + \ + XORQ rDi, rBo; \ + ROLQ $15, rBo; \ + MOVQ rBi, rT1; \ + ORQ rBo, rT1; \ + XORQ rBe, rT1; \ + MOVQ rT1, _me(oState); \ + M_RT1_RCE; \ + \ + XORQ rDo, rBu; \ + ROLQ $56, rBu; \ + NOTQ rBo; \ + MOVQ rBo, rT1; \ + ORQ rBu, rT1; \ + XORQ rBi, rT1; \ + MOVQ rT1, _mi(oState); \ + \ + ORQ rBa, rBe; \ + XORQ rBu, rBe; \ + MOVQ rBe, _mu(oState); \ + \ + ANDQ rBa, rBu; \ + XORQ rBo, rBu; \ + MOVQ rBu, _mo(oState); \ + M_RBE_RCU; \ + \ + /* Result s */ \ + MOVQ _bi(iState), rBa; \ + MOVQ _go(iState), rBe; \ + MOVQ _ku(iState), rBi; \ + XORQ rDi, rBa; \ + MOVQ _ma(iState), rBo; \ + ROLQ $62, rBa; \ + XORQ rDo, rBe; \ + MOVQ _se(iState), rBu; \ + ROLQ $55, rBe; \ + \ + XORQ rDu, rBi; \ + MOVQ rBa, rDu; \ + XORQ rDe, rBu; \ + ROLQ $2, rBu; \ + ANDQ rBe, rDu; \ + XORQ rBu, rDu; \ + MOVQ rDu, _su(oState); \ + \ + ROLQ $39, rBi; \ + S_RDU_RCU; \ + NOTQ rBe; \ + XORQ rDa, rBo; \ + MOVQ rBe, rDa; \ + ANDQ rBi, rDa; \ + XORQ rBa, rDa; \ + MOVQ rDa, _sa(oState); \ + S_RDA_RCA; \ + \ + ROLQ $41, rBo; \ + MOVQ rBi, rDe; \ + ORQ rBo, rDe; \ + XORQ rBe, rDe; \ + MOVQ rDe, _se(oState); \ + S_RDE_RCE; \ + \ + MOVQ rBo, rDi; \ + MOVQ rBu, rDo; \ + ANDQ rBu, rDi; \ + ORQ rBa, rDo; \ + XORQ rBi, rDi; \ + XORQ rBo, rDo; \ + MOVQ rDi, _si(oState); \ + MOVQ rDo, _so(oState) \ + +// func KeccakF1600(state *[25]uint64) +TEXT ·KeccakF1600(SB), 0, $200-8 + MOVQ state+0(FP), rpState + + // Convert the user state into an internal state + NOTQ _be(rpState) + NOTQ _bi(rpState) + NOTQ _go(rpState) + NOTQ _ki(rpState) + NOTQ _mi(rpState) + NOTQ _sa(rpState) + + // Execute the KeccakF permutation + MOVQ _ba(rpState), rCa + MOVQ _be(rpState), rCe + MOVQ _bu(rpState), rCu + + XORQ _ga(rpState), rCa + XORQ _ge(rpState), rCe + XORQ _gu(rpState), rCu + + XORQ _ka(rpState), rCa + XORQ _ke(rpState), rCe + XORQ _ku(rpState), rCu + + XORQ _ma(rpState), rCa + XORQ _me(rpState), rCe + XORQ _mu(rpState), rCu + + XORQ _sa(rpState), rCa + XORQ _se(rpState), rCe + MOVQ _si(rpState), rDi + MOVQ _so(rpState), rDo + XORQ _su(rpState), rCu + + mKeccakRound(rpState, rpStack, $0x0000000000000001, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x0000000000008082, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x800000000000808a, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x8000000080008000, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x000000000000808b, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x0000000080000001, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x8000000080008081, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x8000000000008009, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x000000000000008a, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x0000000000000088, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x0000000080008009, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x000000008000000a, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x000000008000808b, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x800000000000008b, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x8000000000008089, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x8000000000008003, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x8000000000008002, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x8000000000000080, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x000000000000800a, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x800000008000000a, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x8000000080008081, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x8000000000008080, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x0000000080000001, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x8000000080008008, NOP, NOP, NOP, NOP, NOP, NOP, NOP, NOP, NOP, NOP, NOP, NOP, NOP) + + // Revert the internal state to the user state + NOTQ _be(rpState) + NOTQ _bi(rpState) + NOTQ _go(rpState) + NOTQ _ki(rpState) + NOTQ _mi(rpState) + NOTQ _sa(rpState) + + RET diff --git a/vendor/github.com/cloudflare/circl/internal/sha3/rc.go b/vendor/github.com/cloudflare/circl/internal/sha3/rc.go new file mode 100644 index 00000000..6a3df42f --- /dev/null +++ b/vendor/github.com/cloudflare/circl/internal/sha3/rc.go @@ -0,0 +1,29 @@ +package sha3 + +// RC stores the round constants for use in the ι step. +var RC = [24]uint64{ + 0x0000000000000001, + 0x0000000000008082, + 0x800000000000808A, + 0x8000000080008000, + 0x000000000000808B, + 0x0000000080000001, + 0x8000000080008081, + 0x8000000000008009, + 0x000000000000008A, + 0x0000000000000088, + 0x0000000080008009, + 0x000000008000000A, + 0x000000008000808B, + 0x800000000000008B, + 0x8000000000008089, + 0x8000000000008003, + 0x8000000000008002, + 0x8000000000000080, + 0x000000000000800A, + 0x800000008000000A, + 0x8000000080008081, + 0x8000000000008080, + 0x0000000080000001, + 0x8000000080008008, +} diff --git a/vendor/github.com/cloudflare/circl/internal/sha3/sha3.go b/vendor/github.com/cloudflare/circl/internal/sha3/sha3.go new file mode 100644 index 00000000..b35cd006 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/internal/sha3/sha3.go @@ -0,0 +1,195 @@ +// Copyright 2014 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package sha3 + +// spongeDirection indicates the direction bytes are flowing through the sponge. +type spongeDirection int + +const ( + // spongeAbsorbing indicates that the sponge is absorbing input. + spongeAbsorbing spongeDirection = iota + // spongeSqueezing indicates that the sponge is being squeezed. + spongeSqueezing +) + +const ( + // maxRate is the maximum size of the internal buffer. SHAKE-256 + // currently needs the largest buffer. + maxRate = 168 +) + +func (d *State) buf() []byte { + return d.storage.asBytes()[d.bufo:d.bufe] +} + +type State struct { + // Generic sponge components. + a [25]uint64 // main state of the hash + rate int // the number of bytes of state to use + + bufo int // offset of buffer in storage + bufe int // end of buffer in storage + + // dsbyte contains the "domain separation" bits and the first bit of + // the padding. Sections 6.1 and 6.2 of [1] separate the outputs of the + // SHA-3 and SHAKE functions by appending bitstrings to the message. + // Using a little-endian bit-ordering convention, these are "01" for SHA-3 + // and "1111" for SHAKE, or 00000010b and 00001111b, respectively. Then the + // padding rule from section 5.1 is applied to pad the message to a multiple + // of the rate, which involves adding a "1" bit, zero or more "0" bits, and + // a final "1" bit. We merge the first "1" bit from the padding into dsbyte, + // giving 00000110b (0x06) and 00011111b (0x1f). + // [1] http://csrc.nist.gov/publications/drafts/fips-202/fips_202_draft.pdf + // "Draft FIPS 202: SHA-3 Standard: Permutation-Based Hash and + // Extendable-Output Functions (May 2014)" + dsbyte byte + + storage storageBuf + + // Specific to SHA-3 and SHAKE. + outputLen int // the default output size in bytes + state spongeDirection // whether the sponge is absorbing or squeezing +} + +// BlockSize returns the rate of sponge underlying this hash function. +func (d *State) BlockSize() int { return d.rate } + +// Size returns the output size of the hash function in bytes. +func (d *State) Size() int { return d.outputLen } + +// Reset clears the internal state by zeroing the sponge state and +// the byte buffer, and setting Sponge.state to absorbing. +func (d *State) Reset() { + // Zero the permutation's state. + for i := range d.a { + d.a[i] = 0 + } + d.state = spongeAbsorbing + d.bufo = 0 + d.bufe = 0 +} + +func (d *State) clone() *State { + ret := *d + return &ret +} + +// permute applies the KeccakF-1600 permutation. It handles +// any input-output buffering. +func (d *State) permute() { + switch d.state { + case spongeAbsorbing: + // If we're absorbing, we need to xor the input into the state + // before applying the permutation. + xorIn(d, d.buf()) + d.bufe = 0 + d.bufo = 0 + KeccakF1600(&d.a) + case spongeSqueezing: + // If we're squeezing, we need to apply the permutation before + // copying more output. + KeccakF1600(&d.a) + d.bufe = d.rate + d.bufo = 0 + copyOut(d, d.buf()) + } +} + +// pads appends the domain separation bits in dsbyte, applies +// the multi-bitrate 10..1 padding rule, and permutes the state. +func (d *State) padAndPermute(dsbyte byte) { + // Pad with this instance's domain-separator bits. We know that there's + // at least one byte of space in d.buf() because, if it were full, + // permute would have been called to empty it. dsbyte also contains the + // first one bit for the padding. See the comment in the state struct. + zerosStart := d.bufe + 1 + d.bufe = d.rate + buf := d.buf() + buf[zerosStart-1] = dsbyte + for i := zerosStart; i < d.rate; i++ { + buf[i] = 0 + } + // This adds the final one bit for the padding. Because of the way that + // bits are numbered from the LSB upwards, the final bit is the MSB of + // the last byte. + buf[d.rate-1] ^= 0x80 + // Apply the permutation + d.permute() + d.state = spongeSqueezing + d.bufe = d.rate + copyOut(d, buf) +} + +// Write absorbs more data into the hash's state. It produces an error +// if more data is written to the ShakeHash after writing +func (d *State) Write(p []byte) (written int, err error) { + if d.state != spongeAbsorbing { + panic("sha3: write to sponge after read") + } + written = len(p) + + for len(p) > 0 { + bufl := d.bufe - d.bufo + if bufl == 0 && len(p) >= d.rate { + // The fast path; absorb a full "rate" bytes of input and apply the permutation. + xorIn(d, p[:d.rate]) + p = p[d.rate:] + KeccakF1600(&d.a) + } else { + // The slow path; buffer the input until we can fill the sponge, and then xor it in. + todo := d.rate - bufl + if todo > len(p) { + todo = len(p) + } + d.bufe += todo + buf := d.buf() + copy(buf[bufl:], p[:todo]) + p = p[todo:] + + // If the sponge is full, apply the permutation. + if d.bufe == d.rate { + d.permute() + } + } + } + + return written, nil +} + +// Read squeezes an arbitrary number of bytes from the sponge. +func (d *State) Read(out []byte) (n int, err error) { + // If we're still absorbing, pad and apply the permutation. + if d.state == spongeAbsorbing { + d.padAndPermute(d.dsbyte) + } + + n = len(out) + + // Now, do the squeezing. + for len(out) > 0 { + buf := d.buf() + n := copy(out, buf) + d.bufo += n + out = out[n:] + + // Apply the permutation if we've squeezed the sponge dry. + if d.bufo == d.bufe { + d.permute() + } + } + + return +} + +// Sum applies padding to the hash state and then squeezes out the desired +// number of output bytes. +func (d *State) Sum(in []byte) []byte { + // Make a copy of the original hash so that caller can keep writing + // and summing. + dup := d.clone() + hash := make([]byte, dup.outputLen) + _, _ = dup.Read(hash) + return append(in, hash...) +} diff --git a/vendor/github.com/cloudflare/circl/internal/sha3/sha3_s390x.s b/vendor/github.com/cloudflare/circl/internal/sha3/sha3_s390x.s new file mode 100644 index 00000000..8a4458f6 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/internal/sha3/sha3_s390x.s @@ -0,0 +1,33 @@ +// Copyright 2017 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// +build !gccgo,!appengine + +#include "textflag.h" + +// func kimd(function code, chain *[200]byte, src []byte) +TEXT ·kimd(SB), NOFRAME|NOSPLIT, $0-40 + MOVD function+0(FP), R0 + MOVD chain+8(FP), R1 + LMG src+16(FP), R2, R3 // R2=base, R3=len + +continue: + WORD $0xB93E0002 // KIMD --, R2 + BVS continue // continue if interrupted + MOVD $0, R0 // reset R0 for pre-go1.8 compilers + RET + +// func klmd(function code, chain *[200]byte, dst, src []byte) +TEXT ·klmd(SB), NOFRAME|NOSPLIT, $0-64 + // TODO: SHAKE support + MOVD function+0(FP), R0 + MOVD chain+8(FP), R1 + LMG dst+16(FP), R2, R3 // R2=base, R3=len + LMG src+40(FP), R4, R5 // R4=base, R5=len + +continue: + WORD $0xB93F0024 // KLMD R2, R4 + BVS continue // continue if interrupted + MOVD $0, R0 // reset R0 for pre-go1.8 compilers + RET diff --git a/vendor/github.com/cloudflare/circl/internal/sha3/shake.go b/vendor/github.com/cloudflare/circl/internal/sha3/shake.go new file mode 100644 index 00000000..b92c5b7d --- /dev/null +++ b/vendor/github.com/cloudflare/circl/internal/sha3/shake.go @@ -0,0 +1,79 @@ +// Copyright 2014 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package sha3 + +// This file defines the ShakeHash interface, and provides +// functions for creating SHAKE and cSHAKE instances, as well as utility +// functions for hashing bytes to arbitrary-length output. +// +// +// SHAKE implementation is based on FIPS PUB 202 [1] +// cSHAKE implementations is based on NIST SP 800-185 [2] +// +// [1] https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.202.pdf +// [2] https://doi.org/10.6028/NIST.SP.800-185 + +import ( + "io" +) + +// ShakeHash defines the interface to hash functions that +// support arbitrary-length output. +type ShakeHash interface { + // Write absorbs more data into the hash's state. It panics if input is + // written to it after output has been read from it. + io.Writer + + // Read reads more output from the hash; reading affects the hash's + // state. (ShakeHash.Read is thus very different from Hash.Sum) + // It never returns an error. + io.Reader + + // Clone returns a copy of the ShakeHash in its current state. + Clone() ShakeHash + + // Reset resets the ShakeHash to its initial state. + Reset() +} + +// Consts for configuring initial SHA-3 state +const ( + dsbyteShake = 0x1f + rate128 = 168 + rate256 = 136 +) + +// Clone returns copy of SHAKE context within its current state. +func (d *State) Clone() ShakeHash { + return d.clone() +} + +// NewShake128 creates a new SHAKE128 variable-output-length ShakeHash. +// Its generic security strength is 128 bits against all attacks if at +// least 32 bytes of its output are used. +func NewShake128() State { + return State{rate: rate128, dsbyte: dsbyteShake} +} + +// NewShake256 creates a new SHAKE256 variable-output-length ShakeHash. +// Its generic security strength is 256 bits against all attacks if +// at least 64 bytes of its output are used. +func NewShake256() State { + return State{rate: rate256, dsbyte: dsbyteShake} +} + +// ShakeSum128 writes an arbitrary-length digest of data into hash. +func ShakeSum128(hash, data []byte) { + h := NewShake128() + _, _ = h.Write(data) + _, _ = h.Read(hash) +} + +// ShakeSum256 writes an arbitrary-length digest of data into hash. +func ShakeSum256(hash, data []byte) { + h := NewShake256() + _, _ = h.Write(data) + _, _ = h.Read(hash) +} diff --git a/vendor/github.com/cloudflare/circl/internal/sha3/xor.go b/vendor/github.com/cloudflare/circl/internal/sha3/xor.go new file mode 100644 index 00000000..1e213374 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/internal/sha3/xor.go @@ -0,0 +1,15 @@ +// Copyright 2015 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +//go:build (!amd64 && !386 && !ppc64le) || appengine +// +build !amd64,!386,!ppc64le appengine + +package sha3 + +// A storageBuf is an aligned array of maxRate bytes. +type storageBuf [maxRate]byte + +func (b *storageBuf) asBytes() *[maxRate]byte { + return (*[maxRate]byte)(b) +} diff --git a/vendor/github.com/cloudflare/circl/internal/sha3/xor_generic.go b/vendor/github.com/cloudflare/circl/internal/sha3/xor_generic.go new file mode 100644 index 00000000..2b0c6617 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/internal/sha3/xor_generic.go @@ -0,0 +1,33 @@ +// Copyright 2015 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +//go:build (!amd64 || appengine) && (!386 || appengine) && (!ppc64le || appengine) +// +build !amd64 appengine +// +build !386 appengine +// +build !ppc64le appengine + +package sha3 + +import "encoding/binary" + +// xorIn xors the bytes in buf into the state; it +// makes no non-portable assumptions about memory layout +// or alignment. +func xorIn(d *State, buf []byte) { + n := len(buf) / 8 + + for i := 0; i < n; i++ { + a := binary.LittleEndian.Uint64(buf) + d.a[i] ^= a + buf = buf[8:] + } +} + +// copyOut copies ulint64s to a byte buffer. +func copyOut(d *State, b []byte) { + for i := 0; len(b) >= 8; i++ { + binary.LittleEndian.PutUint64(b, d.a[i]) + b = b[8:] + } +} diff --git a/vendor/github.com/cloudflare/circl/internal/sha3/xor_unaligned.go b/vendor/github.com/cloudflare/circl/internal/sha3/xor_unaligned.go new file mode 100644 index 00000000..052fc8d3 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/internal/sha3/xor_unaligned.go @@ -0,0 +1,61 @@ +// Copyright 2015 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +//go:build (amd64 || 386 || ppc64le) && !appengine +// +build amd64 386 ppc64le +// +build !appengine + +package sha3 + +import "unsafe" + +// A storageBuf is an aligned array of maxRate bytes. +type storageBuf [maxRate / 8]uint64 + +func (b *storageBuf) asBytes() *[maxRate]byte { + return (*[maxRate]byte)(unsafe.Pointer(b)) +} + +// xorInuses unaligned reads and writes to update d.a to contain d.a +// XOR buf. +func xorIn(d *State, buf []byte) { + n := len(buf) + bw := (*[maxRate / 8]uint64)(unsafe.Pointer(&buf[0]))[: n/8 : n/8] + if n >= 72 { + d.a[0] ^= bw[0] + d.a[1] ^= bw[1] + d.a[2] ^= bw[2] + d.a[3] ^= bw[3] + d.a[4] ^= bw[4] + d.a[5] ^= bw[5] + d.a[6] ^= bw[6] + d.a[7] ^= bw[7] + d.a[8] ^= bw[8] + } + if n >= 104 { + d.a[9] ^= bw[9] + d.a[10] ^= bw[10] + d.a[11] ^= bw[11] + d.a[12] ^= bw[12] + } + if n >= 136 { + d.a[13] ^= bw[13] + d.a[14] ^= bw[14] + d.a[15] ^= bw[15] + d.a[16] ^= bw[16] + } + if n >= 144 { + d.a[17] ^= bw[17] + } + if n >= 168 { + d.a[18] ^= bw[18] + d.a[19] ^= bw[19] + d.a[20] ^= bw[20] + } +} + +func copyOut(d *State, buf []byte) { + ab := (*[maxRate]uint8)(unsafe.Pointer(&d.a[0])) + copy(buf, ab[:]) +} diff --git a/vendor/github.com/cloudflare/circl/kem/hybrid/hybrid.go b/vendor/github.com/cloudflare/circl/kem/hybrid/hybrid.go new file mode 100644 index 00000000..f0384278 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/kem/hybrid/hybrid.go @@ -0,0 +1,335 @@ +// Package hybrid defines several hybrid classical/quantum KEMs. +// +// KEMs are combined by simple concatenation of shared secrets, cipher texts, +// public keys, etc, see +// +// https://datatracker.ietf.org/doc/draft-ietf-tls-hybrid-design/ +// https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-56Cr2.pdf +// +// Note that this is only fine if the shared secret is used in its entirety +// in a next step, such as being hashed or used as key. +// +// For deriving a KEM keypair deterministically and encapsulating +// deterministically, we expand a single seed to both using SHAKE256, +// so that a non-uniform seed (such as a shared secret generated by a hybrid +// KEM where one of the KEMs is weak) doesn't impact just one of the KEMs. +// +// Of our XOF (SHAKE256), we desire two security properties: +// +// 1. The internal state of the XOF should be big enough so that we +// do not loose entropy. +// 2. From one of the new seeds, we shouldn't be able to derive +// the other or the original seed. +// +// SHAKE256, and all siblings in the SHA3 family, have a 200B internal +// state, so (1) is fine if our seeds are less than 200B. +// If SHAKE256 is computationally indistinguishable from a random +// sponge, then it affords us 256b security against (2) by the +// flat sponge claim [https://keccak.team/files/SpongeFunctions.pdf]. +// None of the implemented schemes claim more than 256b security +// and so SHAKE256 will do fine. +package hybrid + +import ( + "errors" + + "github.com/cloudflare/circl/internal/sha3" + "github.com/cloudflare/circl/kem" + "github.com/cloudflare/circl/kem/kyber/kyber1024" + "github.com/cloudflare/circl/kem/kyber/kyber512" + "github.com/cloudflare/circl/kem/kyber/kyber768" +) + +var ErrUninitialized = errors.New("public or private key not initialized") + +// Returns the hybrid KEM of Kyber512 and X25519. +func Kyber512X25519() kem.Scheme { return kyber512X } + +// Returns the hybrid KEM of Kyber768 and X25519. +func Kyber768X25519() kem.Scheme { return kyber768X } + +// Returns the hybrid KEM of Kyber768 and X448. +func Kyber768X448() kem.Scheme { return kyber768X4 } + +// Returns the hybrid KEM of Kyber1024 and X448. +func Kyber1024X448() kem.Scheme { return kyber1024X } + +var kyber512X kem.Scheme = &scheme{ + "Kyber512-X25519", + x25519Kem, + kyber512.Scheme(), +} + +var kyber768X kem.Scheme = &scheme{ + "Kyber768-X25519", + x25519Kem, + kyber768.Scheme(), +} + +var kyber768X4 kem.Scheme = &scheme{ + "Kyber768-X448", + x448Kem, + kyber768.Scheme(), +} + +var kyber1024X kem.Scheme = &scheme{ + "Kyber1024-X448", + x448Kem, + kyber1024.Scheme(), +} + +// Public key of a hybrid KEM. +type publicKey struct { + scheme *scheme + first kem.PublicKey + second kem.PublicKey +} + +// Private key of a hybrid KEM. +type privateKey struct { + scheme *scheme + first kem.PrivateKey + second kem.PrivateKey +} + +// Scheme for a hybrid KEM. +type scheme struct { + name string + first kem.Scheme + second kem.Scheme +} + +func (sch *scheme) Name() string { return sch.name } +func (sch *scheme) PublicKeySize() int { + return sch.first.PublicKeySize() + sch.second.PublicKeySize() +} + +func (sch *scheme) PrivateKeySize() int { + return sch.first.PrivateKeySize() + sch.second.PrivateKeySize() +} + +func (sch *scheme) SeedSize() int { + first := sch.first.SeedSize() + second := sch.second.SeedSize() + ret := second + if first > second { + ret = first + } + return ret +} + +func (sch *scheme) SharedKeySize() int { + return sch.first.SharedKeySize() + sch.second.SharedKeySize() +} + +func (sch *scheme) CiphertextSize() int { + return sch.first.CiphertextSize() + sch.second.CiphertextSize() +} + +func (sch *scheme) EncapsulationSeedSize() int { + first := sch.first.EncapsulationSeedSize() + second := sch.second.EncapsulationSeedSize() + ret := second + if first > second { + ret = first + } + return ret +} + +func (sk *privateKey) Scheme() kem.Scheme { return sk.scheme } +func (pk *publicKey) Scheme() kem.Scheme { return pk.scheme } + +func (sk *privateKey) MarshalBinary() ([]byte, error) { + if sk.first == nil || sk.second == nil { + return nil, ErrUninitialized + } + first, err := sk.first.MarshalBinary() + if err != nil { + return nil, err + } + second, err := sk.second.MarshalBinary() + if err != nil { + return nil, err + } + return append(first, second...), nil +} + +func (sk *privateKey) Equal(other kem.PrivateKey) bool { + oth, ok := other.(*privateKey) + if !ok { + return false + } + if sk.first == nil && sk.second == nil && oth.first == nil && oth.second == nil { + return true + } + if sk.first == nil || sk.second == nil || oth.first == nil || oth.second == nil { + return false + } + return sk.first.Equal(oth.first) && sk.second.Equal(oth.second) +} + +func (sk *privateKey) Public() kem.PublicKey { + return &publicKey{sk.scheme, sk.first.Public(), sk.second.Public()} +} + +func (pk *publicKey) Equal(other kem.PublicKey) bool { + oth, ok := other.(*publicKey) + if !ok { + return false + } + if pk.first == nil && pk.second == nil && oth.first == nil && oth.second == nil { + return true + } + if pk.first == nil || pk.second == nil || oth.first == nil || oth.second == nil { + return false + } + return pk.first.Equal(oth.first) && pk.second.Equal(oth.second) +} + +func (pk *publicKey) MarshalBinary() ([]byte, error) { + if pk.first == nil || pk.second == nil { + return nil, ErrUninitialized + } + first, err := pk.first.MarshalBinary() + if err != nil { + return nil, err + } + second, err := pk.second.MarshalBinary() + if err != nil { + return nil, err + } + return append(first, second...), nil +} + +func (sch *scheme) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { + pk1, sk1, err := sch.first.GenerateKeyPair() + if err != nil { + return nil, nil, err + } + pk2, sk2, err := sch.second.GenerateKeyPair() + if err != nil { + return nil, nil, err + } + + return &publicKey{sch, pk1, pk2}, &privateKey{sch, sk1, sk2}, nil +} + +func (sch *scheme) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { + if len(seed) != sch.SeedSize() { + panic(kem.ErrSeedSize) + } + h := sha3.NewShake256() + _, _ = h.Write(seed) + first := make([]byte, sch.first.SeedSize()) + second := make([]byte, sch.second.SeedSize()) + _, _ = h.Read(first) + _, _ = h.Read(second) + + pk1, sk1 := sch.first.DeriveKeyPair(first) + pk2, sk2 := sch.second.DeriveKeyPair(second) + + return &publicKey{sch, pk1, pk2}, &privateKey{sch, sk1, sk2} +} + +func (sch *scheme) Encapsulate(pk kem.PublicKey) (ct, ss []byte, err error) { + pub, ok := pk.(*publicKey) + if !ok { + return nil, nil, kem.ErrTypeMismatch + } + + ct1, ss1, err := sch.first.Encapsulate(pub.first) + if err != nil { + return nil, nil, err + } + + ct2, ss2, err := sch.second.Encapsulate(pub.second) + if err != nil { + return nil, nil, err + } + + return append(ct1, ct2...), append(ss1, ss2...), nil +} + +func (sch *scheme) EncapsulateDeterministically( + pk kem.PublicKey, seed []byte, +) (ct, ss []byte, err error) { + if len(seed) != sch.EncapsulationSeedSize() { + return nil, nil, kem.ErrSeedSize + } + + h := sha3.NewShake256() + _, _ = h.Write(seed) + first := make([]byte, sch.first.EncapsulationSeedSize()) + second := make([]byte, sch.second.EncapsulationSeedSize()) + _, _ = h.Read(first) + _, _ = h.Read(second) + + pub, ok := pk.(*publicKey) + if !ok { + return nil, nil, kem.ErrTypeMismatch + } + + ct1, ss1, err := sch.first.EncapsulateDeterministically(pub.first, first) + if err != nil { + return nil, nil, err + } + ct2, ss2, err := sch.second.EncapsulateDeterministically(pub.second, second) + if err != nil { + return nil, nil, err + } + return append(ct1, ct2...), append(ss1, ss2...), nil +} + +func (sch *scheme) Decapsulate(sk kem.PrivateKey, ct []byte) ([]byte, error) { + if len(ct) != sch.CiphertextSize() { + return nil, kem.ErrCiphertextSize + } + + priv, ok := sk.(*privateKey) + if !ok { + return nil, kem.ErrTypeMismatch + } + + firstSize := sch.first.CiphertextSize() + ss1, err := sch.first.Decapsulate(priv.first, ct[:firstSize]) + if err != nil { + return nil, err + } + ss2, err := sch.second.Decapsulate(priv.second, ct[firstSize:]) + if err != nil { + return nil, err + } + return append(ss1, ss2...), nil +} + +func (sch *scheme) UnmarshalBinaryPublicKey(buf []byte) (kem.PublicKey, error) { + if len(buf) != sch.PublicKeySize() { + return nil, kem.ErrPubKeySize + } + firstSize := sch.first.PublicKeySize() + pk1, err := sch.first.UnmarshalBinaryPublicKey(buf[:firstSize]) + if err != nil { + return nil, err + } + pk2, err := sch.second.UnmarshalBinaryPublicKey(buf[firstSize:]) + if err != nil { + return nil, err + } + return &publicKey{sch, pk1, pk2}, nil +} + +func (sch *scheme) UnmarshalBinaryPrivateKey(buf []byte) (kem.PrivateKey, error) { + if len(buf) != sch.PrivateKeySize() { + return nil, kem.ErrPrivKeySize + } + firstSize := sch.first.PrivateKeySize() + sk1, err := sch.first.UnmarshalBinaryPrivateKey(buf[:firstSize]) + if err != nil { + return nil, err + } + sk2, err := sch.second.UnmarshalBinaryPrivateKey(buf[firstSize:]) + if err != nil { + return nil, err + } + return &privateKey{sch, sk1, sk2}, nil +} diff --git a/vendor/github.com/cloudflare/circl/kem/hybrid/xkem.go b/vendor/github.com/cloudflare/circl/kem/hybrid/xkem.go new file mode 100644 index 00000000..919fb8a9 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/kem/hybrid/xkem.go @@ -0,0 +1,208 @@ +package hybrid + +import ( + "bytes" + cryptoRand "crypto/rand" + "crypto/subtle" + + "github.com/cloudflare/circl/dh/x25519" + "github.com/cloudflare/circl/dh/x448" + "github.com/cloudflare/circl/internal/sha3" + "github.com/cloudflare/circl/kem" +) + +type xPublicKey struct { + scheme *xScheme + key []byte +} +type xPrivateKey struct { + scheme *xScheme + key []byte +} +type xScheme struct { + size int +} + +var ( + x25519Kem = &xScheme{x25519.Size} + x448Kem = &xScheme{x448.Size} +) + +func (sch *xScheme) Name() string { + switch sch.size { + case x25519.Size: + return "X25519" + case x448.Size: + return "X448" + } + panic(kem.ErrTypeMismatch) +} + +func (sch *xScheme) PublicKeySize() int { return sch.size } +func (sch *xScheme) PrivateKeySize() int { return sch.size } +func (sch *xScheme) SeedSize() int { return sch.size } +func (sch *xScheme) SharedKeySize() int { return sch.size } +func (sch *xScheme) CiphertextSize() int { return sch.size } +func (sch *xScheme) EncapsulationSeedSize() int { return sch.size } + +func (sk *xPrivateKey) Scheme() kem.Scheme { return sk.scheme } +func (pk *xPublicKey) Scheme() kem.Scheme { return pk.scheme } + +func (sk *xPrivateKey) MarshalBinary() ([]byte, error) { + ret := make([]byte, len(sk.key)) + copy(ret, sk.key) + return ret, nil +} + +func (sk *xPrivateKey) Equal(other kem.PrivateKey) bool { + oth, ok := other.(*xPrivateKey) + if !ok { + return false + } + if oth.scheme != sk.scheme { + return false + } + return subtle.ConstantTimeCompare(oth.key, sk.key) == 1 +} + +func (sk *xPrivateKey) Public() kem.PublicKey { + pk := xPublicKey{sk.scheme, make([]byte, sk.scheme.size)} + switch sk.scheme.size { + case x25519.Size: + var sk2, pk2 x25519.Key + copy(sk2[:], sk.key) + x25519.KeyGen(&pk2, &sk2) + copy(pk.key, pk2[:]) + case x448.Size: + var sk2, pk2 x448.Key + copy(sk2[:], sk.key) + x448.KeyGen(&pk2, &sk2) + copy(pk.key, pk2[:]) + } + return &pk +} + +func (pk *xPublicKey) Equal(other kem.PublicKey) bool { + oth, ok := other.(*xPublicKey) + if !ok { + return false + } + if oth.scheme != pk.scheme { + return false + } + return bytes.Equal(oth.key, pk.key) +} + +func (pk *xPublicKey) MarshalBinary() ([]byte, error) { + ret := make([]byte, pk.scheme.size) + copy(ret, pk.key) + return ret, nil +} + +func (sch *xScheme) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { + seed := make([]byte, sch.SeedSize()) + _, err := cryptoRand.Read(seed) + if err != nil { + return nil, nil, err + } + pk, sk := sch.DeriveKeyPair(seed) + return pk, sk, nil +} + +func (sch *xScheme) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { + if len(seed) != sch.SeedSize() { + panic(kem.ErrSeedSize) + } + sk := xPrivateKey{scheme: sch, key: make([]byte, sch.size)} + + h := sha3.NewShake256() + _, _ = h.Write(seed) + _, _ = h.Read(sk.key) + + return sk.Public(), &sk +} + +func (sch *xScheme) Encapsulate(pk kem.PublicKey) (ct, ss []byte, err error) { + seed := make([]byte, sch.EncapsulationSeedSize()) + _, err = cryptoRand.Read(seed) + if err != nil { + return + } + return sch.EncapsulateDeterministically(pk, seed) +} + +func (pk *xPublicKey) X(sk *xPrivateKey) []byte { + if pk.scheme != sk.scheme { + panic(kem.ErrTypeMismatch) + } + + switch pk.scheme.size { + case x25519.Size: + var ss2, pk2, sk2 x25519.Key + copy(pk2[:], pk.key) + copy(sk2[:], sk.key) + x25519.Shared(&ss2, &sk2, &pk2) + return ss2[:] + case x448.Size: + var ss2, pk2, sk2 x448.Key + copy(pk2[:], pk.key) + copy(sk2[:], sk.key) + x448.Shared(&ss2, &sk2, &pk2) + return ss2[:] + } + panic(kem.ErrTypeMismatch) +} + +func (sch *xScheme) EncapsulateDeterministically( + pk kem.PublicKey, seed []byte, +) (ct, ss []byte, err error) { + if len(seed) != sch.EncapsulationSeedSize() { + return nil, nil, kem.ErrSeedSize + } + pub, ok := pk.(*xPublicKey) + if !ok || pub.scheme != sch { + return nil, nil, kem.ErrTypeMismatch + } + + pk2, sk2 := sch.DeriveKeyPair(seed) + ss = pub.X(sk2.(*xPrivateKey)) + ct, _ = pk2.MarshalBinary() + return +} + +func (sch *xScheme) Decapsulate(sk kem.PrivateKey, ct []byte) ([]byte, error) { + if len(ct) != sch.CiphertextSize() { + return nil, kem.ErrCiphertextSize + } + + priv, ok := sk.(*xPrivateKey) + if !ok || priv.scheme != sch { + return nil, kem.ErrTypeMismatch + } + + pk, err := sch.UnmarshalBinaryPublicKey(ct) + if err != nil { + return nil, err + } + + ss := pk.(*xPublicKey).X(priv) + return ss, nil +} + +func (sch *xScheme) UnmarshalBinaryPublicKey(buf []byte) (kem.PublicKey, error) { + if len(buf) != sch.PublicKeySize() { + return nil, kem.ErrPubKeySize + } + ret := xPublicKey{sch, make([]byte, sch.size)} + copy(ret.key, buf) + return &ret, nil +} + +func (sch *xScheme) UnmarshalBinaryPrivateKey(buf []byte) (kem.PrivateKey, error) { + if len(buf) != sch.PrivateKeySize() { + return nil, kem.ErrPrivKeySize + } + ret := xPrivateKey{sch, make([]byte, sch.size)} + copy(ret.key, buf) + return &ret, nil +} diff --git a/vendor/github.com/cloudflare/circl/kem/kem.go b/vendor/github.com/cloudflare/circl/kem/kem.go new file mode 100644 index 00000000..ca550c65 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/kem/kem.go @@ -0,0 +1,118 @@ +// Package kem provides a unified interface for KEM schemes. +// +// A register of schemes is available in the package +// +// github.com/cloudflare/circl/kem/schemes +package kem + +import ( + "encoding" + "errors" +) + +// A KEM public key +type PublicKey interface { + // Returns the scheme for this public key + Scheme() Scheme + + encoding.BinaryMarshaler + Equal(PublicKey) bool +} + +// A KEM private key +type PrivateKey interface { + // Returns the scheme for this private key + Scheme() Scheme + + encoding.BinaryMarshaler + Equal(PrivateKey) bool + Public() PublicKey +} + +// A Scheme represents a specific instance of a KEM. +type Scheme interface { + // Name of the scheme + Name() string + + // GenerateKeyPair creates a new key pair. + GenerateKeyPair() (PublicKey, PrivateKey, error) + + // Encapsulate generates a shared key ss for the public key and + // encapsulates it into a ciphertext ct. + Encapsulate(pk PublicKey) (ct, ss []byte, err error) + + // Returns the shared key encapsulated in ciphertext ct for the + // private key sk. + Decapsulate(sk PrivateKey, ct []byte) ([]byte, error) + + // Unmarshals a PublicKey from the provided buffer. + UnmarshalBinaryPublicKey([]byte) (PublicKey, error) + + // Unmarshals a PrivateKey from the provided buffer. + UnmarshalBinaryPrivateKey([]byte) (PrivateKey, error) + + // Size of encapsulated keys. + CiphertextSize() int + + // Size of established shared keys. + SharedKeySize() int + + // Size of packed private keys. + PrivateKeySize() int + + // Size of packed public keys. + PublicKeySize() int + + // DeriveKeyPair deterministicallly derives a pair of keys from a seed. + // Panics if the length of seed is not equal to the value returned by + // SeedSize. + DeriveKeyPair(seed []byte) (PublicKey, PrivateKey) + + // Size of seed used in DeriveKey + SeedSize() int + + // EncapsulateDeterministically generates a shared key ss for the public + // key deterministically from the given seed and encapsulates it into + // a ciphertext ct. If unsure, you're better off using Encapsulate(). + EncapsulateDeterministically(pk PublicKey, seed []byte) ( + ct, ss []byte, err error) + + // Size of seed used in EncapsulateDeterministically(). + EncapsulationSeedSize() int +} + +// AuthScheme represents a KEM that supports authenticated key encapsulation. +type AuthScheme interface { + Scheme + AuthEncapsulate(pkr PublicKey, sks PrivateKey) (ct, ss []byte, err error) + AuthEncapsulateDeterministically(pkr PublicKey, sks PrivateKey, seed []byte) (ct, ss []byte, err error) + AuthDecapsulate(skr PrivateKey, ct []byte, pks PublicKey) ([]byte, error) +} + +var ( + // ErrTypeMismatch is the error used if types of, for instance, private + // and public keys don't match + ErrTypeMismatch = errors.New("types mismatch") + + // ErrSeedSize is the error used if the provided seed is of the wrong + // size. + ErrSeedSize = errors.New("wrong seed size") + + // ErrPubKeySize is the error used if the provided public key is of + // the wrong size. + ErrPubKeySize = errors.New("wrong size for public key") + + // ErrCiphertextSize is the error used if the provided ciphertext + // is of the wrong size. + ErrCiphertextSize = errors.New("wrong size for ciphertext") + + // ErrPrivKeySize is the error used if the provided private key is of + // the wrong size. + ErrPrivKeySize = errors.New("wrong size for private key") + + // ErrPubKey is the error used if the provided public key is invalid. + ErrPubKey = errors.New("invalid public key") + + // ErrCipherText is the error used if the provided ciphertext is invalid. + ErrCipherText = errors.New("invalid ciphertext") +) diff --git a/vendor/github.com/cloudflare/circl/kem/kyber/kyber1024/kyber.go b/vendor/github.com/cloudflare/circl/kem/kyber/kyber1024/kyber.go new file mode 100644 index 00000000..223c842e --- /dev/null +++ b/vendor/github.com/cloudflare/circl/kem/kyber/kyber1024/kyber.go @@ -0,0 +1,402 @@ +// Code generated from pkg.templ.go. DO NOT EDIT. + +// Package kyber1024 implements the IND-CCA2 secure key encapsulation mechanism +// Kyber1024.CCAKEM as submitted to round 3 of the NIST PQC competition and +// described in +// +// https://pq-crystals.org/kyber/data/kyber-specification-round3.pdf +package kyber1024 + +import ( + "bytes" + "crypto/subtle" + "io" + + cryptoRand "crypto/rand" + "github.com/cloudflare/circl/internal/sha3" + "github.com/cloudflare/circl/kem" + cpapke "github.com/cloudflare/circl/pke/kyber/kyber1024" +) + +const ( + // Size of seed for NewKeyFromSeed + KeySeedSize = cpapke.KeySeedSize + 32 + + // Size of seed for EncapsulateTo. + EncapsulationSeedSize = 32 + + // Size of the established shared key. + SharedKeySize = 32 + + // Size of the encapsulated shared key. + CiphertextSize = cpapke.CiphertextSize + + // Size of a packed public key. + PublicKeySize = cpapke.PublicKeySize + + // Size of a packed private key. + PrivateKeySize = cpapke.PrivateKeySize + cpapke.PublicKeySize + 64 +) + +// Type of a Kyber1024.CCAKEM public key +type PublicKey struct { + pk *cpapke.PublicKey + + hpk [32]byte // H(pk) +} + +// Type of a Kyber1024.CCAKEM private key +type PrivateKey struct { + sk *cpapke.PrivateKey + pk *cpapke.PublicKey + hpk [32]byte // H(pk) + z [32]byte +} + +// NewKeyFromSeed derives a public/private keypair deterministically +// from the given seed. +// +// Panics if seed is not of length KeySeedSize. +func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { + var sk PrivateKey + var pk PublicKey + + if len(seed) != KeySeedSize { + panic("seed must be of length KeySeedSize") + } + + pk.pk, sk.sk = cpapke.NewKeyFromSeed(seed[:cpapke.KeySeedSize]) + sk.pk = pk.pk + copy(sk.z[:], seed[cpapke.KeySeedSize:]) + + // Compute H(pk) + var ppk [cpapke.PublicKeySize]byte + sk.pk.Pack(ppk[:]) + h := sha3.New256() + h.Write(ppk[:]) + h.Read(sk.hpk[:]) + copy(pk.hpk[:], sk.hpk[:]) + + return &pk, &sk +} + +// GenerateKeyPair generates public and private keys using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKeyPair(rand io.Reader) (*PublicKey, *PrivateKey, error) { + var seed [KeySeedSize]byte + if rand == nil { + rand = cryptoRand.Reader + } + _, err := io.ReadFull(rand, seed[:]) + if err != nil { + return nil, nil, err + } + pk, sk := NewKeyFromSeed(seed[:]) + return pk, sk, nil +} + +// EncapsulateTo generates a shared key and ciphertext that contains it +// for the public key using randomness from seed and writes the shared key +// to ss and ciphertext to ct. +// +// Panics if ss, ct or seed are not of length SharedKeySize, CiphertextSize +// and EncapsulationSeedSize respectively. +// +// seed may be nil, in which case crypto/rand.Reader is used to generate one. +func (pk *PublicKey) EncapsulateTo(ct, ss []byte, seed []byte) { + if seed == nil { + seed = make([]byte, EncapsulationSeedSize) + cryptoRand.Read(seed[:]) + } else { + if len(seed) != EncapsulationSeedSize { + panic("seed must be of length EncapsulationSeedSize") + } + } + + if len(ct) != CiphertextSize { + panic("ct must be of length CiphertextSize") + } + + if len(ss) != SharedKeySize { + panic("ss must be of length SharedKeySize") + } + + // m = H(seed) + var m [32]byte + h := sha3.New256() + h.Write(seed[:]) + h.Read(m[:]) + + // (K', r) = G(m ‖ H(pk)) + var kr [64]byte + g := sha3.New512() + g.Write(m[:]) + g.Write(pk.hpk[:]) + g.Read(kr[:]) + + // c = Kyber.CPAPKE.Enc(pk, m, r) + pk.pk.EncryptTo(ct, m[:], kr[32:]) + + // Compute H(c) and put in second slot of kr, which will be (K', H(c)). + h.Reset() + h.Write(ct[:CiphertextSize]) + h.Read(kr[32:]) + + // K = KDF(K' ‖ H(c)) + kdf := sha3.NewShake256() + kdf.Write(kr[:]) + kdf.Read(ss[:SharedKeySize]) +} + +// DecapsulateTo computes the shared key which is encapsulated in ct +// for the private key. +// +// Panics if ct or ss are not of length CiphertextSize and SharedKeySize +// respectively. +func (sk *PrivateKey) DecapsulateTo(ss, ct []byte) { + if len(ct) != CiphertextSize { + panic("ct must be of length CiphertextSize") + } + + if len(ss) != SharedKeySize { + panic("ss must be of length SharedKeySize") + } + + // m' = Kyber.CPAPKE.Dec(sk, ct) + var m2 [32]byte + sk.sk.DecryptTo(m2[:], ct) + + // (K'', r') = G(m' ‖ H(pk)) + var kr2 [64]byte + g := sha3.New512() + g.Write(m2[:]) + g.Write(sk.hpk[:]) + g.Read(kr2[:]) + + // c' = Kyber.CPAPKE.Enc(pk, m', r') + var ct2 [CiphertextSize]byte + sk.pk.EncryptTo(ct2[:], m2[:], kr2[32:]) + + // Compute H(c) and put in second slot of kr2, which will be (K'', H(c)). + h := sha3.New256() + h.Write(ct[:CiphertextSize]) + h.Read(kr2[32:]) + + // Replace K'' by z in the first slot of kr2 if c ≠ c'. + subtle.ConstantTimeCopy( + 1-subtle.ConstantTimeCompare(ct, ct2[:]), + kr2[:32], + sk.z[:], + ) + + // K = KDF(K''/z, H(c)) + kdf := sha3.NewShake256() + kdf.Write(kr2[:]) + kdf.Read(ss[:SharedKeySize]) +} + +// Packs sk to buf. +// +// Panics if buf is not of size PrivateKeySize. +func (sk *PrivateKey) Pack(buf []byte) { + if len(buf) != PrivateKeySize { + panic("buf must be of length PrivateKeySize") + } + + sk.sk.Pack(buf[:cpapke.PrivateKeySize]) + buf = buf[cpapke.PrivateKeySize:] + sk.pk.Pack(buf[:cpapke.PublicKeySize]) + buf = buf[cpapke.PublicKeySize:] + copy(buf, sk.hpk[:]) + buf = buf[32:] + copy(buf, sk.z[:]) +} + +// Unpacks sk from buf. +// +// Panics if buf is not of size PrivateKeySize. +func (sk *PrivateKey) Unpack(buf []byte) { + if len(buf) != PrivateKeySize { + panic("buf must be of length PrivateKeySize") + } + + sk.sk = new(cpapke.PrivateKey) + sk.sk.Unpack(buf[:cpapke.PrivateKeySize]) + buf = buf[cpapke.PrivateKeySize:] + sk.pk = new(cpapke.PublicKey) + sk.pk.Unpack(buf[:cpapke.PublicKeySize]) + buf = buf[cpapke.PublicKeySize:] + copy(sk.hpk[:], buf[:32]) + copy(sk.z[:], buf[32:]) +} + +// Packs pk to buf. +// +// Panics if buf is not of size PublicKeySize. +func (pk *PublicKey) Pack(buf []byte) { + if len(buf) != PublicKeySize { + panic("buf must be of length PublicKeySize") + } + + pk.pk.Pack(buf) +} + +// Unpacks pk from buf. +// +// Panics if buf is not of size PublicKeySize. +func (pk *PublicKey) Unpack(buf []byte) { + if len(buf) != PublicKeySize { + panic("buf must be of length PublicKeySize") + } + + pk.pk = new(cpapke.PublicKey) + pk.pk.Unpack(buf) + + // Compute cached H(pk) + h := sha3.New256() + h.Write(buf) + h.Read(pk.hpk[:]) +} + +// Boilerplate down below for the KEM scheme API. + +type scheme struct{} + +var sch kem.Scheme = &scheme{} + +// Scheme returns a KEM interface. +func Scheme() kem.Scheme { return sch } + +func (*scheme) Name() string { return "Kyber1024" } +func (*scheme) PublicKeySize() int { return PublicKeySize } +func (*scheme) PrivateKeySize() int { return PrivateKeySize } +func (*scheme) SeedSize() int { return KeySeedSize } +func (*scheme) SharedKeySize() int { return SharedKeySize } +func (*scheme) CiphertextSize() int { return CiphertextSize } +func (*scheme) EncapsulationSeedSize() int { return EncapsulationSeedSize } + +func (sk *PrivateKey) Scheme() kem.Scheme { return sch } +func (pk *PublicKey) Scheme() kem.Scheme { return sch } + +func (sk *PrivateKey) MarshalBinary() ([]byte, error) { + var ret [PrivateKeySize]byte + sk.Pack(ret[:]) + return ret[:], nil +} + +func (sk *PrivateKey) Equal(other kem.PrivateKey) bool { + oth, ok := other.(*PrivateKey) + if !ok { + return false + } + if sk.pk == nil && oth.pk == nil { + return true + } + if sk.pk == nil || oth.pk == nil { + return false + } + if !bytes.Equal(sk.hpk[:], oth.hpk[:]) || + !bytes.Equal(sk.z[:], oth.z[:]) { + return false + } + return sk.sk.Equal(oth.sk) +} + +func (pk *PublicKey) Equal(other kem.PublicKey) bool { + oth, ok := other.(*PublicKey) + if !ok { + return false + } + if pk.pk == nil && oth.pk == nil { + return true + } + if pk.pk == nil || oth.pk == nil { + return false + } + return bytes.Equal(pk.hpk[:], oth.hpk[:]) +} + +func (sk *PrivateKey) Public() kem.PublicKey { + pk := new(PublicKey) + pk.pk = sk.pk + copy(pk.hpk[:], sk.hpk[:]) + return pk +} + +func (pk *PublicKey) MarshalBinary() ([]byte, error) { + var ret [PublicKeySize]byte + pk.Pack(ret[:]) + return ret[:], nil +} + +func (*scheme) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { + return GenerateKeyPair(cryptoRand.Reader) +} + +func (*scheme) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { + if len(seed) != KeySeedSize { + panic(kem.ErrSeedSize) + } + return NewKeyFromSeed(seed[:]) +} + +func (*scheme) Encapsulate(pk kem.PublicKey) (ct, ss []byte, err error) { + ct = make([]byte, CiphertextSize) + ss = make([]byte, SharedKeySize) + + pub, ok := pk.(*PublicKey) + if !ok { + return nil, nil, kem.ErrTypeMismatch + } + pub.EncapsulateTo(ct, ss, nil) + return +} + +func (*scheme) EncapsulateDeterministically(pk kem.PublicKey, seed []byte) ( + ct, ss []byte, err error) { + if len(seed) != EncapsulationSeedSize { + return nil, nil, kem.ErrSeedSize + } + + ct = make([]byte, CiphertextSize) + ss = make([]byte, SharedKeySize) + + pub, ok := pk.(*PublicKey) + if !ok { + return nil, nil, kem.ErrTypeMismatch + } + pub.EncapsulateTo(ct, ss, seed) + return +} + +func (*scheme) Decapsulate(sk kem.PrivateKey, ct []byte) ([]byte, error) { + if len(ct) != CiphertextSize { + return nil, kem.ErrCiphertextSize + } + + priv, ok := sk.(*PrivateKey) + if !ok { + return nil, kem.ErrTypeMismatch + } + ss := make([]byte, SharedKeySize) + priv.DecapsulateTo(ss, ct) + return ss, nil +} + +func (*scheme) UnmarshalBinaryPublicKey(buf []byte) (kem.PublicKey, error) { + if len(buf) != PublicKeySize { + return nil, kem.ErrPubKeySize + } + var ret PublicKey + ret.Unpack(buf) + return &ret, nil +} + +func (*scheme) UnmarshalBinaryPrivateKey(buf []byte) (kem.PrivateKey, error) { + if len(buf) != PrivateKeySize { + return nil, kem.ErrPrivKeySize + } + var ret PrivateKey + ret.Unpack(buf) + return &ret, nil +} diff --git a/vendor/github.com/cloudflare/circl/kem/kyber/kyber512/kyber.go b/vendor/github.com/cloudflare/circl/kem/kyber/kyber512/kyber.go new file mode 100644 index 00000000..8cc1ec76 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/kem/kyber/kyber512/kyber.go @@ -0,0 +1,402 @@ +// Code generated from pkg.templ.go. DO NOT EDIT. + +// Package kyber512 implements the IND-CCA2 secure key encapsulation mechanism +// Kyber512.CCAKEM as submitted to round 3 of the NIST PQC competition and +// described in +// +// https://pq-crystals.org/kyber/data/kyber-specification-round3.pdf +package kyber512 + +import ( + "bytes" + "crypto/subtle" + "io" + + cryptoRand "crypto/rand" + "github.com/cloudflare/circl/internal/sha3" + "github.com/cloudflare/circl/kem" + cpapke "github.com/cloudflare/circl/pke/kyber/kyber512" +) + +const ( + // Size of seed for NewKeyFromSeed + KeySeedSize = cpapke.KeySeedSize + 32 + + // Size of seed for EncapsulateTo. + EncapsulationSeedSize = 32 + + // Size of the established shared key. + SharedKeySize = 32 + + // Size of the encapsulated shared key. + CiphertextSize = cpapke.CiphertextSize + + // Size of a packed public key. + PublicKeySize = cpapke.PublicKeySize + + // Size of a packed private key. + PrivateKeySize = cpapke.PrivateKeySize + cpapke.PublicKeySize + 64 +) + +// Type of a Kyber512.CCAKEM public key +type PublicKey struct { + pk *cpapke.PublicKey + + hpk [32]byte // H(pk) +} + +// Type of a Kyber512.CCAKEM private key +type PrivateKey struct { + sk *cpapke.PrivateKey + pk *cpapke.PublicKey + hpk [32]byte // H(pk) + z [32]byte +} + +// NewKeyFromSeed derives a public/private keypair deterministically +// from the given seed. +// +// Panics if seed is not of length KeySeedSize. +func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { + var sk PrivateKey + var pk PublicKey + + if len(seed) != KeySeedSize { + panic("seed must be of length KeySeedSize") + } + + pk.pk, sk.sk = cpapke.NewKeyFromSeed(seed[:cpapke.KeySeedSize]) + sk.pk = pk.pk + copy(sk.z[:], seed[cpapke.KeySeedSize:]) + + // Compute H(pk) + var ppk [cpapke.PublicKeySize]byte + sk.pk.Pack(ppk[:]) + h := sha3.New256() + h.Write(ppk[:]) + h.Read(sk.hpk[:]) + copy(pk.hpk[:], sk.hpk[:]) + + return &pk, &sk +} + +// GenerateKeyPair generates public and private keys using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKeyPair(rand io.Reader) (*PublicKey, *PrivateKey, error) { + var seed [KeySeedSize]byte + if rand == nil { + rand = cryptoRand.Reader + } + _, err := io.ReadFull(rand, seed[:]) + if err != nil { + return nil, nil, err + } + pk, sk := NewKeyFromSeed(seed[:]) + return pk, sk, nil +} + +// EncapsulateTo generates a shared key and ciphertext that contains it +// for the public key using randomness from seed and writes the shared key +// to ss and ciphertext to ct. +// +// Panics if ss, ct or seed are not of length SharedKeySize, CiphertextSize +// and EncapsulationSeedSize respectively. +// +// seed may be nil, in which case crypto/rand.Reader is used to generate one. +func (pk *PublicKey) EncapsulateTo(ct, ss []byte, seed []byte) { + if seed == nil { + seed = make([]byte, EncapsulationSeedSize) + cryptoRand.Read(seed[:]) + } else { + if len(seed) != EncapsulationSeedSize { + panic("seed must be of length EncapsulationSeedSize") + } + } + + if len(ct) != CiphertextSize { + panic("ct must be of length CiphertextSize") + } + + if len(ss) != SharedKeySize { + panic("ss must be of length SharedKeySize") + } + + // m = H(seed) + var m [32]byte + h := sha3.New256() + h.Write(seed[:]) + h.Read(m[:]) + + // (K', r) = G(m ‖ H(pk)) + var kr [64]byte + g := sha3.New512() + g.Write(m[:]) + g.Write(pk.hpk[:]) + g.Read(kr[:]) + + // c = Kyber.CPAPKE.Enc(pk, m, r) + pk.pk.EncryptTo(ct, m[:], kr[32:]) + + // Compute H(c) and put in second slot of kr, which will be (K', H(c)). + h.Reset() + h.Write(ct[:CiphertextSize]) + h.Read(kr[32:]) + + // K = KDF(K' ‖ H(c)) + kdf := sha3.NewShake256() + kdf.Write(kr[:]) + kdf.Read(ss[:SharedKeySize]) +} + +// DecapsulateTo computes the shared key which is encapsulated in ct +// for the private key. +// +// Panics if ct or ss are not of length CiphertextSize and SharedKeySize +// respectively. +func (sk *PrivateKey) DecapsulateTo(ss, ct []byte) { + if len(ct) != CiphertextSize { + panic("ct must be of length CiphertextSize") + } + + if len(ss) != SharedKeySize { + panic("ss must be of length SharedKeySize") + } + + // m' = Kyber.CPAPKE.Dec(sk, ct) + var m2 [32]byte + sk.sk.DecryptTo(m2[:], ct) + + // (K'', r') = G(m' ‖ H(pk)) + var kr2 [64]byte + g := sha3.New512() + g.Write(m2[:]) + g.Write(sk.hpk[:]) + g.Read(kr2[:]) + + // c' = Kyber.CPAPKE.Enc(pk, m', r') + var ct2 [CiphertextSize]byte + sk.pk.EncryptTo(ct2[:], m2[:], kr2[32:]) + + // Compute H(c) and put in second slot of kr2, which will be (K'', H(c)). + h := sha3.New256() + h.Write(ct[:CiphertextSize]) + h.Read(kr2[32:]) + + // Replace K'' by z in the first slot of kr2 if c ≠ c'. + subtle.ConstantTimeCopy( + 1-subtle.ConstantTimeCompare(ct, ct2[:]), + kr2[:32], + sk.z[:], + ) + + // K = KDF(K''/z, H(c)) + kdf := sha3.NewShake256() + kdf.Write(kr2[:]) + kdf.Read(ss[:SharedKeySize]) +} + +// Packs sk to buf. +// +// Panics if buf is not of size PrivateKeySize. +func (sk *PrivateKey) Pack(buf []byte) { + if len(buf) != PrivateKeySize { + panic("buf must be of length PrivateKeySize") + } + + sk.sk.Pack(buf[:cpapke.PrivateKeySize]) + buf = buf[cpapke.PrivateKeySize:] + sk.pk.Pack(buf[:cpapke.PublicKeySize]) + buf = buf[cpapke.PublicKeySize:] + copy(buf, sk.hpk[:]) + buf = buf[32:] + copy(buf, sk.z[:]) +} + +// Unpacks sk from buf. +// +// Panics if buf is not of size PrivateKeySize. +func (sk *PrivateKey) Unpack(buf []byte) { + if len(buf) != PrivateKeySize { + panic("buf must be of length PrivateKeySize") + } + + sk.sk = new(cpapke.PrivateKey) + sk.sk.Unpack(buf[:cpapke.PrivateKeySize]) + buf = buf[cpapke.PrivateKeySize:] + sk.pk = new(cpapke.PublicKey) + sk.pk.Unpack(buf[:cpapke.PublicKeySize]) + buf = buf[cpapke.PublicKeySize:] + copy(sk.hpk[:], buf[:32]) + copy(sk.z[:], buf[32:]) +} + +// Packs pk to buf. +// +// Panics if buf is not of size PublicKeySize. +func (pk *PublicKey) Pack(buf []byte) { + if len(buf) != PublicKeySize { + panic("buf must be of length PublicKeySize") + } + + pk.pk.Pack(buf) +} + +// Unpacks pk from buf. +// +// Panics if buf is not of size PublicKeySize. +func (pk *PublicKey) Unpack(buf []byte) { + if len(buf) != PublicKeySize { + panic("buf must be of length PublicKeySize") + } + + pk.pk = new(cpapke.PublicKey) + pk.pk.Unpack(buf) + + // Compute cached H(pk) + h := sha3.New256() + h.Write(buf) + h.Read(pk.hpk[:]) +} + +// Boilerplate down below for the KEM scheme API. + +type scheme struct{} + +var sch kem.Scheme = &scheme{} + +// Scheme returns a KEM interface. +func Scheme() kem.Scheme { return sch } + +func (*scheme) Name() string { return "Kyber512" } +func (*scheme) PublicKeySize() int { return PublicKeySize } +func (*scheme) PrivateKeySize() int { return PrivateKeySize } +func (*scheme) SeedSize() int { return KeySeedSize } +func (*scheme) SharedKeySize() int { return SharedKeySize } +func (*scheme) CiphertextSize() int { return CiphertextSize } +func (*scheme) EncapsulationSeedSize() int { return EncapsulationSeedSize } + +func (sk *PrivateKey) Scheme() kem.Scheme { return sch } +func (pk *PublicKey) Scheme() kem.Scheme { return sch } + +func (sk *PrivateKey) MarshalBinary() ([]byte, error) { + var ret [PrivateKeySize]byte + sk.Pack(ret[:]) + return ret[:], nil +} + +func (sk *PrivateKey) Equal(other kem.PrivateKey) bool { + oth, ok := other.(*PrivateKey) + if !ok { + return false + } + if sk.pk == nil && oth.pk == nil { + return true + } + if sk.pk == nil || oth.pk == nil { + return false + } + if !bytes.Equal(sk.hpk[:], oth.hpk[:]) || + !bytes.Equal(sk.z[:], oth.z[:]) { + return false + } + return sk.sk.Equal(oth.sk) +} + +func (pk *PublicKey) Equal(other kem.PublicKey) bool { + oth, ok := other.(*PublicKey) + if !ok { + return false + } + if pk.pk == nil && oth.pk == nil { + return true + } + if pk.pk == nil || oth.pk == nil { + return false + } + return bytes.Equal(pk.hpk[:], oth.hpk[:]) +} + +func (sk *PrivateKey) Public() kem.PublicKey { + pk := new(PublicKey) + pk.pk = sk.pk + copy(pk.hpk[:], sk.hpk[:]) + return pk +} + +func (pk *PublicKey) MarshalBinary() ([]byte, error) { + var ret [PublicKeySize]byte + pk.Pack(ret[:]) + return ret[:], nil +} + +func (*scheme) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { + return GenerateKeyPair(cryptoRand.Reader) +} + +func (*scheme) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { + if len(seed) != KeySeedSize { + panic(kem.ErrSeedSize) + } + return NewKeyFromSeed(seed[:]) +} + +func (*scheme) Encapsulate(pk kem.PublicKey) (ct, ss []byte, err error) { + ct = make([]byte, CiphertextSize) + ss = make([]byte, SharedKeySize) + + pub, ok := pk.(*PublicKey) + if !ok { + return nil, nil, kem.ErrTypeMismatch + } + pub.EncapsulateTo(ct, ss, nil) + return +} + +func (*scheme) EncapsulateDeterministically(pk kem.PublicKey, seed []byte) ( + ct, ss []byte, err error) { + if len(seed) != EncapsulationSeedSize { + return nil, nil, kem.ErrSeedSize + } + + ct = make([]byte, CiphertextSize) + ss = make([]byte, SharedKeySize) + + pub, ok := pk.(*PublicKey) + if !ok { + return nil, nil, kem.ErrTypeMismatch + } + pub.EncapsulateTo(ct, ss, seed) + return +} + +func (*scheme) Decapsulate(sk kem.PrivateKey, ct []byte) ([]byte, error) { + if len(ct) != CiphertextSize { + return nil, kem.ErrCiphertextSize + } + + priv, ok := sk.(*PrivateKey) + if !ok { + return nil, kem.ErrTypeMismatch + } + ss := make([]byte, SharedKeySize) + priv.DecapsulateTo(ss, ct) + return ss, nil +} + +func (*scheme) UnmarshalBinaryPublicKey(buf []byte) (kem.PublicKey, error) { + if len(buf) != PublicKeySize { + return nil, kem.ErrPubKeySize + } + var ret PublicKey + ret.Unpack(buf) + return &ret, nil +} + +func (*scheme) UnmarshalBinaryPrivateKey(buf []byte) (kem.PrivateKey, error) { + if len(buf) != PrivateKeySize { + return nil, kem.ErrPrivKeySize + } + var ret PrivateKey + ret.Unpack(buf) + return &ret, nil +} diff --git a/vendor/github.com/cloudflare/circl/kem/kyber/kyber768/kyber.go b/vendor/github.com/cloudflare/circl/kem/kyber/kyber768/kyber.go new file mode 100644 index 00000000..98c40279 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/kem/kyber/kyber768/kyber.go @@ -0,0 +1,402 @@ +// Code generated from pkg.templ.go. DO NOT EDIT. + +// Package kyber768 implements the IND-CCA2 secure key encapsulation mechanism +// Kyber768.CCAKEM as submitted to round 3 of the NIST PQC competition and +// described in +// +// https://pq-crystals.org/kyber/data/kyber-specification-round3.pdf +package kyber768 + +import ( + "bytes" + "crypto/subtle" + "io" + + cryptoRand "crypto/rand" + "github.com/cloudflare/circl/internal/sha3" + "github.com/cloudflare/circl/kem" + cpapke "github.com/cloudflare/circl/pke/kyber/kyber768" +) + +const ( + // Size of seed for NewKeyFromSeed + KeySeedSize = cpapke.KeySeedSize + 32 + + // Size of seed for EncapsulateTo. + EncapsulationSeedSize = 32 + + // Size of the established shared key. + SharedKeySize = 32 + + // Size of the encapsulated shared key. + CiphertextSize = cpapke.CiphertextSize + + // Size of a packed public key. + PublicKeySize = cpapke.PublicKeySize + + // Size of a packed private key. + PrivateKeySize = cpapke.PrivateKeySize + cpapke.PublicKeySize + 64 +) + +// Type of a Kyber768.CCAKEM public key +type PublicKey struct { + pk *cpapke.PublicKey + + hpk [32]byte // H(pk) +} + +// Type of a Kyber768.CCAKEM private key +type PrivateKey struct { + sk *cpapke.PrivateKey + pk *cpapke.PublicKey + hpk [32]byte // H(pk) + z [32]byte +} + +// NewKeyFromSeed derives a public/private keypair deterministically +// from the given seed. +// +// Panics if seed is not of length KeySeedSize. +func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { + var sk PrivateKey + var pk PublicKey + + if len(seed) != KeySeedSize { + panic("seed must be of length KeySeedSize") + } + + pk.pk, sk.sk = cpapke.NewKeyFromSeed(seed[:cpapke.KeySeedSize]) + sk.pk = pk.pk + copy(sk.z[:], seed[cpapke.KeySeedSize:]) + + // Compute H(pk) + var ppk [cpapke.PublicKeySize]byte + sk.pk.Pack(ppk[:]) + h := sha3.New256() + h.Write(ppk[:]) + h.Read(sk.hpk[:]) + copy(pk.hpk[:], sk.hpk[:]) + + return &pk, &sk +} + +// GenerateKeyPair generates public and private keys using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKeyPair(rand io.Reader) (*PublicKey, *PrivateKey, error) { + var seed [KeySeedSize]byte + if rand == nil { + rand = cryptoRand.Reader + } + _, err := io.ReadFull(rand, seed[:]) + if err != nil { + return nil, nil, err + } + pk, sk := NewKeyFromSeed(seed[:]) + return pk, sk, nil +} + +// EncapsulateTo generates a shared key and ciphertext that contains it +// for the public key using randomness from seed and writes the shared key +// to ss and ciphertext to ct. +// +// Panics if ss, ct or seed are not of length SharedKeySize, CiphertextSize +// and EncapsulationSeedSize respectively. +// +// seed may be nil, in which case crypto/rand.Reader is used to generate one. +func (pk *PublicKey) EncapsulateTo(ct, ss []byte, seed []byte) { + if seed == nil { + seed = make([]byte, EncapsulationSeedSize) + cryptoRand.Read(seed[:]) + } else { + if len(seed) != EncapsulationSeedSize { + panic("seed must be of length EncapsulationSeedSize") + } + } + + if len(ct) != CiphertextSize { + panic("ct must be of length CiphertextSize") + } + + if len(ss) != SharedKeySize { + panic("ss must be of length SharedKeySize") + } + + // m = H(seed) + var m [32]byte + h := sha3.New256() + h.Write(seed[:]) + h.Read(m[:]) + + // (K', r) = G(m ‖ H(pk)) + var kr [64]byte + g := sha3.New512() + g.Write(m[:]) + g.Write(pk.hpk[:]) + g.Read(kr[:]) + + // c = Kyber.CPAPKE.Enc(pk, m, r) + pk.pk.EncryptTo(ct, m[:], kr[32:]) + + // Compute H(c) and put in second slot of kr, which will be (K', H(c)). + h.Reset() + h.Write(ct[:CiphertextSize]) + h.Read(kr[32:]) + + // K = KDF(K' ‖ H(c)) + kdf := sha3.NewShake256() + kdf.Write(kr[:]) + kdf.Read(ss[:SharedKeySize]) +} + +// DecapsulateTo computes the shared key which is encapsulated in ct +// for the private key. +// +// Panics if ct or ss are not of length CiphertextSize and SharedKeySize +// respectively. +func (sk *PrivateKey) DecapsulateTo(ss, ct []byte) { + if len(ct) != CiphertextSize { + panic("ct must be of length CiphertextSize") + } + + if len(ss) != SharedKeySize { + panic("ss must be of length SharedKeySize") + } + + // m' = Kyber.CPAPKE.Dec(sk, ct) + var m2 [32]byte + sk.sk.DecryptTo(m2[:], ct) + + // (K'', r') = G(m' ‖ H(pk)) + var kr2 [64]byte + g := sha3.New512() + g.Write(m2[:]) + g.Write(sk.hpk[:]) + g.Read(kr2[:]) + + // c' = Kyber.CPAPKE.Enc(pk, m', r') + var ct2 [CiphertextSize]byte + sk.pk.EncryptTo(ct2[:], m2[:], kr2[32:]) + + // Compute H(c) and put in second slot of kr2, which will be (K'', H(c)). + h := sha3.New256() + h.Write(ct[:CiphertextSize]) + h.Read(kr2[32:]) + + // Replace K'' by z in the first slot of kr2 if c ≠ c'. + subtle.ConstantTimeCopy( + 1-subtle.ConstantTimeCompare(ct, ct2[:]), + kr2[:32], + sk.z[:], + ) + + // K = KDF(K''/z, H(c)) + kdf := sha3.NewShake256() + kdf.Write(kr2[:]) + kdf.Read(ss[:SharedKeySize]) +} + +// Packs sk to buf. +// +// Panics if buf is not of size PrivateKeySize. +func (sk *PrivateKey) Pack(buf []byte) { + if len(buf) != PrivateKeySize { + panic("buf must be of length PrivateKeySize") + } + + sk.sk.Pack(buf[:cpapke.PrivateKeySize]) + buf = buf[cpapke.PrivateKeySize:] + sk.pk.Pack(buf[:cpapke.PublicKeySize]) + buf = buf[cpapke.PublicKeySize:] + copy(buf, sk.hpk[:]) + buf = buf[32:] + copy(buf, sk.z[:]) +} + +// Unpacks sk from buf. +// +// Panics if buf is not of size PrivateKeySize. +func (sk *PrivateKey) Unpack(buf []byte) { + if len(buf) != PrivateKeySize { + panic("buf must be of length PrivateKeySize") + } + + sk.sk = new(cpapke.PrivateKey) + sk.sk.Unpack(buf[:cpapke.PrivateKeySize]) + buf = buf[cpapke.PrivateKeySize:] + sk.pk = new(cpapke.PublicKey) + sk.pk.Unpack(buf[:cpapke.PublicKeySize]) + buf = buf[cpapke.PublicKeySize:] + copy(sk.hpk[:], buf[:32]) + copy(sk.z[:], buf[32:]) +} + +// Packs pk to buf. +// +// Panics if buf is not of size PublicKeySize. +func (pk *PublicKey) Pack(buf []byte) { + if len(buf) != PublicKeySize { + panic("buf must be of length PublicKeySize") + } + + pk.pk.Pack(buf) +} + +// Unpacks pk from buf. +// +// Panics if buf is not of size PublicKeySize. +func (pk *PublicKey) Unpack(buf []byte) { + if len(buf) != PublicKeySize { + panic("buf must be of length PublicKeySize") + } + + pk.pk = new(cpapke.PublicKey) + pk.pk.Unpack(buf) + + // Compute cached H(pk) + h := sha3.New256() + h.Write(buf) + h.Read(pk.hpk[:]) +} + +// Boilerplate down below for the KEM scheme API. + +type scheme struct{} + +var sch kem.Scheme = &scheme{} + +// Scheme returns a KEM interface. +func Scheme() kem.Scheme { return sch } + +func (*scheme) Name() string { return "Kyber768" } +func (*scheme) PublicKeySize() int { return PublicKeySize } +func (*scheme) PrivateKeySize() int { return PrivateKeySize } +func (*scheme) SeedSize() int { return KeySeedSize } +func (*scheme) SharedKeySize() int { return SharedKeySize } +func (*scheme) CiphertextSize() int { return CiphertextSize } +func (*scheme) EncapsulationSeedSize() int { return EncapsulationSeedSize } + +func (sk *PrivateKey) Scheme() kem.Scheme { return sch } +func (pk *PublicKey) Scheme() kem.Scheme { return sch } + +func (sk *PrivateKey) MarshalBinary() ([]byte, error) { + var ret [PrivateKeySize]byte + sk.Pack(ret[:]) + return ret[:], nil +} + +func (sk *PrivateKey) Equal(other kem.PrivateKey) bool { + oth, ok := other.(*PrivateKey) + if !ok { + return false + } + if sk.pk == nil && oth.pk == nil { + return true + } + if sk.pk == nil || oth.pk == nil { + return false + } + if !bytes.Equal(sk.hpk[:], oth.hpk[:]) || + !bytes.Equal(sk.z[:], oth.z[:]) { + return false + } + return sk.sk.Equal(oth.sk) +} + +func (pk *PublicKey) Equal(other kem.PublicKey) bool { + oth, ok := other.(*PublicKey) + if !ok { + return false + } + if pk.pk == nil && oth.pk == nil { + return true + } + if pk.pk == nil || oth.pk == nil { + return false + } + return bytes.Equal(pk.hpk[:], oth.hpk[:]) +} + +func (sk *PrivateKey) Public() kem.PublicKey { + pk := new(PublicKey) + pk.pk = sk.pk + copy(pk.hpk[:], sk.hpk[:]) + return pk +} + +func (pk *PublicKey) MarshalBinary() ([]byte, error) { + var ret [PublicKeySize]byte + pk.Pack(ret[:]) + return ret[:], nil +} + +func (*scheme) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { + return GenerateKeyPair(cryptoRand.Reader) +} + +func (*scheme) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { + if len(seed) != KeySeedSize { + panic(kem.ErrSeedSize) + } + return NewKeyFromSeed(seed[:]) +} + +func (*scheme) Encapsulate(pk kem.PublicKey) (ct, ss []byte, err error) { + ct = make([]byte, CiphertextSize) + ss = make([]byte, SharedKeySize) + + pub, ok := pk.(*PublicKey) + if !ok { + return nil, nil, kem.ErrTypeMismatch + } + pub.EncapsulateTo(ct, ss, nil) + return +} + +func (*scheme) EncapsulateDeterministically(pk kem.PublicKey, seed []byte) ( + ct, ss []byte, err error) { + if len(seed) != EncapsulationSeedSize { + return nil, nil, kem.ErrSeedSize + } + + ct = make([]byte, CiphertextSize) + ss = make([]byte, SharedKeySize) + + pub, ok := pk.(*PublicKey) + if !ok { + return nil, nil, kem.ErrTypeMismatch + } + pub.EncapsulateTo(ct, ss, seed) + return +} + +func (*scheme) Decapsulate(sk kem.PrivateKey, ct []byte) ([]byte, error) { + if len(ct) != CiphertextSize { + return nil, kem.ErrCiphertextSize + } + + priv, ok := sk.(*PrivateKey) + if !ok { + return nil, kem.ErrTypeMismatch + } + ss := make([]byte, SharedKeySize) + priv.DecapsulateTo(ss, ct) + return ss, nil +} + +func (*scheme) UnmarshalBinaryPublicKey(buf []byte) (kem.PublicKey, error) { + if len(buf) != PublicKeySize { + return nil, kem.ErrPubKeySize + } + var ret PublicKey + ret.Unpack(buf) + return &ret, nil +} + +func (*scheme) UnmarshalBinaryPrivateKey(buf []byte) (kem.PrivateKey, error) { + if len(buf) != PrivateKeySize { + return nil, kem.ErrPrivKeySize + } + var ret PrivateKey + ret.Unpack(buf) + return &ret, nil +} diff --git a/vendor/github.com/cloudflare/circl/math/fp25519/fp.go b/vendor/github.com/cloudflare/circl/math/fp25519/fp.go new file mode 100644 index 00000000..57a50ff5 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/math/fp25519/fp.go @@ -0,0 +1,205 @@ +// Package fp25519 provides prime field arithmetic over GF(2^255-19). +package fp25519 + +import ( + "errors" + + "github.com/cloudflare/circl/internal/conv" +) + +// Size in bytes of an element. +const Size = 32 + +// Elt is a prime field element. +type Elt [Size]byte + +func (e Elt) String() string { return conv.BytesLe2Hex(e[:]) } + +// p is the prime modulus 2^255-19. +var p = Elt{ + 0xed, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, +} + +// P returns the prime modulus 2^255-19. +func P() Elt { return p } + +// ToBytes stores in b the little-endian byte representation of x. +func ToBytes(b []byte, x *Elt) error { + if len(b) != Size { + return errors.New("wrong size") + } + Modp(x) + copy(b, x[:]) + return nil +} + +// IsZero returns true if x is equal to 0. +func IsZero(x *Elt) bool { Modp(x); return *x == Elt{} } + +// SetOne assigns x=1. +func SetOne(x *Elt) { *x = Elt{}; x[0] = 1 } + +// Neg calculates z = -x. +func Neg(z, x *Elt) { Sub(z, &p, x) } + +// InvSqrt calculates z = sqrt(x/y) iff x/y is a quadratic-residue, which is +// indicated by returning isQR = true. Otherwise, when x/y is a quadratic +// non-residue, z will have an undetermined value and isQR = false. +func InvSqrt(z, x, y *Elt) (isQR bool) { + sqrtMinusOne := &Elt{ + 0xb0, 0xa0, 0x0e, 0x4a, 0x27, 0x1b, 0xee, 0xc4, + 0x78, 0xe4, 0x2f, 0xad, 0x06, 0x18, 0x43, 0x2f, + 0xa7, 0xd7, 0xfb, 0x3d, 0x99, 0x00, 0x4d, 0x2b, + 0x0b, 0xdf, 0xc1, 0x4f, 0x80, 0x24, 0x83, 0x2b, + } + t0, t1, t2, t3 := &Elt{}, &Elt{}, &Elt{}, &Elt{} + + Mul(t0, x, y) // t0 = u*v + Sqr(t1, y) // t1 = v^2 + Mul(t2, t0, t1) // t2 = u*v^3 + Sqr(t0, t1) // t0 = v^4 + Mul(t1, t0, t2) // t1 = u*v^7 + + var Tab [4]*Elt + Tab[0] = &Elt{} + Tab[1] = &Elt{} + Tab[2] = t3 + Tab[3] = t1 + + *Tab[0] = *t1 + Sqr(Tab[0], Tab[0]) + Sqr(Tab[1], Tab[0]) + Sqr(Tab[1], Tab[1]) + Mul(Tab[1], Tab[1], Tab[3]) + Mul(Tab[0], Tab[0], Tab[1]) + Sqr(Tab[0], Tab[0]) + Mul(Tab[0], Tab[0], Tab[1]) + Sqr(Tab[1], Tab[0]) + for i := 0; i < 4; i++ { + Sqr(Tab[1], Tab[1]) + } + Mul(Tab[1], Tab[1], Tab[0]) + Sqr(Tab[2], Tab[1]) + for i := 0; i < 4; i++ { + Sqr(Tab[2], Tab[2]) + } + Mul(Tab[2], Tab[2], Tab[0]) + Sqr(Tab[1], Tab[2]) + for i := 0; i < 14; i++ { + Sqr(Tab[1], Tab[1]) + } + Mul(Tab[1], Tab[1], Tab[2]) + Sqr(Tab[2], Tab[1]) + for i := 0; i < 29; i++ { + Sqr(Tab[2], Tab[2]) + } + Mul(Tab[2], Tab[2], Tab[1]) + Sqr(Tab[1], Tab[2]) + for i := 0; i < 59; i++ { + Sqr(Tab[1], Tab[1]) + } + Mul(Tab[1], Tab[1], Tab[2]) + for i := 0; i < 5; i++ { + Sqr(Tab[1], Tab[1]) + } + Mul(Tab[1], Tab[1], Tab[0]) + Sqr(Tab[2], Tab[1]) + for i := 0; i < 124; i++ { + Sqr(Tab[2], Tab[2]) + } + Mul(Tab[2], Tab[2], Tab[1]) + Sqr(Tab[2], Tab[2]) + Sqr(Tab[2], Tab[2]) + Mul(Tab[2], Tab[2], Tab[3]) + + Mul(z, t3, t2) // z = xy^(p+3)/8 = xy^3*(xy^7)^(p-5)/8 + // Checking whether y z^2 == x + Sqr(t0, z) // t0 = z^2 + Mul(t0, t0, y) // t0 = yz^2 + Sub(t1, t0, x) // t1 = t0-u + Add(t2, t0, x) // t2 = t0+u + if IsZero(t1) { + return true + } else if IsZero(t2) { + Mul(z, z, sqrtMinusOne) // z = z*sqrt(-1) + return true + } else { + return false + } +} + +// Inv calculates z = 1/x mod p. +func Inv(z, x *Elt) { + x0, x1, x2 := &Elt{}, &Elt{}, &Elt{} + Sqr(x1, x) + Sqr(x0, x1) + Sqr(x0, x0) + Mul(x0, x0, x) + Mul(z, x0, x1) + Sqr(x1, z) + Mul(x0, x0, x1) + Sqr(x1, x0) + for i := 0; i < 4; i++ { + Sqr(x1, x1) + } + Mul(x0, x0, x1) + Sqr(x1, x0) + for i := 0; i < 9; i++ { + Sqr(x1, x1) + } + Mul(x1, x1, x0) + Sqr(x2, x1) + for i := 0; i < 19; i++ { + Sqr(x2, x2) + } + Mul(x2, x2, x1) + for i := 0; i < 10; i++ { + Sqr(x2, x2) + } + Mul(x2, x2, x0) + Sqr(x0, x2) + for i := 0; i < 49; i++ { + Sqr(x0, x0) + } + Mul(x0, x0, x2) + Sqr(x1, x0) + for i := 0; i < 99; i++ { + Sqr(x1, x1) + } + Mul(x1, x1, x0) + for i := 0; i < 50; i++ { + Sqr(x1, x1) + } + Mul(x1, x1, x2) + for i := 0; i < 5; i++ { + Sqr(x1, x1) + } + Mul(z, z, x1) +} + +// Cmov assigns y to x if n is 1. +func Cmov(x, y *Elt, n uint) { cmov(x, y, n) } + +// Cswap interchanges x and y if n is 1. +func Cswap(x, y *Elt, n uint) { cswap(x, y, n) } + +// Add calculates z = x+y mod p. +func Add(z, x, y *Elt) { add(z, x, y) } + +// Sub calculates z = x-y mod p. +func Sub(z, x, y *Elt) { sub(z, x, y) } + +// AddSub calculates (x,y) = (x+y mod p, x-y mod p). +func AddSub(x, y *Elt) { addsub(x, y) } + +// Mul calculates z = x*y mod p. +func Mul(z, x, y *Elt) { mul(z, x, y) } + +// Sqr calculates z = x^2 mod p. +func Sqr(z, x *Elt) { sqr(z, x) } + +// Modp ensures that z is between [0,p-1]. +func Modp(z *Elt) { modp(z) } diff --git a/vendor/github.com/cloudflare/circl/math/fp25519/fp_amd64.go b/vendor/github.com/cloudflare/circl/math/fp25519/fp_amd64.go new file mode 100644 index 00000000..057f0d28 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/math/fp25519/fp_amd64.go @@ -0,0 +1,45 @@ +//go:build amd64 && !purego +// +build amd64,!purego + +package fp25519 + +import ( + "golang.org/x/sys/cpu" +) + +var hasBmi2Adx = cpu.X86.HasBMI2 && cpu.X86.HasADX + +var _ = hasBmi2Adx + +func cmov(x, y *Elt, n uint) { cmovAmd64(x, y, n) } +func cswap(x, y *Elt, n uint) { cswapAmd64(x, y, n) } +func add(z, x, y *Elt) { addAmd64(z, x, y) } +func sub(z, x, y *Elt) { subAmd64(z, x, y) } +func addsub(x, y *Elt) { addsubAmd64(x, y) } +func mul(z, x, y *Elt) { mulAmd64(z, x, y) } +func sqr(z, x *Elt) { sqrAmd64(z, x) } +func modp(z *Elt) { modpAmd64(z) } + +//go:noescape +func cmovAmd64(x, y *Elt, n uint) + +//go:noescape +func cswapAmd64(x, y *Elt, n uint) + +//go:noescape +func addAmd64(z, x, y *Elt) + +//go:noescape +func subAmd64(z, x, y *Elt) + +//go:noescape +func addsubAmd64(x, y *Elt) + +//go:noescape +func mulAmd64(z, x, y *Elt) + +//go:noescape +func sqrAmd64(z, x *Elt) + +//go:noescape +func modpAmd64(z *Elt) diff --git a/vendor/github.com/cloudflare/circl/math/fp25519/fp_amd64.h b/vendor/github.com/cloudflare/circl/math/fp25519/fp_amd64.h new file mode 100644 index 00000000..7b25f16e --- /dev/null +++ b/vendor/github.com/cloudflare/circl/math/fp25519/fp_amd64.h @@ -0,0 +1,350 @@ +// This code was imported from https://github.com/armfazh/rfc7748_precomputed + +// CHECK_BMI2ADX triggers bmi2adx if supported, +// otherwise it fallbacks to legacy code. +#define CHECK_BMI2ADX(label, legacy, bmi2adx) \ + CMPB ·hasBmi2Adx(SB), $0 \ + JE label \ + bmi2adx \ + RET \ + label: \ + legacy \ + RET + +// cselect is a conditional move +// if b=1: it copies y into x; +// if b=0: x remains with the same value; +// if b<> 0,1: undefined. +// Uses: AX, DX, FLAGS +// Instr: x86_64, cmov +#define cselect(x,y,b) \ + TESTQ b, b \ + MOVQ 0+x, AX; MOVQ 0+y, DX; CMOVQNE DX, AX; MOVQ AX, 0+x; \ + MOVQ 8+x, AX; MOVQ 8+y, DX; CMOVQNE DX, AX; MOVQ AX, 8+x; \ + MOVQ 16+x, AX; MOVQ 16+y, DX; CMOVQNE DX, AX; MOVQ AX, 16+x; \ + MOVQ 24+x, AX; MOVQ 24+y, DX; CMOVQNE DX, AX; MOVQ AX, 24+x; + +// cswap is a conditional swap +// if b=1: x,y <- y,x; +// if b=0: x,y remain with the same values; +// if b<> 0,1: undefined. +// Uses: AX, DX, R8, FLAGS +// Instr: x86_64, cmov +#define cswap(x,y,b) \ + TESTQ b, b \ + MOVQ 0+x, AX; MOVQ AX, R8; MOVQ 0+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 0+x; MOVQ DX, 0+y; \ + MOVQ 8+x, AX; MOVQ AX, R8; MOVQ 8+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 8+x; MOVQ DX, 8+y; \ + MOVQ 16+x, AX; MOVQ AX, R8; MOVQ 16+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 16+x; MOVQ DX, 16+y; \ + MOVQ 24+x, AX; MOVQ AX, R8; MOVQ 24+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 24+x; MOVQ DX, 24+y; + +// additionLeg adds x and y and stores in z +// Uses: AX, DX, R8-R11, FLAGS +// Instr: x86_64, cmov +#define additionLeg(z,x,y) \ + MOVL $38, AX; \ + MOVL $0, DX; \ + MOVQ 0+x, R8; ADDQ 0+y, R8; \ + MOVQ 8+x, R9; ADCQ 8+y, R9; \ + MOVQ 16+x, R10; ADCQ 16+y, R10; \ + MOVQ 24+x, R11; ADCQ 24+y, R11; \ + CMOVQCS AX, DX; \ + ADDQ DX, R8; \ + ADCQ $0, R9; MOVQ R9, 8+z; \ + ADCQ $0, R10; MOVQ R10, 16+z; \ + ADCQ $0, R11; MOVQ R11, 24+z; \ + MOVL $0, DX; \ + CMOVQCS AX, DX; \ + ADDQ DX, R8; MOVQ R8, 0+z; + +// additionAdx adds x and y and stores in z +// Uses: AX, DX, R8-R11, FLAGS +// Instr: x86_64, cmov, adx +#define additionAdx(z,x,y) \ + MOVL $38, AX; \ + XORL DX, DX; \ + MOVQ 0+x, R8; ADCXQ 0+y, R8; \ + MOVQ 8+x, R9; ADCXQ 8+y, R9; \ + MOVQ 16+x, R10; ADCXQ 16+y, R10; \ + MOVQ 24+x, R11; ADCXQ 24+y, R11; \ + CMOVQCS AX, DX ; \ + XORL AX, AX; \ + ADCXQ DX, R8; \ + ADCXQ AX, R9; MOVQ R9, 8+z; \ + ADCXQ AX, R10; MOVQ R10, 16+z; \ + ADCXQ AX, R11; MOVQ R11, 24+z; \ + MOVL $38, DX; \ + CMOVQCS DX, AX; \ + ADDQ AX, R8; MOVQ R8, 0+z; + +// subtraction subtracts y from x and stores in z +// Uses: AX, DX, R8-R11, FLAGS +// Instr: x86_64, cmov +#define subtraction(z,x,y) \ + MOVL $38, AX; \ + MOVQ 0+x, R8; SUBQ 0+y, R8; \ + MOVQ 8+x, R9; SBBQ 8+y, R9; \ + MOVQ 16+x, R10; SBBQ 16+y, R10; \ + MOVQ 24+x, R11; SBBQ 24+y, R11; \ + MOVL $0, DX; \ + CMOVQCS AX, DX; \ + SUBQ DX, R8; \ + SBBQ $0, R9; MOVQ R9, 8+z; \ + SBBQ $0, R10; MOVQ R10, 16+z; \ + SBBQ $0, R11; MOVQ R11, 24+z; \ + MOVL $0, DX; \ + CMOVQCS AX, DX; \ + SUBQ DX, R8; MOVQ R8, 0+z; + +// integerMulAdx multiplies x and y and stores in z +// Uses: AX, DX, R8-R15, FLAGS +// Instr: x86_64, bmi2, adx +#define integerMulAdx(z,x,y) \ + MOVQ 0+y, DX; XORL AX, AX; \ + MULXQ 0+x, AX, R8; MOVQ AX, 0+z; \ + MULXQ 8+x, AX, R9; ADCXQ AX, R8; \ + MULXQ 16+x, AX, R10; ADCXQ AX, R9; \ + MULXQ 24+x, AX, R11; ADCXQ AX, R10; \ + MOVL $0, AX;;;;;;;;; ADCXQ AX, R11; \ + MOVQ 8+y, DX; XORL AX, AX; \ + MULXQ 0+x, AX, R12; ADCXQ R8, AX; MOVQ AX, 8+z; \ + MULXQ 8+x, AX, R13; ADCXQ R9, R12; ADOXQ AX, R12; \ + MULXQ 16+x, AX, R14; ADCXQ R10, R13; ADOXQ AX, R13; \ + MULXQ 24+x, AX, R15; ADCXQ R11, R14; ADOXQ AX, R14; \ + MOVL $0, AX;;;;;;;;; ADCXQ AX, R15; ADOXQ AX, R15; \ + MOVQ 16+y, DX; XORL AX, AX; \ + MULXQ 0+x, AX, R8; ADCXQ R12, AX; MOVQ AX, 16+z; \ + MULXQ 8+x, AX, R9; ADCXQ R13, R8; ADOXQ AX, R8; \ + MULXQ 16+x, AX, R10; ADCXQ R14, R9; ADOXQ AX, R9; \ + MULXQ 24+x, AX, R11; ADCXQ R15, R10; ADOXQ AX, R10; \ + MOVL $0, AX;;;;;;;;; ADCXQ AX, R11; ADOXQ AX, R11; \ + MOVQ 24+y, DX; XORL AX, AX; \ + MULXQ 0+x, AX, R12; ADCXQ R8, AX; MOVQ AX, 24+z; \ + MULXQ 8+x, AX, R13; ADCXQ R9, R12; ADOXQ AX, R12; MOVQ R12, 32+z; \ + MULXQ 16+x, AX, R14; ADCXQ R10, R13; ADOXQ AX, R13; MOVQ R13, 40+z; \ + MULXQ 24+x, AX, R15; ADCXQ R11, R14; ADOXQ AX, R14; MOVQ R14, 48+z; \ + MOVL $0, AX;;;;;;;;; ADCXQ AX, R15; ADOXQ AX, R15; MOVQ R15, 56+z; + +// integerMulLeg multiplies x and y and stores in z +// Uses: AX, DX, R8-R15, FLAGS +// Instr: x86_64 +#define integerMulLeg(z,x,y) \ + MOVQ 0+y, R8; \ + MOVQ 0+x, AX; MULQ R8; MOVQ AX, 0+z; MOVQ DX, R15; \ + MOVQ 8+x, AX; MULQ R8; MOVQ AX, R13; MOVQ DX, R10; \ + MOVQ 16+x, AX; MULQ R8; MOVQ AX, R14; MOVQ DX, R11; \ + MOVQ 24+x, AX; MULQ R8; \ + ADDQ R13, R15; \ + ADCQ R14, R10; MOVQ R10, 16+z; \ + ADCQ AX, R11; MOVQ R11, 24+z; \ + ADCQ $0, DX; MOVQ DX, 32+z; \ + MOVQ 8+y, R8; \ + MOVQ 0+x, AX; MULQ R8; MOVQ AX, R12; MOVQ DX, R9; \ + MOVQ 8+x, AX; MULQ R8; MOVQ AX, R13; MOVQ DX, R10; \ + MOVQ 16+x, AX; MULQ R8; MOVQ AX, R14; MOVQ DX, R11; \ + MOVQ 24+x, AX; MULQ R8; \ + ADDQ R12, R15; MOVQ R15, 8+z; \ + ADCQ R13, R9; \ + ADCQ R14, R10; \ + ADCQ AX, R11; \ + ADCQ $0, DX; \ + ADCQ 16+z, R9; MOVQ R9, R15; \ + ADCQ 24+z, R10; MOVQ R10, 24+z; \ + ADCQ 32+z, R11; MOVQ R11, 32+z; \ + ADCQ $0, DX; MOVQ DX, 40+z; \ + MOVQ 16+y, R8; \ + MOVQ 0+x, AX; MULQ R8; MOVQ AX, R12; MOVQ DX, R9; \ + MOVQ 8+x, AX; MULQ R8; MOVQ AX, R13; MOVQ DX, R10; \ + MOVQ 16+x, AX; MULQ R8; MOVQ AX, R14; MOVQ DX, R11; \ + MOVQ 24+x, AX; MULQ R8; \ + ADDQ R12, R15; MOVQ R15, 16+z; \ + ADCQ R13, R9; \ + ADCQ R14, R10; \ + ADCQ AX, R11; \ + ADCQ $0, DX; \ + ADCQ 24+z, R9; MOVQ R9, R15; \ + ADCQ 32+z, R10; MOVQ R10, 32+z; \ + ADCQ 40+z, R11; MOVQ R11, 40+z; \ + ADCQ $0, DX; MOVQ DX, 48+z; \ + MOVQ 24+y, R8; \ + MOVQ 0+x, AX; MULQ R8; MOVQ AX, R12; MOVQ DX, R9; \ + MOVQ 8+x, AX; MULQ R8; MOVQ AX, R13; MOVQ DX, R10; \ + MOVQ 16+x, AX; MULQ R8; MOVQ AX, R14; MOVQ DX, R11; \ + MOVQ 24+x, AX; MULQ R8; \ + ADDQ R12, R15; MOVQ R15, 24+z; \ + ADCQ R13, R9; \ + ADCQ R14, R10; \ + ADCQ AX, R11; \ + ADCQ $0, DX; \ + ADCQ 32+z, R9; MOVQ R9, 32+z; \ + ADCQ 40+z, R10; MOVQ R10, 40+z; \ + ADCQ 48+z, R11; MOVQ R11, 48+z; \ + ADCQ $0, DX; MOVQ DX, 56+z; + +// integerSqrLeg squares x and stores in z +// Uses: AX, CX, DX, R8-R15, FLAGS +// Instr: x86_64 +#define integerSqrLeg(z,x) \ + MOVQ 0+x, R8; \ + MOVQ 8+x, AX; MULQ R8; MOVQ AX, R9; MOVQ DX, R10; /* A[0]*A[1] */ \ + MOVQ 16+x, AX; MULQ R8; MOVQ AX, R14; MOVQ DX, R11; /* A[0]*A[2] */ \ + MOVQ 24+x, AX; MULQ R8; MOVQ AX, R15; MOVQ DX, R12; /* A[0]*A[3] */ \ + MOVQ 24+x, R8; \ + MOVQ 8+x, AX; MULQ R8; MOVQ AX, CX; MOVQ DX, R13; /* A[3]*A[1] */ \ + MOVQ 16+x, AX; MULQ R8; /* A[3]*A[2] */ \ + \ + ADDQ R14, R10;\ + ADCQ R15, R11; MOVL $0, R15;\ + ADCQ CX, R12;\ + ADCQ AX, R13;\ + ADCQ $0, DX; MOVQ DX, R14;\ + MOVQ 8+x, AX; MULQ 16+x;\ + \ + ADDQ AX, R11;\ + ADCQ DX, R12;\ + ADCQ $0, R13;\ + ADCQ $0, R14;\ + ADCQ $0, R15;\ + \ + SHLQ $1, R14, R15; MOVQ R15, 56+z;\ + SHLQ $1, R13, R14; MOVQ R14, 48+z;\ + SHLQ $1, R12, R13; MOVQ R13, 40+z;\ + SHLQ $1, R11, R12; MOVQ R12, 32+z;\ + SHLQ $1, R10, R11; MOVQ R11, 24+z;\ + SHLQ $1, R9, R10; MOVQ R10, 16+z;\ + SHLQ $1, R9; MOVQ R9, 8+z;\ + \ + MOVQ 0+x,AX; MULQ AX; MOVQ AX, 0+z; MOVQ DX, R9;\ + MOVQ 8+x,AX; MULQ AX; MOVQ AX, R10; MOVQ DX, R11;\ + MOVQ 16+x,AX; MULQ AX; MOVQ AX, R12; MOVQ DX, R13;\ + MOVQ 24+x,AX; MULQ AX; MOVQ AX, R14; MOVQ DX, R15;\ + \ + ADDQ 8+z, R9; MOVQ R9, 8+z;\ + ADCQ 16+z, R10; MOVQ R10, 16+z;\ + ADCQ 24+z, R11; MOVQ R11, 24+z;\ + ADCQ 32+z, R12; MOVQ R12, 32+z;\ + ADCQ 40+z, R13; MOVQ R13, 40+z;\ + ADCQ 48+z, R14; MOVQ R14, 48+z;\ + ADCQ 56+z, R15; MOVQ R15, 56+z; + +// integerSqrAdx squares x and stores in z +// Uses: AX, CX, DX, R8-R15, FLAGS +// Instr: x86_64, bmi2, adx +#define integerSqrAdx(z,x) \ + MOVQ 0+x, DX; /* A[0] */ \ + MULXQ 8+x, R8, R14; /* A[1]*A[0] */ XORL R15, R15; \ + MULXQ 16+x, R9, R10; /* A[2]*A[0] */ ADCXQ R14, R9; \ + MULXQ 24+x, AX, CX; /* A[3]*A[0] */ ADCXQ AX, R10; \ + MOVQ 24+x, DX; /* A[3] */ \ + MULXQ 8+x, R11, R12; /* A[1]*A[3] */ ADCXQ CX, R11; \ + MULXQ 16+x, AX, R13; /* A[2]*A[3] */ ADCXQ AX, R12; \ + MOVQ 8+x, DX; /* A[1] */ ADCXQ R15, R13; \ + MULXQ 16+x, AX, CX; /* A[2]*A[1] */ MOVL $0, R14; \ + ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ADCXQ R15, R14; \ + XORL R15, R15; \ + ADOXQ AX, R10; ADCXQ R8, R8; \ + ADOXQ CX, R11; ADCXQ R9, R9; \ + ADOXQ R15, R12; ADCXQ R10, R10; \ + ADOXQ R15, R13; ADCXQ R11, R11; \ + ADOXQ R15, R14; ADCXQ R12, R12; \ + ;;;;;;;;;;;;;;; ADCXQ R13, R13; \ + ;;;;;;;;;;;;;;; ADCXQ R14, R14; \ + MOVQ 0+x, DX; MULXQ DX, AX, CX; /* A[0]^2 */ \ + ;;;;;;;;;;;;;;; MOVQ AX, 0+z; \ + ADDQ CX, R8; MOVQ R8, 8+z; \ + MOVQ 8+x, DX; MULXQ DX, AX, CX; /* A[1]^2 */ \ + ADCQ AX, R9; MOVQ R9, 16+z; \ + ADCQ CX, R10; MOVQ R10, 24+z; \ + MOVQ 16+x, DX; MULXQ DX, AX, CX; /* A[2]^2 */ \ + ADCQ AX, R11; MOVQ R11, 32+z; \ + ADCQ CX, R12; MOVQ R12, 40+z; \ + MOVQ 24+x, DX; MULXQ DX, AX, CX; /* A[3]^2 */ \ + ADCQ AX, R13; MOVQ R13, 48+z; \ + ADCQ CX, R14; MOVQ R14, 56+z; + +// reduceFromDouble finds z congruent to x modulo p such that 0> 63) + // PUT BIT 255 IN CARRY FLAG AND CLEAR + x3 &^= 1 << 63 + + x0, c0 := bits.Add64(x0, cx, 0) + x1, c1 := bits.Add64(x1, 0, c0) + x2, c2 := bits.Add64(x2, 0, c1) + x3, _ = bits.Add64(x3, 0, c2) + + // TEST FOR BIT 255 AGAIN; ONLY TRIGGERED ON OVERFLOW MODULO 2^255-19 + // cx = C[255] ? 0 : 19 + cx = uint64(19) &^ (-(x3 >> 63)) + // CLEAR BIT 255 + x3 &^= 1 << 63 + + x0, c0 = bits.Sub64(x0, cx, 0) + x1, c1 = bits.Sub64(x1, 0, c0) + x2, c2 = bits.Sub64(x2, 0, c1) + x3, _ = bits.Sub64(x3, 0, c2) + + binary.LittleEndian.PutUint64(x[0*8:1*8], x0) + binary.LittleEndian.PutUint64(x[1*8:2*8], x1) + binary.LittleEndian.PutUint64(x[2*8:3*8], x2) + binary.LittleEndian.PutUint64(x[3*8:4*8], x3) +} + +func red64(z *Elt, x0, x1, x2, x3, x4, x5, x6, x7 uint64) { + h0, l0 := bits.Mul64(x4, 38) + h1, l1 := bits.Mul64(x5, 38) + h2, l2 := bits.Mul64(x6, 38) + h3, l3 := bits.Mul64(x7, 38) + + l1, c0 := bits.Add64(h0, l1, 0) + l2, c1 := bits.Add64(h1, l2, c0) + l3, c2 := bits.Add64(h2, l3, c1) + l4, _ := bits.Add64(h3, 0, c2) + + l0, c0 = bits.Add64(l0, x0, 0) + l1, c1 = bits.Add64(l1, x1, c0) + l2, c2 = bits.Add64(l2, x2, c1) + l3, c3 := bits.Add64(l3, x3, c2) + l4, _ = bits.Add64(l4, 0, c3) + + _, l4 = bits.Mul64(l4, 38) + l0, c0 = bits.Add64(l0, l4, 0) + z1, c1 := bits.Add64(l1, 0, c0) + z2, c2 := bits.Add64(l2, 0, c1) + z3, c3 := bits.Add64(l3, 0, c2) + z0, _ := bits.Add64(l0, (-c3)&38, 0) + + binary.LittleEndian.PutUint64(z[0*8:1*8], z0) + binary.LittleEndian.PutUint64(z[1*8:2*8], z1) + binary.LittleEndian.PutUint64(z[2*8:3*8], z2) + binary.LittleEndian.PutUint64(z[3*8:4*8], z3) +} diff --git a/vendor/github.com/cloudflare/circl/math/fp25519/fp_noasm.go b/vendor/github.com/cloudflare/circl/math/fp25519/fp_noasm.go new file mode 100644 index 00000000..26ca4d01 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/math/fp25519/fp_noasm.go @@ -0,0 +1,13 @@ +//go:build !amd64 || purego +// +build !amd64 purego + +package fp25519 + +func cmov(x, y *Elt, n uint) { cmovGeneric(x, y, n) } +func cswap(x, y *Elt, n uint) { cswapGeneric(x, y, n) } +func add(z, x, y *Elt) { addGeneric(z, x, y) } +func sub(z, x, y *Elt) { subGeneric(z, x, y) } +func addsub(x, y *Elt) { addsubGeneric(x, y) } +func mul(z, x, y *Elt) { mulGeneric(z, x, y) } +func sqr(z, x *Elt) { sqrGeneric(z, x) } +func modp(z *Elt) { modpGeneric(z) } diff --git a/vendor/github.com/cloudflare/circl/math/fp448/fp.go b/vendor/github.com/cloudflare/circl/math/fp448/fp.go new file mode 100644 index 00000000..a5e36600 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/math/fp448/fp.go @@ -0,0 +1,164 @@ +// Package fp448 provides prime field arithmetic over GF(2^448-2^224-1). +package fp448 + +import ( + "errors" + + "github.com/cloudflare/circl/internal/conv" +) + +// Size in bytes of an element. +const Size = 56 + +// Elt is a prime field element. +type Elt [Size]byte + +func (e Elt) String() string { return conv.BytesLe2Hex(e[:]) } + +// p is the prime modulus 2^448-2^224-1. +var p = Elt{ + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, +} + +// P returns the prime modulus 2^448-2^224-1. +func P() Elt { return p } + +// ToBytes stores in b the little-endian byte representation of x. +func ToBytes(b []byte, x *Elt) error { + if len(b) != Size { + return errors.New("wrong size") + } + Modp(x) + copy(b, x[:]) + return nil +} + +// IsZero returns true if x is equal to 0. +func IsZero(x *Elt) bool { Modp(x); return *x == Elt{} } + +// IsOne returns true if x is equal to 1. +func IsOne(x *Elt) bool { Modp(x); return *x == Elt{1} } + +// SetOne assigns x=1. +func SetOne(x *Elt) { *x = Elt{1} } + +// One returns the 1 element. +func One() (x Elt) { x = Elt{1}; return } + +// Neg calculates z = -x. +func Neg(z, x *Elt) { Sub(z, &p, x) } + +// Modp ensures that z is between [0,p-1]. +func Modp(z *Elt) { Sub(z, z, &p) } + +// InvSqrt calculates z = sqrt(x/y) iff x/y is a quadratic-residue. If so, +// isQR = true; otherwise, isQR = false, since x/y is a quadratic non-residue, +// and z = sqrt(-x/y). +func InvSqrt(z, x, y *Elt) (isQR bool) { + // First note that x^(2(k+1)) = x^(p-1)/2 * x = legendre(x) * x + // so that's x if x is a quadratic residue and -x otherwise. + // Next, y^(6k+3) = y^(4k+2) * y^(2k+1) = y^(p-1) * y^((p-1)/2) = legendre(y). + // So the z we compute satisfies z^2 y = x^(2(k+1)) y^(6k+3) = legendre(x)*legendre(y). + // Thus if x and y are quadratic residues, then z is indeed sqrt(x/y). + t0, t1 := &Elt{}, &Elt{} + Mul(t0, x, y) // x*y + Sqr(t1, y) // y^2 + Mul(t1, t0, t1) // x*y^3 + powPminus3div4(z, t1) // (x*y^3)^k + Mul(z, z, t0) // z = x*y*(x*y^3)^k = x^(k+1) * y^(3k+1) + + // Check if x/y is a quadratic residue + Sqr(t0, z) // z^2 + Mul(t0, t0, y) // y*z^2 + Sub(t0, t0, x) // y*z^2-x + return IsZero(t0) +} + +// Inv calculates z = 1/x mod p. +func Inv(z, x *Elt) { + // Calculates z = x^(4k+1) = x^(p-3+1) = x^(p-2) = x^-1, where k = (p-3)/4. + t := &Elt{} + powPminus3div4(t, x) // t = x^k + Sqr(t, t) // t = x^2k + Sqr(t, t) // t = x^4k + Mul(z, t, x) // z = x^(4k+1) +} + +// powPminus3div4 calculates z = x^k mod p, where k = (p-3)/4. +func powPminus3div4(z, x *Elt) { + x0, x1 := &Elt{}, &Elt{} + Sqr(z, x) + Mul(z, z, x) + Sqr(x0, z) + Mul(x0, x0, x) + Sqr(z, x0) + Sqr(z, z) + Sqr(z, z) + Mul(z, z, x0) + Sqr(x1, z) + for i := 0; i < 5; i++ { + Sqr(x1, x1) + } + Mul(x1, x1, z) + Sqr(z, x1) + for i := 0; i < 11; i++ { + Sqr(z, z) + } + Mul(z, z, x1) + Sqr(z, z) + Sqr(z, z) + Sqr(z, z) + Mul(z, z, x0) + Sqr(x1, z) + for i := 0; i < 26; i++ { + Sqr(x1, x1) + } + Mul(x1, x1, z) + Sqr(z, x1) + for i := 0; i < 53; i++ { + Sqr(z, z) + } + Mul(z, z, x1) + Sqr(z, z) + Sqr(z, z) + Sqr(z, z) + Mul(z, z, x0) + Sqr(x1, z) + for i := 0; i < 110; i++ { + Sqr(x1, x1) + } + Mul(x1, x1, z) + Sqr(z, x1) + Mul(z, z, x) + for i := 0; i < 223; i++ { + Sqr(z, z) + } + Mul(z, z, x1) +} + +// Cmov assigns y to x if n is 1. +func Cmov(x, y *Elt, n uint) { cmov(x, y, n) } + +// Cswap interchanges x and y if n is 1. +func Cswap(x, y *Elt, n uint) { cswap(x, y, n) } + +// Add calculates z = x+y mod p. +func Add(z, x, y *Elt) { add(z, x, y) } + +// Sub calculates z = x-y mod p. +func Sub(z, x, y *Elt) { sub(z, x, y) } + +// AddSub calculates (x,y) = (x+y mod p, x-y mod p). +func AddSub(x, y *Elt) { addsub(x, y) } + +// Mul calculates z = x*y mod p. +func Mul(z, x, y *Elt) { mul(z, x, y) } + +// Sqr calculates z = x^2 mod p. +func Sqr(z, x *Elt) { sqr(z, x) } diff --git a/vendor/github.com/cloudflare/circl/math/fp448/fp_amd64.go b/vendor/github.com/cloudflare/circl/math/fp448/fp_amd64.go new file mode 100644 index 00000000..6a12209a --- /dev/null +++ b/vendor/github.com/cloudflare/circl/math/fp448/fp_amd64.go @@ -0,0 +1,43 @@ +//go:build amd64 && !purego +// +build amd64,!purego + +package fp448 + +import ( + "golang.org/x/sys/cpu" +) + +var hasBmi2Adx = cpu.X86.HasBMI2 && cpu.X86.HasADX + +var _ = hasBmi2Adx + +func cmov(x, y *Elt, n uint) { cmovAmd64(x, y, n) } +func cswap(x, y *Elt, n uint) { cswapAmd64(x, y, n) } +func add(z, x, y *Elt) { addAmd64(z, x, y) } +func sub(z, x, y *Elt) { subAmd64(z, x, y) } +func addsub(x, y *Elt) { addsubAmd64(x, y) } +func mul(z, x, y *Elt) { mulAmd64(z, x, y) } +func sqr(z, x *Elt) { sqrAmd64(z, x) } + +/* Functions defined in fp_amd64.s */ + +//go:noescape +func cmovAmd64(x, y *Elt, n uint) + +//go:noescape +func cswapAmd64(x, y *Elt, n uint) + +//go:noescape +func addAmd64(z, x, y *Elt) + +//go:noescape +func subAmd64(z, x, y *Elt) + +//go:noescape +func addsubAmd64(x, y *Elt) + +//go:noescape +func mulAmd64(z, x, y *Elt) + +//go:noescape +func sqrAmd64(z, x *Elt) diff --git a/vendor/github.com/cloudflare/circl/math/fp448/fp_amd64.h b/vendor/github.com/cloudflare/circl/math/fp448/fp_amd64.h new file mode 100644 index 00000000..0b7dea17 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/math/fp448/fp_amd64.h @@ -0,0 +1,590 @@ +// This code was imported from https://github.com/armfazh/rfc7748_precomputed + +// CHECK_BMI2ADX triggers bmi2adx if supported, +// otherwise it fallbacks to legacy code. +#define CHECK_BMI2ADX(label, legacy, bmi2adx) \ + CMPB ·hasBmi2Adx(SB), $0 \ + JE label \ + bmi2adx \ + RET \ + label: \ + legacy \ + RET + +// cselect is a conditional move +// if b=1: it copies y into x; +// if b=0: x remains with the same value; +// if b<> 0,1: undefined. +// Uses: AX, DX, FLAGS +// Instr: x86_64, cmov +#define cselect(x,y,b) \ + TESTQ b, b \ + MOVQ 0+x, AX; MOVQ 0+y, DX; CMOVQNE DX, AX; MOVQ AX, 0+x; \ + MOVQ 8+x, AX; MOVQ 8+y, DX; CMOVQNE DX, AX; MOVQ AX, 8+x; \ + MOVQ 16+x, AX; MOVQ 16+y, DX; CMOVQNE DX, AX; MOVQ AX, 16+x; \ + MOVQ 24+x, AX; MOVQ 24+y, DX; CMOVQNE DX, AX; MOVQ AX, 24+x; \ + MOVQ 32+x, AX; MOVQ 32+y, DX; CMOVQNE DX, AX; MOVQ AX, 32+x; \ + MOVQ 40+x, AX; MOVQ 40+y, DX; CMOVQNE DX, AX; MOVQ AX, 40+x; \ + MOVQ 48+x, AX; MOVQ 48+y, DX; CMOVQNE DX, AX; MOVQ AX, 48+x; + +// cswap is a conditional swap +// if b=1: x,y <- y,x; +// if b=0: x,y remain with the same values; +// if b<> 0,1: undefined. +// Uses: AX, DX, R8, FLAGS +// Instr: x86_64, cmov +#define cswap(x,y,b) \ + TESTQ b, b \ + MOVQ 0+x, AX; MOVQ AX, R8; MOVQ 0+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 0+x; MOVQ DX, 0+y; \ + MOVQ 8+x, AX; MOVQ AX, R8; MOVQ 8+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 8+x; MOVQ DX, 8+y; \ + MOVQ 16+x, AX; MOVQ AX, R8; MOVQ 16+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 16+x; MOVQ DX, 16+y; \ + MOVQ 24+x, AX; MOVQ AX, R8; MOVQ 24+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 24+x; MOVQ DX, 24+y; \ + MOVQ 32+x, AX; MOVQ AX, R8; MOVQ 32+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 32+x; MOVQ DX, 32+y; \ + MOVQ 40+x, AX; MOVQ AX, R8; MOVQ 40+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 40+x; MOVQ DX, 40+y; \ + MOVQ 48+x, AX; MOVQ AX, R8; MOVQ 48+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 48+x; MOVQ DX, 48+y; + +// additionLeg adds x and y and stores in z +// Uses: AX, DX, R8-R14, FLAGS +// Instr: x86_64 +#define additionLeg(z,x,y) \ + MOVQ 0+x, R8; ADDQ 0+y, R8; \ + MOVQ 8+x, R9; ADCQ 8+y, R9; \ + MOVQ 16+x, R10; ADCQ 16+y, R10; \ + MOVQ 24+x, R11; ADCQ 24+y, R11; \ + MOVQ 32+x, R12; ADCQ 32+y, R12; \ + MOVQ 40+x, R13; ADCQ 40+y, R13; \ + MOVQ 48+x, R14; ADCQ 48+y, R14; \ + MOVQ $0, AX; ADCQ $0, AX; \ + MOVQ AX, DX; \ + SHLQ $32, DX; \ + ADDQ AX, R8; MOVQ $0, AX; \ + ADCQ $0, R9; \ + ADCQ $0, R10; \ + ADCQ DX, R11; \ + ADCQ $0, R12; \ + ADCQ $0, R13; \ + ADCQ $0, R14; \ + ADCQ $0, AX; \ + MOVQ AX, DX; \ + SHLQ $32, DX; \ + ADDQ AX, R8; MOVQ R8, 0+z; \ + ADCQ $0, R9; MOVQ R9, 8+z; \ + ADCQ $0, R10; MOVQ R10, 16+z; \ + ADCQ DX, R11; MOVQ R11, 24+z; \ + ADCQ $0, R12; MOVQ R12, 32+z; \ + ADCQ $0, R13; MOVQ R13, 40+z; \ + ADCQ $0, R14; MOVQ R14, 48+z; + + +// additionAdx adds x and y and stores in z +// Uses: AX, DX, R8-R15, FLAGS +// Instr: x86_64, adx +#define additionAdx(z,x,y) \ + MOVL $32, R15; \ + XORL DX, DX; \ + MOVQ 0+x, R8; ADCXQ 0+y, R8; \ + MOVQ 8+x, R9; ADCXQ 8+y, R9; \ + MOVQ 16+x, R10; ADCXQ 16+y, R10; \ + MOVQ 24+x, R11; ADCXQ 24+y, R11; \ + MOVQ 32+x, R12; ADCXQ 32+y, R12; \ + MOVQ 40+x, R13; ADCXQ 40+y, R13; \ + MOVQ 48+x, R14; ADCXQ 48+y, R14; \ + ;;;;;;;;;;;;;;; ADCXQ DX, DX; \ + XORL AX, AX; \ + ADCXQ DX, R8; SHLXQ R15, DX, DX; \ + ADCXQ AX, R9; \ + ADCXQ AX, R10; \ + ADCXQ DX, R11; \ + ADCXQ AX, R12; \ + ADCXQ AX, R13; \ + ADCXQ AX, R14; \ + ADCXQ AX, AX; \ + XORL DX, DX; \ + ADCXQ AX, R8; MOVQ R8, 0+z; SHLXQ R15, AX, AX; \ + ADCXQ DX, R9; MOVQ R9, 8+z; \ + ADCXQ DX, R10; MOVQ R10, 16+z; \ + ADCXQ AX, R11; MOVQ R11, 24+z; \ + ADCXQ DX, R12; MOVQ R12, 32+z; \ + ADCXQ DX, R13; MOVQ R13, 40+z; \ + ADCXQ DX, R14; MOVQ R14, 48+z; + +// subtraction subtracts y from x and stores in z +// Uses: AX, DX, R8-R14, FLAGS +// Instr: x86_64 +#define subtraction(z,x,y) \ + MOVQ 0+x, R8; SUBQ 0+y, R8; \ + MOVQ 8+x, R9; SBBQ 8+y, R9; \ + MOVQ 16+x, R10; SBBQ 16+y, R10; \ + MOVQ 24+x, R11; SBBQ 24+y, R11; \ + MOVQ 32+x, R12; SBBQ 32+y, R12; \ + MOVQ 40+x, R13; SBBQ 40+y, R13; \ + MOVQ 48+x, R14; SBBQ 48+y, R14; \ + MOVQ $0, AX; SETCS AX; \ + MOVQ AX, DX; \ + SHLQ $32, DX; \ + SUBQ AX, R8; MOVQ $0, AX; \ + SBBQ $0, R9; \ + SBBQ $0, R10; \ + SBBQ DX, R11; \ + SBBQ $0, R12; \ + SBBQ $0, R13; \ + SBBQ $0, R14; \ + SETCS AX; \ + MOVQ AX, DX; \ + SHLQ $32, DX; \ + SUBQ AX, R8; MOVQ R8, 0+z; \ + SBBQ $0, R9; MOVQ R9, 8+z; \ + SBBQ $0, R10; MOVQ R10, 16+z; \ + SBBQ DX, R11; MOVQ R11, 24+z; \ + SBBQ $0, R12; MOVQ R12, 32+z; \ + SBBQ $0, R13; MOVQ R13, 40+z; \ + SBBQ $0, R14; MOVQ R14, 48+z; + +// maddBmi2Adx multiplies x and y and accumulates in z +// Uses: AX, DX, R15, FLAGS +// Instr: x86_64, bmi2, adx +#define maddBmi2Adx(z,x,y,i,r0,r1,r2,r3,r4,r5,r6) \ + MOVQ i+y, DX; XORL AX, AX; \ + MULXQ 0+x, AX, R8; ADOXQ AX, r0; ADCXQ R8, r1; MOVQ r0,i+z; \ + MULXQ 8+x, AX, r0; ADOXQ AX, r1; ADCXQ r0, r2; MOVQ $0, R8; \ + MULXQ 16+x, AX, r0; ADOXQ AX, r2; ADCXQ r0, r3; \ + MULXQ 24+x, AX, r0; ADOXQ AX, r3; ADCXQ r0, r4; \ + MULXQ 32+x, AX, r0; ADOXQ AX, r4; ADCXQ r0, r5; \ + MULXQ 40+x, AX, r0; ADOXQ AX, r5; ADCXQ r0, r6; \ + MULXQ 48+x, AX, r0; ADOXQ AX, r6; ADCXQ R8, r0; \ + ;;;;;;;;;;;;;;;;;;; ADOXQ R8, r0; + +// integerMulAdx multiplies x and y and stores in z +// Uses: AX, DX, R8-R15, FLAGS +// Instr: x86_64, bmi2, adx +#define integerMulAdx(z,x,y) \ + MOVQ 0+y, DX; XORL AX, AX; MOVQ $0, R8; \ + MULXQ 0+x, AX, R9; MOVQ AX, 0+z; \ + MULXQ 8+x, AX, R10; ADCXQ AX, R9; \ + MULXQ 16+x, AX, R11; ADCXQ AX, R10; \ + MULXQ 24+x, AX, R12; ADCXQ AX, R11; \ + MULXQ 32+x, AX, R13; ADCXQ AX, R12; \ + MULXQ 40+x, AX, R14; ADCXQ AX, R13; \ + MULXQ 48+x, AX, R15; ADCXQ AX, R14; \ + ;;;;;;;;;;;;;;;;;;;; ADCXQ R8, R15; \ + maddBmi2Adx(z,x,y, 8, R9,R10,R11,R12,R13,R14,R15) \ + maddBmi2Adx(z,x,y,16,R10,R11,R12,R13,R14,R15, R9) \ + maddBmi2Adx(z,x,y,24,R11,R12,R13,R14,R15, R9,R10) \ + maddBmi2Adx(z,x,y,32,R12,R13,R14,R15, R9,R10,R11) \ + maddBmi2Adx(z,x,y,40,R13,R14,R15, R9,R10,R11,R12) \ + maddBmi2Adx(z,x,y,48,R14,R15, R9,R10,R11,R12,R13) \ + MOVQ R15, 56+z; \ + MOVQ R9, 64+z; \ + MOVQ R10, 72+z; \ + MOVQ R11, 80+z; \ + MOVQ R12, 88+z; \ + MOVQ R13, 96+z; \ + MOVQ R14, 104+z; + +// maddLegacy multiplies x and y and accumulates in z +// Uses: AX, DX, R15, FLAGS +// Instr: x86_64 +#define maddLegacy(z,x,y,i) \ + MOVQ i+y, R15; \ + MOVQ 0+x, AX; MULQ R15; MOVQ AX, R8; ;;;;;;;;;;;; MOVQ DX, R9; \ + MOVQ 8+x, AX; MULQ R15; ADDQ AX, R9; ADCQ $0, DX; MOVQ DX, R10; \ + MOVQ 16+x, AX; MULQ R15; ADDQ AX, R10; ADCQ $0, DX; MOVQ DX, R11; \ + MOVQ 24+x, AX; MULQ R15; ADDQ AX, R11; ADCQ $0, DX; MOVQ DX, R12; \ + MOVQ 32+x, AX; MULQ R15; ADDQ AX, R12; ADCQ $0, DX; MOVQ DX, R13; \ + MOVQ 40+x, AX; MULQ R15; ADDQ AX, R13; ADCQ $0, DX; MOVQ DX, R14; \ + MOVQ 48+x, AX; MULQ R15; ADDQ AX, R14; ADCQ $0, DX; \ + ADDQ 0+i+z, R8; MOVQ R8, 0+i+z; \ + ADCQ 8+i+z, R9; MOVQ R9, 8+i+z; \ + ADCQ 16+i+z, R10; MOVQ R10, 16+i+z; \ + ADCQ 24+i+z, R11; MOVQ R11, 24+i+z; \ + ADCQ 32+i+z, R12; MOVQ R12, 32+i+z; \ + ADCQ 40+i+z, R13; MOVQ R13, 40+i+z; \ + ADCQ 48+i+z, R14; MOVQ R14, 48+i+z; \ + ADCQ $0, DX; MOVQ DX, 56+i+z; + +// integerMulLeg multiplies x and y and stores in z +// Uses: AX, DX, R8-R15, FLAGS +// Instr: x86_64 +#define integerMulLeg(z,x,y) \ + MOVQ 0+y, R15; \ + MOVQ 0+x, AX; MULQ R15; MOVQ AX, 0+z; ;;;;;;;;;;;; MOVQ DX, R8; \ + MOVQ 8+x, AX; MULQ R15; ADDQ AX, R8; ADCQ $0, DX; MOVQ DX, R9; MOVQ R8, 8+z; \ + MOVQ 16+x, AX; MULQ R15; ADDQ AX, R9; ADCQ $0, DX; MOVQ DX, R10; MOVQ R9, 16+z; \ + MOVQ 24+x, AX; MULQ R15; ADDQ AX, R10; ADCQ $0, DX; MOVQ DX, R11; MOVQ R10, 24+z; \ + MOVQ 32+x, AX; MULQ R15; ADDQ AX, R11; ADCQ $0, DX; MOVQ DX, R12; MOVQ R11, 32+z; \ + MOVQ 40+x, AX; MULQ R15; ADDQ AX, R12; ADCQ $0, DX; MOVQ DX, R13; MOVQ R12, 40+z; \ + MOVQ 48+x, AX; MULQ R15; ADDQ AX, R13; ADCQ $0, DX; MOVQ DX,56+z; MOVQ R13, 48+z; \ + maddLegacy(z,x,y, 8) \ + maddLegacy(z,x,y,16) \ + maddLegacy(z,x,y,24) \ + maddLegacy(z,x,y,32) \ + maddLegacy(z,x,y,40) \ + maddLegacy(z,x,y,48) + +// integerSqrLeg squares x and stores in z +// Uses: AX, CX, DX, R8-R15, FLAGS +// Instr: x86_64 +#define integerSqrLeg(z,x) \ + XORL R15, R15; \ + MOVQ 0+x, CX; \ + MOVQ CX, AX; MULQ CX; MOVQ AX, 0+z; MOVQ DX, R8; \ + ADDQ CX, CX; ADCQ $0, R15; \ + MOVQ 8+x, AX; MULQ CX; ADDQ AX, R8; ADCQ $0, DX; MOVQ DX, R9; MOVQ R8, 8+z; \ + MOVQ 16+x, AX; MULQ CX; ADDQ AX, R9; ADCQ $0, DX; MOVQ DX, R10; \ + MOVQ 24+x, AX; MULQ CX; ADDQ AX, R10; ADCQ $0, DX; MOVQ DX, R11; \ + MOVQ 32+x, AX; MULQ CX; ADDQ AX, R11; ADCQ $0, DX; MOVQ DX, R12; \ + MOVQ 40+x, AX; MULQ CX; ADDQ AX, R12; ADCQ $0, DX; MOVQ DX, R13; \ + MOVQ 48+x, AX; MULQ CX; ADDQ AX, R13; ADCQ $0, DX; MOVQ DX, R14; \ + \ + MOVQ 8+x, CX; \ + MOVQ CX, AX; ADDQ R15, CX; MOVQ $0, R15; ADCQ $0, R15; \ + ;;;;;;;;;;;;;; MULQ CX; ADDQ AX, R9; ADCQ $0, DX; MOVQ R9,16+z; \ + MOVQ R15, AX; NEGQ AX; ANDQ 8+x, AX; ADDQ AX, DX; ADCQ $0, R11; MOVQ DX, R8; \ + ADDQ 8+x, CX; ADCQ $0, R15; \ + MOVQ 16+x, AX; MULQ CX; ADDQ AX, R10; ADCQ $0, DX; ADDQ R8, R10; ADCQ $0, DX; MOVQ DX, R8; MOVQ R10, 24+z; \ + MOVQ 24+x, AX; MULQ CX; ADDQ AX, R11; ADCQ $0, DX; ADDQ R8, R11; ADCQ $0, DX; MOVQ DX, R8; \ + MOVQ 32+x, AX; MULQ CX; ADDQ AX, R12; ADCQ $0, DX; ADDQ R8, R12; ADCQ $0, DX; MOVQ DX, R8; \ + MOVQ 40+x, AX; MULQ CX; ADDQ AX, R13; ADCQ $0, DX; ADDQ R8, R13; ADCQ $0, DX; MOVQ DX, R8; \ + MOVQ 48+x, AX; MULQ CX; ADDQ AX, R14; ADCQ $0, DX; ADDQ R8, R14; ADCQ $0, DX; MOVQ DX, R9; \ + \ + MOVQ 16+x, CX; \ + MOVQ CX, AX; ADDQ R15, CX; MOVQ $0, R15; ADCQ $0, R15; \ + ;;;;;;;;;;;;;; MULQ CX; ADDQ AX, R11; ADCQ $0, DX; MOVQ R11, 32+z; \ + MOVQ R15, AX; NEGQ AX; ANDQ 16+x,AX; ADDQ AX, DX; ADCQ $0, R13; MOVQ DX, R8; \ + ADDQ 16+x, CX; ADCQ $0, R15; \ + MOVQ 24+x, AX; MULQ CX; ADDQ AX, R12; ADCQ $0, DX; ADDQ R8, R12; ADCQ $0, DX; MOVQ DX, R8; MOVQ R12, 40+z; \ + MOVQ 32+x, AX; MULQ CX; ADDQ AX, R13; ADCQ $0, DX; ADDQ R8, R13; ADCQ $0, DX; MOVQ DX, R8; \ + MOVQ 40+x, AX; MULQ CX; ADDQ AX, R14; ADCQ $0, DX; ADDQ R8, R14; ADCQ $0, DX; MOVQ DX, R8; \ + MOVQ 48+x, AX; MULQ CX; ADDQ AX, R9; ADCQ $0, DX; ADDQ R8, R9; ADCQ $0, DX; MOVQ DX,R10; \ + \ + MOVQ 24+x, CX; \ + MOVQ CX, AX; ADDQ R15, CX; MOVQ $0, R15; ADCQ $0, R15; \ + ;;;;;;;;;;;;;; MULQ CX; ADDQ AX, R13; ADCQ $0, DX; MOVQ R13, 48+z; \ + MOVQ R15, AX; NEGQ AX; ANDQ 24+x,AX; ADDQ AX, DX; ADCQ $0, R9; MOVQ DX, R8; \ + ADDQ 24+x, CX; ADCQ $0, R15; \ + MOVQ 32+x, AX; MULQ CX; ADDQ AX, R14; ADCQ $0, DX; ADDQ R8, R14; ADCQ $0, DX; MOVQ DX, R8; MOVQ R14, 56+z; \ + MOVQ 40+x, AX; MULQ CX; ADDQ AX, R9; ADCQ $0, DX; ADDQ R8, R9; ADCQ $0, DX; MOVQ DX, R8; \ + MOVQ 48+x, AX; MULQ CX; ADDQ AX, R10; ADCQ $0, DX; ADDQ R8, R10; ADCQ $0, DX; MOVQ DX,R11; \ + \ + MOVQ 32+x, CX; \ + MOVQ CX, AX; ADDQ R15, CX; MOVQ $0, R15; ADCQ $0, R15; \ + ;;;;;;;;;;;;;; MULQ CX; ADDQ AX, R9; ADCQ $0, DX; MOVQ R9, 64+z; \ + MOVQ R15, AX; NEGQ AX; ANDQ 32+x,AX; ADDQ AX, DX; ADCQ $0, R11; MOVQ DX, R8; \ + ADDQ 32+x, CX; ADCQ $0, R15; \ + MOVQ 40+x, AX; MULQ CX; ADDQ AX, R10; ADCQ $0, DX; ADDQ R8, R10; ADCQ $0, DX; MOVQ DX, R8; MOVQ R10, 72+z; \ + MOVQ 48+x, AX; MULQ CX; ADDQ AX, R11; ADCQ $0, DX; ADDQ R8, R11; ADCQ $0, DX; MOVQ DX,R12; \ + \ + XORL R13, R13; \ + XORL R14, R14; \ + MOVQ 40+x, CX; \ + MOVQ CX, AX; ADDQ R15, CX; MOVQ $0, R15; ADCQ $0, R15; \ + ;;;;;;;;;;;;;; MULQ CX; ADDQ AX, R11; ADCQ $0, DX; MOVQ R11, 80+z; \ + MOVQ R15, AX; NEGQ AX; ANDQ 40+x,AX; ADDQ AX, DX; ADCQ $0, R13; MOVQ DX, R8; \ + ADDQ 40+x, CX; ADCQ $0, R15; \ + MOVQ 48+x, AX; MULQ CX; ADDQ AX, R12; ADCQ $0, DX; ADDQ R8, R12; ADCQ $0, DX; MOVQ DX, R8; MOVQ R12, 88+z; \ + ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ADDQ R8, R13; ADCQ $0,R14; \ + \ + XORL R9, R9; \ + MOVQ 48+x, CX; \ + MOVQ CX, AX; ADDQ R15, CX; MOVQ $0, R15; ADCQ $0, R15; \ + ;;;;;;;;;;;;;; MULQ CX; ADDQ AX, R13; ADCQ $0, DX; MOVQ R13, 96+z; \ + MOVQ R15, AX; NEGQ AX; ANDQ 48+x,AX; ADDQ AX, DX; ADCQ $0, R9; MOVQ DX, R8; \ + ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ADDQ R8,R14; ADCQ $0, R9; MOVQ R14, 104+z; + + +// integerSqrAdx squares x and stores in z +// Uses: AX, CX, DX, R8-R15, FLAGS +// Instr: x86_64, bmi2, adx +#define integerSqrAdx(z,x) \ + XORL R15, R15; \ + MOVQ 0+x, DX; \ + ;;;;;;;;;;;;;; MULXQ DX, AX, R8; MOVQ AX, 0+z; \ + ADDQ DX, DX; ADCQ $0, R15; CLC; \ + MULXQ 8+x, AX, R9; ADCXQ AX, R8; MOVQ R8, 8+z; \ + MULXQ 16+x, AX, R10; ADCXQ AX, R9; MOVQ $0, R8;\ + MULXQ 24+x, AX, R11; ADCXQ AX, R10; \ + MULXQ 32+x, AX, R12; ADCXQ AX, R11; \ + MULXQ 40+x, AX, R13; ADCXQ AX, R12; \ + MULXQ 48+x, AX, R14; ADCXQ AX, R13; \ + ;;;;;;;;;;;;;;;;;;;; ADCXQ R8, R14; \ + \ + MOVQ 8+x, DX; \ + MOVQ DX, AX; ADDQ R15, DX; MOVQ $0, R15; ADCQ $0, R15; \ + MULXQ AX, AX, CX; \ + MOVQ R15, R8; NEGQ R8; ANDQ 8+x, R8; \ + ADDQ AX, R9; MOVQ R9, 16+z; \ + ADCQ CX, R8; \ + ADCQ $0, R11; \ + ADDQ 8+x, DX; \ + ADCQ $0, R15; \ + XORL R9, R9; ;;;;;;;;;;;;;;;;;;;;; ADOXQ R8, R10; \ + MULXQ 16+x, AX, CX; ADCXQ AX, R10; ADOXQ CX, R11; MOVQ R10, 24+z; \ + MULXQ 24+x, AX, CX; ADCXQ AX, R11; ADOXQ CX, R12; MOVQ $0, R10; \ + MULXQ 32+x, AX, CX; ADCXQ AX, R12; ADOXQ CX, R13; \ + MULXQ 40+x, AX, CX; ADCXQ AX, R13; ADOXQ CX, R14; \ + MULXQ 48+x, AX, CX; ADCXQ AX, R14; ADOXQ CX, R9; \ + ;;;;;;;;;;;;;;;;;;; ADCXQ R10, R9; \ + \ + MOVQ 16+x, DX; \ + MOVQ DX, AX; ADDQ R15, DX; MOVQ $0, R15; ADCQ $0, R15; \ + MULXQ AX, AX, CX; \ + MOVQ R15, R8; NEGQ R8; ANDQ 16+x, R8; \ + ADDQ AX, R11; MOVQ R11, 32+z; \ + ADCQ CX, R8; \ + ADCQ $0, R13; \ + ADDQ 16+x, DX; \ + ADCQ $0, R15; \ + XORL R11, R11; ;;;;;;;;;;;;;;;;;;; ADOXQ R8, R12; \ + MULXQ 24+x, AX, CX; ADCXQ AX, R12; ADOXQ CX, R13; MOVQ R12, 40+z; \ + MULXQ 32+x, AX, CX; ADCXQ AX, R13; ADOXQ CX, R14; MOVQ $0, R12; \ + MULXQ 40+x, AX, CX; ADCXQ AX, R14; ADOXQ CX, R9; \ + MULXQ 48+x, AX, CX; ADCXQ AX, R9; ADOXQ CX, R10; \ + ;;;;;;;;;;;;;;;;;;; ADCXQ R11,R10; \ + \ + MOVQ 24+x, DX; \ + MOVQ DX, AX; ADDQ R15, DX; MOVQ $0, R15; ADCQ $0, R15; \ + MULXQ AX, AX, CX; \ + MOVQ R15, R8; NEGQ R8; ANDQ 24+x, R8; \ + ADDQ AX, R13; MOVQ R13, 48+z; \ + ADCQ CX, R8; \ + ADCQ $0, R9; \ + ADDQ 24+x, DX; \ + ADCQ $0, R15; \ + XORL R13, R13; ;;;;;;;;;;;;;;;;;;; ADOXQ R8, R14; \ + MULXQ 32+x, AX, CX; ADCXQ AX, R14; ADOXQ CX, R9; MOVQ R14, 56+z; \ + MULXQ 40+x, AX, CX; ADCXQ AX, R9; ADOXQ CX, R10; MOVQ $0, R14; \ + MULXQ 48+x, AX, CX; ADCXQ AX, R10; ADOXQ CX, R11; \ + ;;;;;;;;;;;;;;;;;;; ADCXQ R12,R11; \ + \ + MOVQ 32+x, DX; \ + MOVQ DX, AX; ADDQ R15, DX; MOVQ $0, R15; ADCQ $0, R15; \ + MULXQ AX, AX, CX; \ + MOVQ R15, R8; NEGQ R8; ANDQ 32+x, R8; \ + ADDQ AX, R9; MOVQ R9, 64+z; \ + ADCQ CX, R8; \ + ADCQ $0, R11; \ + ADDQ 32+x, DX; \ + ADCQ $0, R15; \ + XORL R9, R9; ;;;;;;;;;;;;;;;;;;;;; ADOXQ R8, R10; \ + MULXQ 40+x, AX, CX; ADCXQ AX, R10; ADOXQ CX, R11; MOVQ R10, 72+z; \ + MULXQ 48+x, AX, CX; ADCXQ AX, R11; ADOXQ CX, R12; \ + ;;;;;;;;;;;;;;;;;;; ADCXQ R13,R12; \ + \ + MOVQ 40+x, DX; \ + MOVQ DX, AX; ADDQ R15, DX; MOVQ $0, R15; ADCQ $0, R15; \ + MULXQ AX, AX, CX; \ + MOVQ R15, R8; NEGQ R8; ANDQ 40+x, R8; \ + ADDQ AX, R11; MOVQ R11, 80+z; \ + ADCQ CX, R8; \ + ADCQ $0, R13; \ + ADDQ 40+x, DX; \ + ADCQ $0, R15; \ + XORL R11, R11; ;;;;;;;;;;;;;;;;;;; ADOXQ R8, R12; \ + MULXQ 48+x, AX, CX; ADCXQ AX, R12; ADOXQ CX, R13; MOVQ R12, 88+z; \ + ;;;;;;;;;;;;;;;;;;; ADCXQ R14,R13; \ + \ + MOVQ 48+x, DX; \ + MOVQ DX, AX; ADDQ R15, DX; MOVQ $0, R15; ADCQ $0, R15; \ + MULXQ AX, AX, CX; \ + MOVQ R15, R8; NEGQ R8; ANDQ 48+x, R8; \ + XORL R10, R10; ;;;;;;;;;;;;;; ADOXQ CX, R14; \ + ;;;;;;;;;;;;;; ADCXQ AX, R13; ;;;;;;;;;;;;;; MOVQ R13, 96+z; \ + ;;;;;;;;;;;;;; ADCXQ R8, R14; MOVQ R14, 104+z; + +// reduceFromDoubleLeg finds a z=x modulo p such that z<2^448 and stores in z +// Uses: AX, R8-R15, FLAGS +// Instr: x86_64 +#define reduceFromDoubleLeg(z,x) \ + /* ( ,2C13,2C12,2C11,2C10|C10,C9,C8, C7) + (C6,...,C0) */ \ + /* (r14, r13, r12, r11, r10,r9,r8,r15) */ \ + MOVQ 80+x,AX; MOVQ AX,R10; \ + MOVQ $0xFFFFFFFF00000000, R8; \ + ANDQ R8,R10; \ + \ + MOVQ $0,R14; \ + MOVQ 104+x,R13; SHLQ $1,R13,R14; \ + MOVQ 96+x,R12; SHLQ $1,R12,R13; \ + MOVQ 88+x,R11; SHLQ $1,R11,R12; \ + MOVQ 72+x, R9; SHLQ $1,R10,R11; \ + MOVQ 64+x, R8; SHLQ $1,R10; \ + MOVQ $0xFFFFFFFF,R15; ANDQ R15,AX; ORQ AX,R10; \ + MOVQ 56+x,R15; \ + \ + ADDQ 0+x,R15; MOVQ R15, 0+z; MOVQ 56+x,R15; \ + ADCQ 8+x, R8; MOVQ R8, 8+z; MOVQ 64+x, R8; \ + ADCQ 16+x, R9; MOVQ R9,16+z; MOVQ 72+x, R9; \ + ADCQ 24+x,R10; MOVQ R10,24+z; MOVQ 80+x,R10; \ + ADCQ 32+x,R11; MOVQ R11,32+z; MOVQ 88+x,R11; \ + ADCQ 40+x,R12; MOVQ R12,40+z; MOVQ 96+x,R12; \ + ADCQ 48+x,R13; MOVQ R13,48+z; MOVQ 104+x,R13; \ + ADCQ $0,R14; \ + /* (c10c9,c9c8,c8c7,c7c13,c13c12,c12c11,c11c10) + (c6,...,c0) */ \ + /* ( r9, r8, r15, r13, r12, r11, r10) */ \ + MOVQ R10, AX; \ + SHRQ $32,R11,R10; \ + SHRQ $32,R12,R11; \ + SHRQ $32,R13,R12; \ + SHRQ $32,R15,R13; \ + SHRQ $32, R8,R15; \ + SHRQ $32, R9, R8; \ + SHRQ $32, AX, R9; \ + \ + ADDQ 0+z,R10; \ + ADCQ 8+z,R11; \ + ADCQ 16+z,R12; \ + ADCQ 24+z,R13; \ + ADCQ 32+z,R15; \ + ADCQ 40+z, R8; \ + ADCQ 48+z, R9; \ + ADCQ $0,R14; \ + /* ( c7) + (c6,...,c0) */ \ + /* (r14) */ \ + MOVQ R14, AX; SHLQ $32, AX; \ + ADDQ R14,R10; MOVQ $0,R14; \ + ADCQ $0,R11; \ + ADCQ $0,R12; \ + ADCQ AX,R13; \ + ADCQ $0,R15; \ + ADCQ $0, R8; \ + ADCQ $0, R9; \ + ADCQ $0,R14; \ + /* ( c7) + (c6,...,c0) */ \ + /* (r14) */ \ + MOVQ R14, AX; SHLQ $32,AX; \ + ADDQ R14,R10; MOVQ R10, 0+z; \ + ADCQ $0,R11; MOVQ R11, 8+z; \ + ADCQ $0,R12; MOVQ R12,16+z; \ + ADCQ AX,R13; MOVQ R13,24+z; \ + ADCQ $0,R15; MOVQ R15,32+z; \ + ADCQ $0, R8; MOVQ R8,40+z; \ + ADCQ $0, R9; MOVQ R9,48+z; + +// reduceFromDoubleAdx finds a z=x modulo p such that z<2^448 and stores in z +// Uses: AX, R8-R15, FLAGS +// Instr: x86_64, adx +#define reduceFromDoubleAdx(z,x) \ + /* ( ,2C13,2C12,2C11,2C10|C10,C9,C8, C7) + (C6,...,C0) */ \ + /* (r14, r13, r12, r11, r10,r9,r8,r15) */ \ + MOVQ 80+x,AX; MOVQ AX,R10; \ + MOVQ $0xFFFFFFFF00000000, R8; \ + ANDQ R8,R10; \ + \ + MOVQ $0,R14; \ + MOVQ 104+x,R13; SHLQ $1,R13,R14; \ + MOVQ 96+x,R12; SHLQ $1,R12,R13; \ + MOVQ 88+x,R11; SHLQ $1,R11,R12; \ + MOVQ 72+x, R9; SHLQ $1,R10,R11; \ + MOVQ 64+x, R8; SHLQ $1,R10; \ + MOVQ $0xFFFFFFFF,R15; ANDQ R15,AX; ORQ AX,R10; \ + MOVQ 56+x,R15; \ + \ + XORL AX,AX; \ + ADCXQ 0+x,R15; MOVQ R15, 0+z; MOVQ 56+x,R15; \ + ADCXQ 8+x, R8; MOVQ R8, 8+z; MOVQ 64+x, R8; \ + ADCXQ 16+x, R9; MOVQ R9,16+z; MOVQ 72+x, R9; \ + ADCXQ 24+x,R10; MOVQ R10,24+z; MOVQ 80+x,R10; \ + ADCXQ 32+x,R11; MOVQ R11,32+z; MOVQ 88+x,R11; \ + ADCXQ 40+x,R12; MOVQ R12,40+z; MOVQ 96+x,R12; \ + ADCXQ 48+x,R13; MOVQ R13,48+z; MOVQ 104+x,R13; \ + ADCXQ AX,R14; \ + /* (c10c9,c9c8,c8c7,c7c13,c13c12,c12c11,c11c10) + (c6,...,c0) */ \ + /* ( r9, r8, r15, r13, r12, r11, r10) */ \ + MOVQ R10, AX; \ + SHRQ $32,R11,R10; \ + SHRQ $32,R12,R11; \ + SHRQ $32,R13,R12; \ + SHRQ $32,R15,R13; \ + SHRQ $32, R8,R15; \ + SHRQ $32, R9, R8; \ + SHRQ $32, AX, R9; \ + \ + XORL AX,AX; \ + ADCXQ 0+z,R10; \ + ADCXQ 8+z,R11; \ + ADCXQ 16+z,R12; \ + ADCXQ 24+z,R13; \ + ADCXQ 32+z,R15; \ + ADCXQ 40+z, R8; \ + ADCXQ 48+z, R9; \ + ADCXQ AX,R14; \ + /* ( c7) + (c6,...,c0) */ \ + /* (r14) */ \ + MOVQ R14, AX; SHLQ $32, AX; \ + CLC; \ + ADCXQ R14,R10; MOVQ $0,R14; \ + ADCXQ R14,R11; \ + ADCXQ R14,R12; \ + ADCXQ AX,R13; \ + ADCXQ R14,R15; \ + ADCXQ R14, R8; \ + ADCXQ R14, R9; \ + ADCXQ R14,R14; \ + /* ( c7) + (c6,...,c0) */ \ + /* (r14) */ \ + MOVQ R14, AX; SHLQ $32, AX; \ + CLC; \ + ADCXQ R14,R10; MOVQ R10, 0+z; MOVQ $0,R14; \ + ADCXQ R14,R11; MOVQ R11, 8+z; \ + ADCXQ R14,R12; MOVQ R12,16+z; \ + ADCXQ AX,R13; MOVQ R13,24+z; \ + ADCXQ R14,R15; MOVQ R15,32+z; \ + ADCXQ R14, R8; MOVQ R8,40+z; \ + ADCXQ R14, R9; MOVQ R9,48+z; + +// addSub calculates two operations: x,y = x+y,x-y +// Uses: AX, DX, R8-R15, FLAGS +#define addSub(x,y) \ + MOVQ 0+x, R8; ADDQ 0+y, R8; \ + MOVQ 8+x, R9; ADCQ 8+y, R9; \ + MOVQ 16+x, R10; ADCQ 16+y, R10; \ + MOVQ 24+x, R11; ADCQ 24+y, R11; \ + MOVQ 32+x, R12; ADCQ 32+y, R12; \ + MOVQ 40+x, R13; ADCQ 40+y, R13; \ + MOVQ 48+x, R14; ADCQ 48+y, R14; \ + MOVQ $0, AX; ADCQ $0, AX; \ + MOVQ AX, DX; \ + SHLQ $32, DX; \ + ADDQ AX, R8; MOVQ $0, AX; \ + ADCQ $0, R9; \ + ADCQ $0, R10; \ + ADCQ DX, R11; \ + ADCQ $0, R12; \ + ADCQ $0, R13; \ + ADCQ $0, R14; \ + ADCQ $0, AX; \ + MOVQ AX, DX; \ + SHLQ $32, DX; \ + ADDQ AX, R8; MOVQ 0+x,AX; MOVQ R8, 0+x; MOVQ AX, R8; \ + ADCQ $0, R9; MOVQ 8+x,AX; MOVQ R9, 8+x; MOVQ AX, R9; \ + ADCQ $0, R10; MOVQ 16+x,AX; MOVQ R10, 16+x; MOVQ AX, R10; \ + ADCQ DX, R11; MOVQ 24+x,AX; MOVQ R11, 24+x; MOVQ AX, R11; \ + ADCQ $0, R12; MOVQ 32+x,AX; MOVQ R12, 32+x; MOVQ AX, R12; \ + ADCQ $0, R13; MOVQ 40+x,AX; MOVQ R13, 40+x; MOVQ AX, R13; \ + ADCQ $0, R14; MOVQ 48+x,AX; MOVQ R14, 48+x; MOVQ AX, R14; \ + SUBQ 0+y, R8; \ + SBBQ 8+y, R9; \ + SBBQ 16+y, R10; \ + SBBQ 24+y, R11; \ + SBBQ 32+y, R12; \ + SBBQ 40+y, R13; \ + SBBQ 48+y, R14; \ + MOVQ $0, AX; SETCS AX; \ + MOVQ AX, DX; \ + SHLQ $32, DX; \ + SUBQ AX, R8; MOVQ $0, AX; \ + SBBQ $0, R9; \ + SBBQ $0, R10; \ + SBBQ DX, R11; \ + SBBQ $0, R12; \ + SBBQ $0, R13; \ + SBBQ $0, R14; \ + SETCS AX; \ + MOVQ AX, DX; \ + SHLQ $32, DX; \ + SUBQ AX, R8; MOVQ R8, 0+y; \ + SBBQ $0, R9; MOVQ R9, 8+y; \ + SBBQ $0, R10; MOVQ R10, 16+y; \ + SBBQ DX, R11; MOVQ R11, 24+y; \ + SBBQ $0, R12; MOVQ R12, 32+y; \ + SBBQ $0, R13; MOVQ R13, 40+y; \ + SBBQ $0, R14; MOVQ R14, 48+y; diff --git a/vendor/github.com/cloudflare/circl/math/fp448/fp_amd64.s b/vendor/github.com/cloudflare/circl/math/fp448/fp_amd64.s new file mode 100644 index 00000000..435addf5 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/math/fp448/fp_amd64.s @@ -0,0 +1,74 @@ +// +build amd64 + +#include "textflag.h" +#include "fp_amd64.h" + +// func cmovAmd64(x, y *Elt, n uint) +TEXT ·cmovAmd64(SB),NOSPLIT,$0-24 + MOVQ x+0(FP), DI + MOVQ y+8(FP), SI + MOVQ n+16(FP), BX + cselect(0(DI),0(SI),BX) + RET + +// func cswapAmd64(x, y *Elt, n uint) +TEXT ·cswapAmd64(SB),NOSPLIT,$0-24 + MOVQ x+0(FP), DI + MOVQ y+8(FP), SI + MOVQ n+16(FP), BX + cswap(0(DI),0(SI),BX) + RET + +// func subAmd64(z, x, y *Elt) +TEXT ·subAmd64(SB),NOSPLIT,$0-24 + MOVQ z+0(FP), DI + MOVQ x+8(FP), SI + MOVQ y+16(FP), BX + subtraction(0(DI),0(SI),0(BX)) + RET + +// func addsubAmd64(x, y *Elt) +TEXT ·addsubAmd64(SB),NOSPLIT,$0-16 + MOVQ x+0(FP), DI + MOVQ y+8(FP), SI + addSub(0(DI),0(SI)) + RET + +#define addLegacy \ + additionLeg(0(DI),0(SI),0(BX)) +#define addBmi2Adx \ + additionAdx(0(DI),0(SI),0(BX)) + +#define mulLegacy \ + integerMulLeg(0(SP),0(SI),0(BX)) \ + reduceFromDoubleLeg(0(DI),0(SP)) +#define mulBmi2Adx \ + integerMulAdx(0(SP),0(SI),0(BX)) \ + reduceFromDoubleAdx(0(DI),0(SP)) + +#define sqrLegacy \ + integerSqrLeg(0(SP),0(SI)) \ + reduceFromDoubleLeg(0(DI),0(SP)) +#define sqrBmi2Adx \ + integerSqrAdx(0(SP),0(SI)) \ + reduceFromDoubleAdx(0(DI),0(SP)) + +// func addAmd64(z, x, y *Elt) +TEXT ·addAmd64(SB),NOSPLIT,$0-24 + MOVQ z+0(FP), DI + MOVQ x+8(FP), SI + MOVQ y+16(FP), BX + CHECK_BMI2ADX(LADD, addLegacy, addBmi2Adx) + +// func mulAmd64(z, x, y *Elt) +TEXT ·mulAmd64(SB),NOSPLIT,$112-24 + MOVQ z+0(FP), DI + MOVQ x+8(FP), SI + MOVQ y+16(FP), BX + CHECK_BMI2ADX(LMUL, mulLegacy, mulBmi2Adx) + +// func sqrAmd64(z, x *Elt) +TEXT ·sqrAmd64(SB),NOSPLIT,$112-16 + MOVQ z+0(FP), DI + MOVQ x+8(FP), SI + CHECK_BMI2ADX(LSQR, sqrLegacy, sqrBmi2Adx) diff --git a/vendor/github.com/cloudflare/circl/math/fp448/fp_generic.go b/vendor/github.com/cloudflare/circl/math/fp448/fp_generic.go new file mode 100644 index 00000000..47a0b632 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/math/fp448/fp_generic.go @@ -0,0 +1,339 @@ +package fp448 + +import ( + "encoding/binary" + "math/bits" +) + +func cmovGeneric(x, y *Elt, n uint) { + m := -uint64(n & 0x1) + x0 := binary.LittleEndian.Uint64(x[0*8 : 1*8]) + x1 := binary.LittleEndian.Uint64(x[1*8 : 2*8]) + x2 := binary.LittleEndian.Uint64(x[2*8 : 3*8]) + x3 := binary.LittleEndian.Uint64(x[3*8 : 4*8]) + x4 := binary.LittleEndian.Uint64(x[4*8 : 5*8]) + x5 := binary.LittleEndian.Uint64(x[5*8 : 6*8]) + x6 := binary.LittleEndian.Uint64(x[6*8 : 7*8]) + + y0 := binary.LittleEndian.Uint64(y[0*8 : 1*8]) + y1 := binary.LittleEndian.Uint64(y[1*8 : 2*8]) + y2 := binary.LittleEndian.Uint64(y[2*8 : 3*8]) + y3 := binary.LittleEndian.Uint64(y[3*8 : 4*8]) + y4 := binary.LittleEndian.Uint64(y[4*8 : 5*8]) + y5 := binary.LittleEndian.Uint64(y[5*8 : 6*8]) + y6 := binary.LittleEndian.Uint64(y[6*8 : 7*8]) + + x0 = (x0 &^ m) | (y0 & m) + x1 = (x1 &^ m) | (y1 & m) + x2 = (x2 &^ m) | (y2 & m) + x3 = (x3 &^ m) | (y3 & m) + x4 = (x4 &^ m) | (y4 & m) + x5 = (x5 &^ m) | (y5 & m) + x6 = (x6 &^ m) | (y6 & m) + + binary.LittleEndian.PutUint64(x[0*8:1*8], x0) + binary.LittleEndian.PutUint64(x[1*8:2*8], x1) + binary.LittleEndian.PutUint64(x[2*8:3*8], x2) + binary.LittleEndian.PutUint64(x[3*8:4*8], x3) + binary.LittleEndian.PutUint64(x[4*8:5*8], x4) + binary.LittleEndian.PutUint64(x[5*8:6*8], x5) + binary.LittleEndian.PutUint64(x[6*8:7*8], x6) +} + +func cswapGeneric(x, y *Elt, n uint) { + m := -uint64(n & 0x1) + x0 := binary.LittleEndian.Uint64(x[0*8 : 1*8]) + x1 := binary.LittleEndian.Uint64(x[1*8 : 2*8]) + x2 := binary.LittleEndian.Uint64(x[2*8 : 3*8]) + x3 := binary.LittleEndian.Uint64(x[3*8 : 4*8]) + x4 := binary.LittleEndian.Uint64(x[4*8 : 5*8]) + x5 := binary.LittleEndian.Uint64(x[5*8 : 6*8]) + x6 := binary.LittleEndian.Uint64(x[6*8 : 7*8]) + + y0 := binary.LittleEndian.Uint64(y[0*8 : 1*8]) + y1 := binary.LittleEndian.Uint64(y[1*8 : 2*8]) + y2 := binary.LittleEndian.Uint64(y[2*8 : 3*8]) + y3 := binary.LittleEndian.Uint64(y[3*8 : 4*8]) + y4 := binary.LittleEndian.Uint64(y[4*8 : 5*8]) + y5 := binary.LittleEndian.Uint64(y[5*8 : 6*8]) + y6 := binary.LittleEndian.Uint64(y[6*8 : 7*8]) + + t0 := m & (x0 ^ y0) + t1 := m & (x1 ^ y1) + t2 := m & (x2 ^ y2) + t3 := m & (x3 ^ y3) + t4 := m & (x4 ^ y4) + t5 := m & (x5 ^ y5) + t6 := m & (x6 ^ y6) + x0 ^= t0 + x1 ^= t1 + x2 ^= t2 + x3 ^= t3 + x4 ^= t4 + x5 ^= t5 + x6 ^= t6 + y0 ^= t0 + y1 ^= t1 + y2 ^= t2 + y3 ^= t3 + y4 ^= t4 + y5 ^= t5 + y6 ^= t6 + + binary.LittleEndian.PutUint64(x[0*8:1*8], x0) + binary.LittleEndian.PutUint64(x[1*8:2*8], x1) + binary.LittleEndian.PutUint64(x[2*8:3*8], x2) + binary.LittleEndian.PutUint64(x[3*8:4*8], x3) + binary.LittleEndian.PutUint64(x[4*8:5*8], x4) + binary.LittleEndian.PutUint64(x[5*8:6*8], x5) + binary.LittleEndian.PutUint64(x[6*8:7*8], x6) + + binary.LittleEndian.PutUint64(y[0*8:1*8], y0) + binary.LittleEndian.PutUint64(y[1*8:2*8], y1) + binary.LittleEndian.PutUint64(y[2*8:3*8], y2) + binary.LittleEndian.PutUint64(y[3*8:4*8], y3) + binary.LittleEndian.PutUint64(y[4*8:5*8], y4) + binary.LittleEndian.PutUint64(y[5*8:6*8], y5) + binary.LittleEndian.PutUint64(y[6*8:7*8], y6) +} + +func addGeneric(z, x, y *Elt) { + x0 := binary.LittleEndian.Uint64(x[0*8 : 1*8]) + x1 := binary.LittleEndian.Uint64(x[1*8 : 2*8]) + x2 := binary.LittleEndian.Uint64(x[2*8 : 3*8]) + x3 := binary.LittleEndian.Uint64(x[3*8 : 4*8]) + x4 := binary.LittleEndian.Uint64(x[4*8 : 5*8]) + x5 := binary.LittleEndian.Uint64(x[5*8 : 6*8]) + x6 := binary.LittleEndian.Uint64(x[6*8 : 7*8]) + + y0 := binary.LittleEndian.Uint64(y[0*8 : 1*8]) + y1 := binary.LittleEndian.Uint64(y[1*8 : 2*8]) + y2 := binary.LittleEndian.Uint64(y[2*8 : 3*8]) + y3 := binary.LittleEndian.Uint64(y[3*8 : 4*8]) + y4 := binary.LittleEndian.Uint64(y[4*8 : 5*8]) + y5 := binary.LittleEndian.Uint64(y[5*8 : 6*8]) + y6 := binary.LittleEndian.Uint64(y[6*8 : 7*8]) + + z0, c0 := bits.Add64(x0, y0, 0) + z1, c1 := bits.Add64(x1, y1, c0) + z2, c2 := bits.Add64(x2, y2, c1) + z3, c3 := bits.Add64(x3, y3, c2) + z4, c4 := bits.Add64(x4, y4, c3) + z5, c5 := bits.Add64(x5, y5, c4) + z6, z7 := bits.Add64(x6, y6, c5) + + z0, c0 = bits.Add64(z0, z7, 0) + z1, c1 = bits.Add64(z1, 0, c0) + z2, c2 = bits.Add64(z2, 0, c1) + z3, c3 = bits.Add64(z3, z7<<32, c2) + z4, c4 = bits.Add64(z4, 0, c3) + z5, c5 = bits.Add64(z5, 0, c4) + z6, z7 = bits.Add64(z6, 0, c5) + + z0, c0 = bits.Add64(z0, z7, 0) + z1, c1 = bits.Add64(z1, 0, c0) + z2, c2 = bits.Add64(z2, 0, c1) + z3, c3 = bits.Add64(z3, z7<<32, c2) + z4, c4 = bits.Add64(z4, 0, c3) + z5, c5 = bits.Add64(z5, 0, c4) + z6, _ = bits.Add64(z6, 0, c5) + + binary.LittleEndian.PutUint64(z[0*8:1*8], z0) + binary.LittleEndian.PutUint64(z[1*8:2*8], z1) + binary.LittleEndian.PutUint64(z[2*8:3*8], z2) + binary.LittleEndian.PutUint64(z[3*8:4*8], z3) + binary.LittleEndian.PutUint64(z[4*8:5*8], z4) + binary.LittleEndian.PutUint64(z[5*8:6*8], z5) + binary.LittleEndian.PutUint64(z[6*8:7*8], z6) +} + +func subGeneric(z, x, y *Elt) { + x0 := binary.LittleEndian.Uint64(x[0*8 : 1*8]) + x1 := binary.LittleEndian.Uint64(x[1*8 : 2*8]) + x2 := binary.LittleEndian.Uint64(x[2*8 : 3*8]) + x3 := binary.LittleEndian.Uint64(x[3*8 : 4*8]) + x4 := binary.LittleEndian.Uint64(x[4*8 : 5*8]) + x5 := binary.LittleEndian.Uint64(x[5*8 : 6*8]) + x6 := binary.LittleEndian.Uint64(x[6*8 : 7*8]) + + y0 := binary.LittleEndian.Uint64(y[0*8 : 1*8]) + y1 := binary.LittleEndian.Uint64(y[1*8 : 2*8]) + y2 := binary.LittleEndian.Uint64(y[2*8 : 3*8]) + y3 := binary.LittleEndian.Uint64(y[3*8 : 4*8]) + y4 := binary.LittleEndian.Uint64(y[4*8 : 5*8]) + y5 := binary.LittleEndian.Uint64(y[5*8 : 6*8]) + y6 := binary.LittleEndian.Uint64(y[6*8 : 7*8]) + + z0, c0 := bits.Sub64(x0, y0, 0) + z1, c1 := bits.Sub64(x1, y1, c0) + z2, c2 := bits.Sub64(x2, y2, c1) + z3, c3 := bits.Sub64(x3, y3, c2) + z4, c4 := bits.Sub64(x4, y4, c3) + z5, c5 := bits.Sub64(x5, y5, c4) + z6, z7 := bits.Sub64(x6, y6, c5) + + z0, c0 = bits.Sub64(z0, z7, 0) + z1, c1 = bits.Sub64(z1, 0, c0) + z2, c2 = bits.Sub64(z2, 0, c1) + z3, c3 = bits.Sub64(z3, z7<<32, c2) + z4, c4 = bits.Sub64(z4, 0, c3) + z5, c5 = bits.Sub64(z5, 0, c4) + z6, z7 = bits.Sub64(z6, 0, c5) + + z0, c0 = bits.Sub64(z0, z7, 0) + z1, c1 = bits.Sub64(z1, 0, c0) + z2, c2 = bits.Sub64(z2, 0, c1) + z3, c3 = bits.Sub64(z3, z7<<32, c2) + z4, c4 = bits.Sub64(z4, 0, c3) + z5, c5 = bits.Sub64(z5, 0, c4) + z6, _ = bits.Sub64(z6, 0, c5) + + binary.LittleEndian.PutUint64(z[0*8:1*8], z0) + binary.LittleEndian.PutUint64(z[1*8:2*8], z1) + binary.LittleEndian.PutUint64(z[2*8:3*8], z2) + binary.LittleEndian.PutUint64(z[3*8:4*8], z3) + binary.LittleEndian.PutUint64(z[4*8:5*8], z4) + binary.LittleEndian.PutUint64(z[5*8:6*8], z5) + binary.LittleEndian.PutUint64(z[6*8:7*8], z6) +} + +func addsubGeneric(x, y *Elt) { + z := &Elt{} + addGeneric(z, x, y) + subGeneric(y, x, y) + *x = *z +} + +func mulGeneric(z, x, y *Elt) { + x0 := binary.LittleEndian.Uint64(x[0*8 : 1*8]) + x1 := binary.LittleEndian.Uint64(x[1*8 : 2*8]) + x2 := binary.LittleEndian.Uint64(x[2*8 : 3*8]) + x3 := binary.LittleEndian.Uint64(x[3*8 : 4*8]) + x4 := binary.LittleEndian.Uint64(x[4*8 : 5*8]) + x5 := binary.LittleEndian.Uint64(x[5*8 : 6*8]) + x6 := binary.LittleEndian.Uint64(x[6*8 : 7*8]) + + y0 := binary.LittleEndian.Uint64(y[0*8 : 1*8]) + y1 := binary.LittleEndian.Uint64(y[1*8 : 2*8]) + y2 := binary.LittleEndian.Uint64(y[2*8 : 3*8]) + y3 := binary.LittleEndian.Uint64(y[3*8 : 4*8]) + y4 := binary.LittleEndian.Uint64(y[4*8 : 5*8]) + y5 := binary.LittleEndian.Uint64(y[5*8 : 6*8]) + y6 := binary.LittleEndian.Uint64(y[6*8 : 7*8]) + + yy := [7]uint64{y0, y1, y2, y3, y4, y5, y6} + zz := [7]uint64{} + + yi := yy[0] + h0, l0 := bits.Mul64(x0, yi) + h1, l1 := bits.Mul64(x1, yi) + h2, l2 := bits.Mul64(x2, yi) + h3, l3 := bits.Mul64(x3, yi) + h4, l4 := bits.Mul64(x4, yi) + h5, l5 := bits.Mul64(x5, yi) + h6, l6 := bits.Mul64(x6, yi) + + zz[0] = l0 + a0, c0 := bits.Add64(h0, l1, 0) + a1, c1 := bits.Add64(h1, l2, c0) + a2, c2 := bits.Add64(h2, l3, c1) + a3, c3 := bits.Add64(h3, l4, c2) + a4, c4 := bits.Add64(h4, l5, c3) + a5, c5 := bits.Add64(h5, l6, c4) + a6, _ := bits.Add64(h6, 0, c5) + + for i := 1; i < 7; i++ { + yi = yy[i] + h0, l0 = bits.Mul64(x0, yi) + h1, l1 = bits.Mul64(x1, yi) + h2, l2 = bits.Mul64(x2, yi) + h3, l3 = bits.Mul64(x3, yi) + h4, l4 = bits.Mul64(x4, yi) + h5, l5 = bits.Mul64(x5, yi) + h6, l6 = bits.Mul64(x6, yi) + + zz[i], c0 = bits.Add64(a0, l0, 0) + a0, c1 = bits.Add64(a1, l1, c0) + a1, c2 = bits.Add64(a2, l2, c1) + a2, c3 = bits.Add64(a3, l3, c2) + a3, c4 = bits.Add64(a4, l4, c3) + a4, c5 = bits.Add64(a5, l5, c4) + a5, a6 = bits.Add64(a6, l6, c5) + + a0, c0 = bits.Add64(a0, h0, 0) + a1, c1 = bits.Add64(a1, h1, c0) + a2, c2 = bits.Add64(a2, h2, c1) + a3, c3 = bits.Add64(a3, h3, c2) + a4, c4 = bits.Add64(a4, h4, c3) + a5, c5 = bits.Add64(a5, h5, c4) + a6, _ = bits.Add64(a6, h6, c5) + } + red64(z, &zz, &[7]uint64{a0, a1, a2, a3, a4, a5, a6}) +} + +func sqrGeneric(z, x *Elt) { mulGeneric(z, x, x) } + +func red64(z *Elt, l, h *[7]uint64) { + /* (2C13, 2C12, 2C11, 2C10|C10, C9, C8, C7) + (C6,...,C0) */ + h0 := h[0] + h1 := h[1] + h2 := h[2] + h3 := ((h[3] & (0xFFFFFFFF << 32)) << 1) | (h[3] & 0xFFFFFFFF) + h4 := (h[3] >> 63) | (h[4] << 1) + h5 := (h[4] >> 63) | (h[5] << 1) + h6 := (h[5] >> 63) | (h[6] << 1) + h7 := (h[6] >> 63) + + l0, c0 := bits.Add64(h0, l[0], 0) + l1, c1 := bits.Add64(h1, l[1], c0) + l2, c2 := bits.Add64(h2, l[2], c1) + l3, c3 := bits.Add64(h3, l[3], c2) + l4, c4 := bits.Add64(h4, l[4], c3) + l5, c5 := bits.Add64(h5, l[5], c4) + l6, c6 := bits.Add64(h6, l[6], c5) + l7, _ := bits.Add64(h7, 0, c6) + + /* (C10C9, C9C8,C8C7,C7C13,C13C12,C12C11,C11C10) + (C6,...,C0) */ + h0 = (h[3] >> 32) | (h[4] << 32) + h1 = (h[4] >> 32) | (h[5] << 32) + h2 = (h[5] >> 32) | (h[6] << 32) + h3 = (h[6] >> 32) | (h[0] << 32) + h4 = (h[0] >> 32) | (h[1] << 32) + h5 = (h[1] >> 32) | (h[2] << 32) + h6 = (h[2] >> 32) | (h[3] << 32) + + l0, c0 = bits.Add64(l0, h0, 0) + l1, c1 = bits.Add64(l1, h1, c0) + l2, c2 = bits.Add64(l2, h2, c1) + l3, c3 = bits.Add64(l3, h3, c2) + l4, c4 = bits.Add64(l4, h4, c3) + l5, c5 = bits.Add64(l5, h5, c4) + l6, c6 = bits.Add64(l6, h6, c5) + l7, _ = bits.Add64(l7, 0, c6) + + /* (C7) + (C6,...,C0) */ + l0, c0 = bits.Add64(l0, l7, 0) + l1, c1 = bits.Add64(l1, 0, c0) + l2, c2 = bits.Add64(l2, 0, c1) + l3, c3 = bits.Add64(l3, l7<<32, c2) + l4, c4 = bits.Add64(l4, 0, c3) + l5, c5 = bits.Add64(l5, 0, c4) + l6, l7 = bits.Add64(l6, 0, c5) + + /* (C7) + (C6,...,C0) */ + l0, c0 = bits.Add64(l0, l7, 0) + l1, c1 = bits.Add64(l1, 0, c0) + l2, c2 = bits.Add64(l2, 0, c1) + l3, c3 = bits.Add64(l3, l7<<32, c2) + l4, c4 = bits.Add64(l4, 0, c3) + l5, c5 = bits.Add64(l5, 0, c4) + l6, _ = bits.Add64(l6, 0, c5) + + binary.LittleEndian.PutUint64(z[0*8:1*8], l0) + binary.LittleEndian.PutUint64(z[1*8:2*8], l1) + binary.LittleEndian.PutUint64(z[2*8:3*8], l2) + binary.LittleEndian.PutUint64(z[3*8:4*8], l3) + binary.LittleEndian.PutUint64(z[4*8:5*8], l4) + binary.LittleEndian.PutUint64(z[5*8:6*8], l5) + binary.LittleEndian.PutUint64(z[6*8:7*8], l6) +} diff --git a/vendor/github.com/cloudflare/circl/math/fp448/fp_noasm.go b/vendor/github.com/cloudflare/circl/math/fp448/fp_noasm.go new file mode 100644 index 00000000..a62225d2 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/math/fp448/fp_noasm.go @@ -0,0 +1,12 @@ +//go:build !amd64 || purego +// +build !amd64 purego + +package fp448 + +func cmov(x, y *Elt, n uint) { cmovGeneric(x, y, n) } +func cswap(x, y *Elt, n uint) { cswapGeneric(x, y, n) } +func add(z, x, y *Elt) { addGeneric(z, x, y) } +func sub(z, x, y *Elt) { subGeneric(z, x, y) } +func addsub(x, y *Elt) { addsubGeneric(x, y) } +func mul(z, x, y *Elt) { mulGeneric(z, x, y) } +func sqr(z, x *Elt) { sqrGeneric(z, x) } diff --git a/vendor/github.com/cloudflare/circl/math/fp448/fuzzer.go b/vendor/github.com/cloudflare/circl/math/fp448/fuzzer.go new file mode 100644 index 00000000..2d7afc80 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/math/fp448/fuzzer.go @@ -0,0 +1,75 @@ +//go:build gofuzz +// +build gofuzz + +// How to run the fuzzer: +// +// $ go get -u github.com/dvyukov/go-fuzz/go-fuzz +// $ go get -u github.com/dvyukov/go-fuzz/go-fuzz-build +// $ go-fuzz-build -libfuzzer -func FuzzReduction -o lib.a +// $ clang -fsanitize=fuzzer lib.a -o fu.exe +// $ ./fu.exe +package fp448 + +import ( + "encoding/binary" + "fmt" + "math/big" + + "github.com/cloudflare/circl/internal/conv" +) + +// FuzzReduction is a fuzzer target for red64 function, which reduces t +// (112 bits) to a number t' (56 bits) congruent modulo p448. +func FuzzReduction(data []byte) int { + if len(data) != 2*Size { + return -1 + } + var got, want Elt + var lo, hi [7]uint64 + a := data[:Size] + b := data[Size:] + lo[0] = binary.LittleEndian.Uint64(a[0*8 : 1*8]) + lo[1] = binary.LittleEndian.Uint64(a[1*8 : 2*8]) + lo[2] = binary.LittleEndian.Uint64(a[2*8 : 3*8]) + lo[3] = binary.LittleEndian.Uint64(a[3*8 : 4*8]) + lo[4] = binary.LittleEndian.Uint64(a[4*8 : 5*8]) + lo[5] = binary.LittleEndian.Uint64(a[5*8 : 6*8]) + lo[6] = binary.LittleEndian.Uint64(a[6*8 : 7*8]) + + hi[0] = binary.LittleEndian.Uint64(b[0*8 : 1*8]) + hi[1] = binary.LittleEndian.Uint64(b[1*8 : 2*8]) + hi[2] = binary.LittleEndian.Uint64(b[2*8 : 3*8]) + hi[3] = binary.LittleEndian.Uint64(b[3*8 : 4*8]) + hi[4] = binary.LittleEndian.Uint64(b[4*8 : 5*8]) + hi[5] = binary.LittleEndian.Uint64(b[5*8 : 6*8]) + hi[6] = binary.LittleEndian.Uint64(b[6*8 : 7*8]) + + red64(&got, &lo, &hi) + + t := conv.BytesLe2BigInt(data[:2*Size]) + + two448 := big.NewInt(1) + two448.Lsh(two448, 448) // 2^448 + mask448 := big.NewInt(1) + mask448.Sub(two448, mask448) // 2^448-1 + two224plus1 := big.NewInt(1) + two224plus1.Lsh(two224plus1, 224) + two224plus1.Add(two224plus1, big.NewInt(1)) // 2^224+1 + + var loBig, hiBig big.Int + for t.Cmp(two448) >= 0 { + loBig.And(t, mask448) + hiBig.Rsh(t, 448) + t.Mul(&hiBig, two224plus1) + t.Add(t, &loBig) + } + conv.BigInt2BytesLe(want[:], t) + + if got != want { + fmt.Printf("in: %v\n", conv.BytesLe2BigInt(data[:2*Size])) + fmt.Printf("got: %v\n", got) + fmt.Printf("want: %v\n", want) + panic("error found") + } + return 1 +} diff --git a/vendor/github.com/cloudflare/circl/pke/kyber/internal/common/amd64.go b/vendor/github.com/cloudflare/circl/pke/kyber/internal/common/amd64.go new file mode 100644 index 00000000..79629160 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/pke/kyber/internal/common/amd64.go @@ -0,0 +1,302 @@ +//go:build amd64 +// +build amd64 + +package common + +import ( + "golang.org/x/sys/cpu" +) + +// ZetasAVX2 contains all ζ used in NTT (like the Zetas array), but also +// the values int16(zeta * 62209) for each zeta, which is used in +// Montgomery reduction. There is some duplication and reordering as +// compared to Zetas to make it more covenient for use with AVX2. +var ZetasAVX2 = [...]int16{ + // level 1: int16(Zetas[1]*62209) and Zetas[1] + 31499, 2571, + + // level 2 + // + // int16(Zetas[2]*62209), Zetas[2], int16(Zetas[3]*62209), Zetas[3] + 14746, 2970, 788, 1812, + + // level 3, like level 2. + 13525, 1493, -12402, 1422, 28191, 287, -16694, 202, + + 0, 0, // padding + + // layer 4. offset: 1*16 + // + // The precomputed multiplication and zetas are grouped by 16 at a + // time as used in the set of butterflies, etc. + -20906, -20906, -20906, -20906, -20906, -20906, -20906, -20906, + 27758, 27758, 27758, 27758, 27758, 27758, 27758, 27758, + 3158, 3158, 3158, 3158, 3158, 3158, 3158, 3158, + 622, 622, 622, 622, 622, 622, 622, 622, + -3799, -3799, -3799, -3799, -3799, -3799, -3799, -3799, + -15690, -15690, -15690, -15690, -15690, -15690, -15690, -15690, + 1577, 1577, 1577, 1577, 1577, 1577, 1577, 1577, + 182, 182, 182, 182, 182, 182, 182, 182, + 10690, 10690, 10690, 10690, 10690, 10690, 10690, 10690, + 1359, 1359, 1359, 1359, 1359, 1359, 1359, 1359, + 962, 962, 962, 962, 962, 962, 962, 962, + 2127, 2127, 2127, 2127, 2127, 2127, 2127, 2127, + -11201, -11201, -11201, -11201, -11201, -11201, -11201, -11201, + 31164, 31164, 31164, 31164, 31164, 31164, 31164, 31164, + 1855, 1855, 1855, 1855, 1855, 1855, 1855, 1855, + 1468, 1468, 1468, 1468, 1468, 1468, 1468, 1468, + + // layer 5. offset: 9*16 + -5827, -5827, -5827, -5827, 17364, 17364, 17364, 17364, + -26360, -26360, -26360, -26360, -29057, -29057, -29057, -29057, + 573, 573, 573, 573, 2004, 2004, 2004, 2004, + 264, 264, 264, 264, 383, 383, 383, 383, + 5572, 5572, 5572, 5572, -1102, -1102, -1102, -1102, + 21439, 21439, 21439, 21439, -26241, -26241, -26241, -26241, + 2500, 2500, 2500, 2500, 1458, 1458, 1458, 1458, + 1727, 1727, 1727, 1727, 3199, 3199, 3199, 3199, + -28072, -28072, -28072, -28072, 24313, 24313, 24313, 24313, + -10532, -10532, -10532, -10532, 8800, 8800, 8800, 8800, + 2648, 2648, 2648, 2648, 1017, 1017, 1017, 1017, + 732, 732, 732, 732, 608, 608, 608, 608, + 18427, 18427, 18427, 18427, 8859, 8859, 8859, 8859, + 26676, 26676, 26676, 26676, -16162, -16162, -16162, -16162, + 1787, 1787, 1787, 1787, 411, 411, 411, 411, + 3124, 3124, 3124, 3124, 1758, 1758, 1758, 1758, + + // layer 6. offset: 17*16 + -5689, -5689, -6516, -6516, 1497, 1497, 30967, 30967, + -23564, -23564, 20179, 20179, 20711, 20711, 25081, 25081, + 1223, 1223, 652, 652, 2777, 2777, 1015, 1015, + 2036, 2036, 1491, 1491, 3047, 3047, 1785, 1785, + -12796, -12796, 26617, 26617, 16065, 16065, -12441, -12441, + 9135, 9135, -649, -649, -25986, -25986, 27837, 27837, + 516, 516, 3321, 3321, 3009, 3009, 2663, 2663, + 1711, 1711, 2167, 2167, 126, 126, 1469, 1469, + 19884, 19884, -28249, -28249, -15886, -15886, -8898, -8898, + -28309, -28309, 9076, 9076, -30198, -30198, 18250, 18250, + 2476, 2476, 3239, 3239, 3058, 3058, 830, 830, + 107, 107, 1908, 1908, 3082, 3082, 2378, 2378, + 13427, 13427, 14017, 14017, -29155, -29155, -12756, -12756, + 16832, 16832, 4312, 4312, -24155, -24155, -17914, -17914, + 2931, 2931, 961, 961, 1821, 1821, 2604, 2604, + 448, 448, 2264, 2264, 677, 677, 2054, 2054, + + // layer 7. offset: 25*16 + -334, 11182, -11477, 13387, -32226, -14233, 20494, -21655, + -27738, 13131, 945, -4586, -14882, 23093, 6182, 5493, + 2226, 430, 555, 843, 2078, 871, 1550, 105, + 422, 587, 177, 3094, 3038, 2869, 1574, 1653, + 32011, -32502, 10631, 30318, 29176, -18741, -28761, 12639, + -18485, 20100, 17561, 18525, -14430, 19529, -5275, -12618, + 3083, 778, 1159, 3182, 2552, 1483, 2727, 1119, + 1739, 644, 2457, 349, 418, 329, 3173, 3254, + -31183, 20297, 25435, 2146, -7382, 15356, 24392, -32384, + -20926, -6279, 10946, -14902, 24215, -11044, 16990, 14470, + 817, 1097, 603, 610, 1322, 2044, 1864, 384, + 2114, 3193, 1218, 1994, 2455, 220, 2142, 1670, + 10336, -21497, -7933, -20198, -22501, 23211, 10907, -17442, + 31637, -23859, 28644, -20257, 23998, 7757, -17422, 23132, + 2144, 1799, 2051, 794, 1819, 2475, 2459, 478, + 3221, 3021, 996, 991, 958, 1869, 1522, 1628, + + // layer 1 inverse + 23132, -17422, 7757, 23998, -20257, 28644, -23859, 31637, + -17442, 10907, 23211, -22501, -20198, -7933, -21497, 10336, + 1628, 1522, 1869, 958, 991, 996, 3021, 3221, + 478, 2459, 2475, 1819, 794, 2051, 1799, 2144, + 14470, 16990, -11044, 24215, -14902, 10946, -6279, -20926, + -32384, 24392, 15356, -7382, 2146, 25435, 20297, -31183, + 1670, 2142, 220, 2455, 1994, 1218, 3193, 2114, + 384, 1864, 2044, 1322, 610, 603, 1097, 817, + -12618, -5275, 19529, -14430, 18525, 17561, 20100, -18485, + 12639, -28761, -18741, 29176, 30318, 10631, -32502, 32011, + 3254, 3173, 329, 418, 349, 2457, 644, 1739, + 1119, 2727, 1483, 2552, 3182, 1159, 778, 3083, + 5493, 6182, 23093, -14882, -4586, 945, 13131, -27738, + -21655, 20494, -14233, -32226, 13387, -11477, 11182, -334, + 1653, 1574, 2869, 3038, 3094, 177, 587, 422, + 105, 1550, 871, 2078, 843, 555, 430, 2226, + + // layer 2 inverse + -17914, -17914, -24155, -24155, 4312, 4312, 16832, 16832, + -12756, -12756, -29155, -29155, 14017, 14017, 13427, 13427, + 2054, 2054, 677, 677, 2264, 2264, 448, 448, + 2604, 2604, 1821, 1821, 961, 961, 2931, 2931, + 18250, 18250, -30198, -30198, 9076, 9076, -28309, -28309, + -8898, -8898, -15886, -15886, -28249, -28249, 19884, 19884, + 2378, 2378, 3082, 3082, 1908, 1908, 107, 107, + 830, 830, 3058, 3058, 3239, 3239, 2476, 2476, + 27837, 27837, -25986, -25986, -649, -649, 9135, 9135, + -12441, -12441, 16065, 16065, 26617, 26617, -12796, -12796, + 1469, 1469, 126, 126, 2167, 2167, 1711, 1711, + 2663, 2663, 3009, 3009, 3321, 3321, 516, 516, + 25081, 25081, 20711, 20711, 20179, 20179, -23564, -23564, + 30967, 30967, 1497, 1497, -6516, -6516, -5689, -5689, + 1785, 1785, 3047, 3047, 1491, 1491, 2036, 2036, + 1015, 1015, 2777, 2777, 652, 652, 1223, 1223, + + // layer 3 inverse + -16162, -16162, -16162, -16162, 26676, 26676, 26676, 26676, + 8859, 8859, 8859, 8859, 18427, 18427, 18427, 18427, + 1758, 1758, 1758, 1758, 3124, 3124, 3124, 3124, + 411, 411, 411, 411, 1787, 1787, 1787, 1787, + 8800, 8800, 8800, 8800, -10532, -10532, -10532, -10532, + 24313, 24313, 24313, 24313, -28072, -28072, -28072, -28072, + 608, 608, 608, 608, 732, 732, 732, 732, + 1017, 1017, 1017, 1017, 2648, 2648, 2648, 2648, + -26241, -26241, -26241, -26241, 21439, 21439, 21439, 21439, + -1102, -1102, -1102, -1102, 5572, 5572, 5572, 5572, + 3199, 3199, 3199, 3199, 1727, 1727, 1727, 1727, + 1458, 1458, 1458, 1458, 2500, 2500, 2500, 2500, + -29057, -29057, -29057, -29057, -26360, -26360, -26360, -26360, + 17364, 17364, 17364, 17364, -5827, -5827, -5827, -5827, + 383, 383, 383, 383, 264, 264, 264, 264, + 2004, 2004, 2004, 2004, 573, 573, 573, 573, + + // layer 4 inverse + 31164, 31164, 31164, 31164, 31164, 31164, 31164, 31164, + -11201, -11201, -11201, -11201, -11201, -11201, -11201, -11201, + 1468, 1468, 1468, 1468, 1468, 1468, 1468, 1468, + 1855, 1855, 1855, 1855, 1855, 1855, 1855, 1855, + 1359, 1359, 1359, 1359, 1359, 1359, 1359, 1359, + 10690, 10690, 10690, 10690, 10690, 10690, 10690, 10690, + 2127, 2127, 2127, 2127, 2127, 2127, 2127, 2127, + 962, 962, 962, 962, 962, 962, 962, 962, + -15690, -15690, -15690, -15690, -15690, -15690, -15690, -15690, + -3799, -3799, -3799, -3799, -3799, -3799, -3799, -3799, + 182, 182, 182, 182, 182, 182, 182, 182, + 1577, 1577, 1577, 1577, 1577, 1577, 1577, 1577, + 27758, 27758, 27758, 27758, 27758, 27758, 27758, 27758, + -20906, -20906, -20906, -20906, -20906, -20906, -20906, -20906, + 622, 622, 622, 622, 622, 622, 622, 622, + 3158, 3158, 3158, 3158, 3158, 3158, 3158, 3158, + + // layer 5 inverse + -16694, 202, 28191, 287, -12402, 1422, 13525, 1493, + + // layer 6 inverse + 788, 1812, 14746, 2970, + + // layer 7 inverse + 31499, 2571, +} + +// Sets p to a + b. Does not normalize coefficients. +func (p *Poly) Add(a, b *Poly) { + if cpu.X86.HasAVX2 { + addAVX2( + (*[N]int16)(p), + (*[N]int16)(a), + (*[N]int16)(b), + ) + } else { + p.addGeneric(a, b) + } +} + +// Sets p to a - b. Does not normalize coefficients. +func (p *Poly) Sub(a, b *Poly) { + if cpu.X86.HasAVX2 { + subAVX2( + (*[N]int16)(p), + (*[N]int16)(a), + (*[N]int16)(b), + ) + } else { + p.subGeneric(a, b) + } +} + +// Executes an in-place forward "NTT" on p. +// +// Assumes the coefficients are in absolute value ≤q. The resulting +// coefficients are in absolute value ≤7q. If the input is in Montgomery +// form, then the result is in Montgomery form and so (by linearity of the NTT) +// if the input is in regular form, then the result is also in regular form. +// The order of coefficients will be "tangled". These can be put back into +// their proper order by calling Detangle(). +func (p *Poly) NTT() { + if cpu.X86.HasAVX2 { + nttAVX2((*[N]int16)(p)) + } else { + p.nttGeneric() + } +} + +// Executes an in-place inverse "NTT" on p and multiply by the Montgomery +// factor R. +// +// Requires coefficients to be in "tangled" order, see Tangle(). +// Assumes the coefficients are in absolute value ≤q. The resulting +// coefficients are in absolute value ≤q. If the input is in Montgomery +// form, then the result is in Montgomery form and so (by linearity) +// if the input is in regular form, then the result is also in regular form. +func (p *Poly) InvNTT() { + if cpu.X86.HasAVX2 { + invNttAVX2((*[N]int16)(p)) + } else { + p.invNTTGeneric() + } +} + +// Sets p to the "pointwise" multiplication of a and b. +// +// That is: InvNTT(p) = InvNTT(a) * InvNTT(b). Assumes a and b are in +// Montgomery form. Products between coefficients of a and b must be strictly +// bounded in absolute value by 2¹⁵q. p will be in Montgomery form and +// bounded in absolute value by 2q. +// +// Requires a and b to be in "tangled" order, see Tangle(). p will be in +// tangled order as well. +func (p *Poly) MulHat(a, b *Poly) { + if cpu.X86.HasAVX2 { + mulHatAVX2( + (*[N]int16)(p), + (*[N]int16)(a), + (*[N]int16)(b), + ) + } else { + p.mulHatGeneric(a, b) + } +} + +// Puts p into the right form to be used with (among others) InvNTT(). +func (p *Poly) Tangle() { + if cpu.X86.HasAVX2 { + tangleAVX2((*[N]int16)(p)) + } + + // When AVX2 is not available, we use the standard order. +} + +// Puts p back into standard form. +func (p *Poly) Detangle() { + if cpu.X86.HasAVX2 { + detangleAVX2((*[N]int16)(p)) + } + + // When AVX2 is not available, we use the standard order. +} + +// Almost normalizes coefficients. +// +// Ensures each coefficient is in {0, …, q}. +func (p *Poly) BarrettReduce() { + if cpu.X86.HasAVX2 { + barrettReduceAVX2((*[N]int16)(p)) + } else { + p.barrettReduceGeneric() + } +} + +// Normalizes coefficients. +// +// Ensures each coefficient is in {0, …, q-1}. +func (p *Poly) Normalize() { + if cpu.X86.HasAVX2 { + normalizeAVX2((*[N]int16)(p)) + } else { + p.normalizeGeneric() + } +} diff --git a/vendor/github.com/cloudflare/circl/pke/kyber/internal/common/amd64.s b/vendor/github.com/cloudflare/circl/pke/kyber/internal/common/amd64.s new file mode 100644 index 00000000..d8205465 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/pke/kyber/internal/common/amd64.s @@ -0,0 +1,2354 @@ +// Code generated by command: go run src.go -out ../amd64.s -stubs ../stubs_amd64.go -pkg common. DO NOT EDIT. + +// +build amd64 + +#include "textflag.h" + +// func addAVX2(p *[256]int16, a *[256]int16, b *[256]int16) +// Requires: AVX, AVX2 +TEXT ·addAVX2(SB), NOSPLIT, $0-24 + MOVQ p+0(FP), AX + MOVQ a+8(FP), CX + MOVQ b+16(FP), DX + VMOVDQU (CX), Y0 + VMOVDQU 32(CX), Y2 + VMOVDQU 64(CX), Y4 + VMOVDQU 96(CX), Y6 + VMOVDQU 128(CX), Y8 + VMOVDQU 160(CX), Y10 + VMOVDQU 192(CX), Y12 + VMOVDQU 224(CX), Y14 + VMOVDQU (DX), Y1 + VMOVDQU 32(DX), Y3 + VMOVDQU 64(DX), Y5 + VMOVDQU 96(DX), Y7 + VMOVDQU 128(DX), Y9 + VMOVDQU 160(DX), Y11 + VMOVDQU 192(DX), Y13 + VMOVDQU 224(DX), Y15 + VPADDW Y0, Y1, Y1 + VPADDW Y2, Y3, Y3 + VPADDW Y4, Y5, Y5 + VPADDW Y6, Y7, Y7 + VPADDW Y8, Y9, Y9 + VPADDW Y10, Y11, Y11 + VPADDW Y12, Y13, Y13 + VPADDW Y14, Y15, Y15 + VMOVDQU Y1, (AX) + VMOVDQU Y3, 32(AX) + VMOVDQU Y5, 64(AX) + VMOVDQU Y7, 96(AX) + VMOVDQU Y9, 128(AX) + VMOVDQU Y11, 160(AX) + VMOVDQU Y13, 192(AX) + VMOVDQU Y15, 224(AX) + VMOVDQU 256(CX), Y0 + VMOVDQU 288(CX), Y2 + VMOVDQU 320(CX), Y4 + VMOVDQU 352(CX), Y6 + VMOVDQU 384(CX), Y8 + VMOVDQU 416(CX), Y10 + VMOVDQU 448(CX), Y12 + VMOVDQU 480(CX), Y14 + VMOVDQU 256(DX), Y1 + VMOVDQU 288(DX), Y3 + VMOVDQU 320(DX), Y5 + VMOVDQU 352(DX), Y7 + VMOVDQU 384(DX), Y9 + VMOVDQU 416(DX), Y11 + VMOVDQU 448(DX), Y13 + VMOVDQU 480(DX), Y15 + VPADDW Y0, Y1, Y1 + VPADDW Y2, Y3, Y3 + VPADDW Y4, Y5, Y5 + VPADDW Y6, Y7, Y7 + VPADDW Y8, Y9, Y9 + VPADDW Y10, Y11, Y11 + VPADDW Y12, Y13, Y13 + VPADDW Y14, Y15, Y15 + VMOVDQU Y1, 256(AX) + VMOVDQU Y3, 288(AX) + VMOVDQU Y5, 320(AX) + VMOVDQU Y7, 352(AX) + VMOVDQU Y9, 384(AX) + VMOVDQU Y11, 416(AX) + VMOVDQU Y13, 448(AX) + VMOVDQU Y15, 480(AX) + RET + +// func subAVX2(p *[256]int16, a *[256]int16, b *[256]int16) +// Requires: AVX, AVX2 +TEXT ·subAVX2(SB), NOSPLIT, $0-24 + MOVQ p+0(FP), AX + MOVQ a+8(FP), CX + MOVQ b+16(FP), DX + VMOVDQU (CX), Y0 + VMOVDQU 32(CX), Y2 + VMOVDQU 64(CX), Y4 + VMOVDQU 96(CX), Y6 + VMOVDQU 128(CX), Y8 + VMOVDQU 160(CX), Y10 + VMOVDQU 192(CX), Y12 + VMOVDQU 224(CX), Y14 + VMOVDQU (DX), Y1 + VMOVDQU 32(DX), Y3 + VMOVDQU 64(DX), Y5 + VMOVDQU 96(DX), Y7 + VMOVDQU 128(DX), Y9 + VMOVDQU 160(DX), Y11 + VMOVDQU 192(DX), Y13 + VMOVDQU 224(DX), Y15 + VPSUBW Y1, Y0, Y1 + VPSUBW Y3, Y2, Y3 + VPSUBW Y5, Y4, Y5 + VPSUBW Y7, Y6, Y7 + VPSUBW Y9, Y8, Y9 + VPSUBW Y11, Y10, Y11 + VPSUBW Y13, Y12, Y13 + VPSUBW Y15, Y14, Y15 + VMOVDQU Y1, (AX) + VMOVDQU Y3, 32(AX) + VMOVDQU Y5, 64(AX) + VMOVDQU Y7, 96(AX) + VMOVDQU Y9, 128(AX) + VMOVDQU Y11, 160(AX) + VMOVDQU Y13, 192(AX) + VMOVDQU Y15, 224(AX) + VMOVDQU 256(CX), Y0 + VMOVDQU 288(CX), Y2 + VMOVDQU 320(CX), Y4 + VMOVDQU 352(CX), Y6 + VMOVDQU 384(CX), Y8 + VMOVDQU 416(CX), Y10 + VMOVDQU 448(CX), Y12 + VMOVDQU 480(CX), Y14 + VMOVDQU 256(DX), Y1 + VMOVDQU 288(DX), Y3 + VMOVDQU 320(DX), Y5 + VMOVDQU 352(DX), Y7 + VMOVDQU 384(DX), Y9 + VMOVDQU 416(DX), Y11 + VMOVDQU 448(DX), Y13 + VMOVDQU 480(DX), Y15 + VPSUBW Y1, Y0, Y1 + VPSUBW Y3, Y2, Y3 + VPSUBW Y5, Y4, Y5 + VPSUBW Y7, Y6, Y7 + VPSUBW Y9, Y8, Y9 + VPSUBW Y11, Y10, Y11 + VPSUBW Y13, Y12, Y13 + VPSUBW Y15, Y14, Y15 + VMOVDQU Y1, 256(AX) + VMOVDQU Y3, 288(AX) + VMOVDQU Y5, 320(AX) + VMOVDQU Y7, 352(AX) + VMOVDQU Y9, 384(AX) + VMOVDQU Y11, 416(AX) + VMOVDQU Y13, 448(AX) + VMOVDQU Y15, 480(AX) + RET + +// func nttAVX2(p *[256]int16) +// Requires: AVX, AVX2 +TEXT ·nttAVX2(SB), NOSPLIT, $0-8 + MOVQ p+0(FP), AX + LEAQ ·ZetasAVX2+0(SB), CX + MOVL $0x00000d01, DX + VMOVD DX, X0 + VPBROADCASTW X0, Y15 + VPBROADCASTW (CX), Y0 + VPBROADCASTW 2(CX), Y1 + VMOVDQU (AX), Y7 + VMOVDQU 32(AX), Y8 + VMOVDQU 64(AX), Y9 + VMOVDQU 96(AX), Y10 + VMOVDQU 256(AX), Y11 + VMOVDQU 288(AX), Y12 + VMOVDQU 320(AX), Y13 + VMOVDQU 352(AX), Y14 + VPMULLW Y11, Y0, Y2 + VPMULLW Y12, Y0, Y3 + VPMULLW Y13, Y0, Y4 + VPMULLW Y14, Y0, Y5 + VPMULHW Y11, Y1, Y11 + VPMULHW Y12, Y1, Y12 + VPMULHW Y13, Y1, Y13 + VPMULHW Y14, Y1, Y14 + VPMULHW Y2, Y15, Y2 + VPMULHW Y3, Y15, Y3 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPSUBW Y2, Y11, Y2 + VPSUBW Y3, Y12, Y3 + VPSUBW Y4, Y13, Y4 + VPSUBW Y5, Y14, Y5 + VPSUBW Y2, Y7, Y11 + VPSUBW Y3, Y8, Y12 + VPSUBW Y4, Y9, Y13 + VPSUBW Y5, Y10, Y14 + VPADDW Y2, Y7, Y7 + VPADDW Y3, Y8, Y8 + VPADDW Y4, Y9, Y9 + VPADDW Y5, Y10, Y10 + VMOVDQU Y7, (AX) + VMOVDQU Y8, 32(AX) + VMOVDQU Y9, 64(AX) + VMOVDQU Y10, 96(AX) + VMOVDQU Y11, 256(AX) + VMOVDQU Y12, 288(AX) + VMOVDQU Y13, 320(AX) + VMOVDQU Y14, 352(AX) + VMOVDQU 128(AX), Y7 + VMOVDQU 160(AX), Y8 + VMOVDQU 192(AX), Y9 + VMOVDQU 224(AX), Y10 + VMOVDQU 384(AX), Y11 + VMOVDQU 416(AX), Y12 + VMOVDQU 448(AX), Y13 + VMOVDQU 480(AX), Y14 + VPMULLW Y11, Y0, Y2 + VPMULLW Y12, Y0, Y3 + VPMULLW Y13, Y0, Y4 + VPMULLW Y14, Y0, Y5 + VPMULHW Y11, Y1, Y11 + VPMULHW Y12, Y1, Y12 + VPMULHW Y13, Y1, Y13 + VPMULHW Y14, Y1, Y14 + VPMULHW Y2, Y15, Y2 + VPMULHW Y3, Y15, Y3 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPSUBW Y2, Y11, Y2 + VPSUBW Y3, Y12, Y3 + VPSUBW Y4, Y13, Y4 + VPSUBW Y5, Y14, Y5 + VPSUBW Y2, Y7, Y11 + VPSUBW Y3, Y8, Y12 + VPSUBW Y4, Y9, Y13 + VPSUBW Y5, Y10, Y14 + VPADDW Y2, Y7, Y7 + VPADDW Y3, Y8, Y8 + VPADDW Y4, Y9, Y9 + VPADDW Y5, Y10, Y10 + VMOVDQU Y7, 128(AX) + VMOVDQU Y8, 160(AX) + VMOVDQU Y9, 192(AX) + VMOVDQU Y10, 224(AX) + VMOVDQU Y11, 384(AX) + VMOVDQU Y12, 416(AX) + VMOVDQU Y13, 448(AX) + VMOVDQU Y14, 480(AX) + VPBROADCASTW 4(CX), Y0 + VPBROADCASTW 6(CX), Y1 + VMOVDQU (AX), Y7 + VMOVDQU 32(AX), Y8 + VMOVDQU 64(AX), Y9 + VMOVDQU 96(AX), Y10 + VMOVDQU 128(AX), Y11 + VMOVDQU 160(AX), Y12 + VMOVDQU 192(AX), Y13 + VMOVDQU 224(AX), Y14 + VPMULLW Y11, Y0, Y2 + VPMULLW Y12, Y0, Y3 + VPMULLW Y13, Y0, Y4 + VPMULLW Y14, Y0, Y5 + VPMULHW Y11, Y1, Y11 + VPMULHW Y12, Y1, Y12 + VPMULHW Y13, Y1, Y13 + VPMULHW Y14, Y1, Y14 + VPMULHW Y2, Y15, Y2 + VPMULHW Y3, Y15, Y3 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPSUBW Y2, Y11, Y2 + VPSUBW Y3, Y12, Y3 + VPSUBW Y4, Y13, Y4 + VPSUBW Y5, Y14, Y5 + VPSUBW Y2, Y7, Y11 + VPSUBW Y3, Y8, Y12 + VPSUBW Y4, Y9, Y13 + VPSUBW Y5, Y10, Y14 + VPADDW Y2, Y7, Y7 + VPADDW Y3, Y8, Y8 + VPADDW Y4, Y9, Y9 + VPADDW Y5, Y10, Y10 + VPBROADCASTW 12(CX), Y0 + VPBROADCASTW 14(CX), Y1 + VPBROADCASTW 16(CX), Y2 + VPBROADCASTW 18(CX), Y3 + VPMULLW Y9, Y0, Y4 + VPMULLW Y10, Y0, Y5 + VPMULLW Y13, Y2, Y6 + VPMULLW Y14, Y2, Y0 + VPMULHW Y9, Y1, Y9 + VPMULHW Y10, Y1, Y10 + VPMULHW Y13, Y3, Y13 + VPMULHW Y14, Y3, Y14 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPMULHW Y6, Y15, Y6 + VPMULHW Y0, Y15, Y0 + VPSUBW Y4, Y9, Y4 + VPSUBW Y5, Y10, Y5 + VPSUBW Y6, Y13, Y6 + VPSUBW Y0, Y14, Y0 + VPSUBW Y4, Y7, Y9 + VPSUBW Y5, Y8, Y10 + VPSUBW Y6, Y11, Y13 + VPSUBW Y0, Y12, Y14 + VPADDW Y4, Y7, Y7 + VPADDW Y5, Y8, Y8 + VPADDW Y6, Y11, Y11 + VPADDW Y0, Y12, Y12 + VMOVDQU 32(CX), Y0 + VMOVDQU 64(CX), Y1 + VMOVDQU 96(CX), Y2 + VMOVDQU 128(CX), Y3 + VPERM2I128 $0x20, Y9, Y7, Y4 + VPERM2I128 $0x31, Y9, Y7, Y9 + VMOVDQA Y4, Y7 + VPERM2I128 $0x20, Y10, Y8, Y4 + VPERM2I128 $0x31, Y10, Y8, Y10 + VMOVDQA Y4, Y8 + VPERM2I128 $0x20, Y13, Y11, Y4 + VPERM2I128 $0x31, Y13, Y11, Y13 + VMOVDQA Y4, Y11 + VPERM2I128 $0x20, Y14, Y12, Y4 + VPERM2I128 $0x31, Y14, Y12, Y14 + VMOVDQA Y4, Y12 + VPMULLW Y8, Y0, Y4 + VPMULLW Y10, Y0, Y5 + VPMULLW Y12, Y2, Y6 + VPMULLW Y14, Y2, Y0 + VPMULHW Y8, Y1, Y8 + VPMULHW Y10, Y1, Y10 + VPMULHW Y12, Y3, Y12 + VPMULHW Y14, Y3, Y14 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPMULHW Y6, Y15, Y6 + VPMULHW Y0, Y15, Y0 + VPSUBW Y4, Y8, Y4 + VPSUBW Y5, Y10, Y5 + VPSUBW Y6, Y12, Y6 + VPSUBW Y0, Y14, Y0 + VPSUBW Y4, Y7, Y8 + VPSUBW Y5, Y9, Y10 + VPSUBW Y6, Y11, Y12 + VPSUBW Y0, Y13, Y14 + VPADDW Y4, Y7, Y7 + VPADDW Y5, Y9, Y9 + VPADDW Y6, Y11, Y11 + VPADDW Y0, Y13, Y13 + VMOVDQU 288(CX), Y0 + VMOVDQU 320(CX), Y1 + VMOVDQU 352(CX), Y2 + VMOVDQU 384(CX), Y3 + VPUNPCKLQDQ Y8, Y7, Y4 + VPUNPCKHQDQ Y8, Y7, Y8 + VMOVDQA Y4, Y7 + VPUNPCKLQDQ Y10, Y9, Y4 + VPUNPCKHQDQ Y10, Y9, Y10 + VMOVDQA Y4, Y9 + VPUNPCKLQDQ Y12, Y11, Y4 + VPUNPCKHQDQ Y12, Y11, Y12 + VMOVDQA Y4, Y11 + VPUNPCKLQDQ Y14, Y13, Y4 + VPUNPCKHQDQ Y14, Y13, Y14 + VMOVDQA Y4, Y13 + VPMULLW Y9, Y0, Y4 + VPMULLW Y10, Y0, Y5 + VPMULLW Y13, Y2, Y6 + VPMULLW Y14, Y2, Y0 + VPMULHW Y9, Y1, Y9 + VPMULHW Y10, Y1, Y10 + VPMULHW Y13, Y3, Y13 + VPMULHW Y14, Y3, Y14 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPMULHW Y6, Y15, Y6 + VPMULHW Y0, Y15, Y0 + VPSUBW Y4, Y9, Y4 + VPSUBW Y5, Y10, Y5 + VPSUBW Y6, Y13, Y6 + VPSUBW Y0, Y14, Y0 + VPSUBW Y4, Y7, Y9 + VPSUBW Y5, Y8, Y10 + VPSUBW Y6, Y11, Y13 + VPSUBW Y0, Y12, Y14 + VPADDW Y4, Y7, Y7 + VPADDW Y5, Y8, Y8 + VPADDW Y6, Y11, Y11 + VPADDW Y0, Y12, Y12 + VMOVDQU 544(CX), Y0 + VMOVDQU 576(CX), Y1 + VMOVDQU 608(CX), Y2 + VMOVDQU 640(CX), Y3 + VMOVSLDUP Y9, Y4 + VPBLENDD $0xaa, Y4, Y7, Y4 + VPSRLQ $0x20, Y7, Y7 + VPBLENDD $0xaa, Y9, Y7, Y9 + VMOVDQA Y4, Y7 + VMOVSLDUP Y10, Y4 + VPBLENDD $0xaa, Y4, Y8, Y4 + VPSRLQ $0x20, Y8, Y8 + VPBLENDD $0xaa, Y10, Y8, Y10 + VMOVDQA Y4, Y8 + VMOVSLDUP Y13, Y4 + VPBLENDD $0xaa, Y4, Y11, Y4 + VPSRLQ $0x20, Y11, Y11 + VPBLENDD $0xaa, Y13, Y11, Y13 + VMOVDQA Y4, Y11 + VMOVSLDUP Y14, Y4 + VPBLENDD $0xaa, Y4, Y12, Y4 + VPSRLQ $0x20, Y12, Y12 + VPBLENDD $0xaa, Y14, Y12, Y14 + VMOVDQA Y4, Y12 + VPMULLW Y8, Y0, Y4 + VPMULLW Y10, Y0, Y5 + VPMULLW Y12, Y2, Y6 + VPMULLW Y14, Y2, Y0 + VPMULHW Y8, Y1, Y8 + VPMULHW Y10, Y1, Y10 + VPMULHW Y12, Y3, Y12 + VPMULHW Y14, Y3, Y14 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPMULHW Y6, Y15, Y6 + VPMULHW Y0, Y15, Y0 + VPSUBW Y4, Y8, Y4 + VPSUBW Y5, Y10, Y5 + VPSUBW Y6, Y12, Y6 + VPSUBW Y0, Y14, Y0 + VPSUBW Y4, Y7, Y8 + VPSUBW Y5, Y9, Y10 + VPSUBW Y6, Y11, Y12 + VPSUBW Y0, Y13, Y14 + VPADDW Y4, Y7, Y7 + VPADDW Y5, Y9, Y9 + VPADDW Y6, Y11, Y11 + VPADDW Y0, Y13, Y13 + VMOVDQU 800(CX), Y0 + VMOVDQU 832(CX), Y1 + VMOVDQU 864(CX), Y2 + VMOVDQU 896(CX), Y3 + VPSLLD $0x10, Y8, Y4 + VPBLENDW $0xaa, Y4, Y7, Y4 + VPSRLD $0x10, Y7, Y7 + VPBLENDW $0xaa, Y8, Y7, Y8 + VMOVDQA Y4, Y7 + VPSLLD $0x10, Y10, Y4 + VPBLENDW $0xaa, Y4, Y9, Y4 + VPSRLD $0x10, Y9, Y9 + VPBLENDW $0xaa, Y10, Y9, Y10 + VMOVDQA Y4, Y9 + VPSLLD $0x10, Y12, Y4 + VPBLENDW $0xaa, Y4, Y11, Y4 + VPSRLD $0x10, Y11, Y11 + VPBLENDW $0xaa, Y12, Y11, Y12 + VMOVDQA Y4, Y11 + VPSLLD $0x10, Y14, Y4 + VPBLENDW $0xaa, Y4, Y13, Y4 + VPSRLD $0x10, Y13, Y13 + VPBLENDW $0xaa, Y14, Y13, Y14 + VMOVDQA Y4, Y13 + VPMULLW Y9, Y0, Y4 + VPMULLW Y10, Y0, Y5 + VPMULLW Y13, Y2, Y6 + VPMULLW Y14, Y2, Y0 + VPMULHW Y9, Y1, Y9 + VPMULHW Y10, Y1, Y10 + VPMULHW Y13, Y3, Y13 + VPMULHW Y14, Y3, Y14 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPMULHW Y6, Y15, Y6 + VPMULHW Y0, Y15, Y0 + VPSUBW Y4, Y9, Y4 + VPSUBW Y5, Y10, Y5 + VPSUBW Y6, Y13, Y6 + VPSUBW Y0, Y14, Y0 + VPSUBW Y4, Y7, Y9 + VPSUBW Y5, Y8, Y10 + VPSUBW Y6, Y11, Y13 + VPSUBW Y0, Y12, Y14 + VPADDW Y4, Y7, Y7 + VPADDW Y5, Y8, Y8 + VPADDW Y6, Y11, Y11 + VPADDW Y0, Y12, Y12 + VMOVDQU Y7, (AX) + VMOVDQU Y8, 32(AX) + VMOVDQU Y9, 64(AX) + VMOVDQU Y10, 96(AX) + VMOVDQU Y11, 128(AX) + VMOVDQU Y12, 160(AX) + VMOVDQU Y13, 192(AX) + VMOVDQU Y14, 224(AX) + VPBROADCASTW 8(CX), Y0 + VPBROADCASTW 10(CX), Y1 + VMOVDQU 256(AX), Y7 + VMOVDQU 288(AX), Y8 + VMOVDQU 320(AX), Y9 + VMOVDQU 352(AX), Y10 + VMOVDQU 384(AX), Y11 + VMOVDQU 416(AX), Y12 + VMOVDQU 448(AX), Y13 + VMOVDQU 480(AX), Y14 + VPMULLW Y11, Y0, Y2 + VPMULLW Y12, Y0, Y3 + VPMULLW Y13, Y0, Y4 + VPMULLW Y14, Y0, Y5 + VPMULHW Y11, Y1, Y11 + VPMULHW Y12, Y1, Y12 + VPMULHW Y13, Y1, Y13 + VPMULHW Y14, Y1, Y14 + VPMULHW Y2, Y15, Y2 + VPMULHW Y3, Y15, Y3 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPSUBW Y2, Y11, Y2 + VPSUBW Y3, Y12, Y3 + VPSUBW Y4, Y13, Y4 + VPSUBW Y5, Y14, Y5 + VPSUBW Y2, Y7, Y11 + VPSUBW Y3, Y8, Y12 + VPSUBW Y4, Y9, Y13 + VPSUBW Y5, Y10, Y14 + VPADDW Y2, Y7, Y7 + VPADDW Y3, Y8, Y8 + VPADDW Y4, Y9, Y9 + VPADDW Y5, Y10, Y10 + VPBROADCASTW 20(CX), Y0 + VPBROADCASTW 22(CX), Y1 + VPBROADCASTW 24(CX), Y2 + VPBROADCASTW 26(CX), Y3 + VPMULLW Y9, Y0, Y4 + VPMULLW Y10, Y0, Y5 + VPMULLW Y13, Y2, Y6 + VPMULLW Y14, Y2, Y0 + VPMULHW Y9, Y1, Y9 + VPMULHW Y10, Y1, Y10 + VPMULHW Y13, Y3, Y13 + VPMULHW Y14, Y3, Y14 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPMULHW Y6, Y15, Y6 + VPMULHW Y0, Y15, Y0 + VPSUBW Y4, Y9, Y4 + VPSUBW Y5, Y10, Y5 + VPSUBW Y6, Y13, Y6 + VPSUBW Y0, Y14, Y0 + VPSUBW Y4, Y7, Y9 + VPSUBW Y5, Y8, Y10 + VPSUBW Y6, Y11, Y13 + VPSUBW Y0, Y12, Y14 + VPADDW Y4, Y7, Y7 + VPADDW Y5, Y8, Y8 + VPADDW Y6, Y11, Y11 + VPADDW Y0, Y12, Y12 + VMOVDQU 160(CX), Y0 + VMOVDQU 192(CX), Y1 + VMOVDQU 224(CX), Y2 + VMOVDQU 256(CX), Y3 + VPERM2I128 $0x20, Y9, Y7, Y4 + VPERM2I128 $0x31, Y9, Y7, Y9 + VMOVDQA Y4, Y7 + VPERM2I128 $0x20, Y10, Y8, Y4 + VPERM2I128 $0x31, Y10, Y8, Y10 + VMOVDQA Y4, Y8 + VPERM2I128 $0x20, Y13, Y11, Y4 + VPERM2I128 $0x31, Y13, Y11, Y13 + VMOVDQA Y4, Y11 + VPERM2I128 $0x20, Y14, Y12, Y4 + VPERM2I128 $0x31, Y14, Y12, Y14 + VMOVDQA Y4, Y12 + VPMULLW Y8, Y0, Y4 + VPMULLW Y10, Y0, Y5 + VPMULLW Y12, Y2, Y6 + VPMULLW Y14, Y2, Y0 + VPMULHW Y8, Y1, Y8 + VPMULHW Y10, Y1, Y10 + VPMULHW Y12, Y3, Y12 + VPMULHW Y14, Y3, Y14 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPMULHW Y6, Y15, Y6 + VPMULHW Y0, Y15, Y0 + VPSUBW Y4, Y8, Y4 + VPSUBW Y5, Y10, Y5 + VPSUBW Y6, Y12, Y6 + VPSUBW Y0, Y14, Y0 + VPSUBW Y4, Y7, Y8 + VPSUBW Y5, Y9, Y10 + VPSUBW Y6, Y11, Y12 + VPSUBW Y0, Y13, Y14 + VPADDW Y4, Y7, Y7 + VPADDW Y5, Y9, Y9 + VPADDW Y6, Y11, Y11 + VPADDW Y0, Y13, Y13 + VMOVDQU 416(CX), Y0 + VMOVDQU 448(CX), Y1 + VMOVDQU 480(CX), Y2 + VMOVDQU 512(CX), Y3 + VPUNPCKLQDQ Y8, Y7, Y4 + VPUNPCKHQDQ Y8, Y7, Y8 + VMOVDQA Y4, Y7 + VPUNPCKLQDQ Y10, Y9, Y4 + VPUNPCKHQDQ Y10, Y9, Y10 + VMOVDQA Y4, Y9 + VPUNPCKLQDQ Y12, Y11, Y4 + VPUNPCKHQDQ Y12, Y11, Y12 + VMOVDQA Y4, Y11 + VPUNPCKLQDQ Y14, Y13, Y4 + VPUNPCKHQDQ Y14, Y13, Y14 + VMOVDQA Y4, Y13 + VPMULLW Y9, Y0, Y4 + VPMULLW Y10, Y0, Y5 + VPMULLW Y13, Y2, Y6 + VPMULLW Y14, Y2, Y0 + VPMULHW Y9, Y1, Y9 + VPMULHW Y10, Y1, Y10 + VPMULHW Y13, Y3, Y13 + VPMULHW Y14, Y3, Y14 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPMULHW Y6, Y15, Y6 + VPMULHW Y0, Y15, Y0 + VPSUBW Y4, Y9, Y4 + VPSUBW Y5, Y10, Y5 + VPSUBW Y6, Y13, Y6 + VPSUBW Y0, Y14, Y0 + VPSUBW Y4, Y7, Y9 + VPSUBW Y5, Y8, Y10 + VPSUBW Y6, Y11, Y13 + VPSUBW Y0, Y12, Y14 + VPADDW Y4, Y7, Y7 + VPADDW Y5, Y8, Y8 + VPADDW Y6, Y11, Y11 + VPADDW Y0, Y12, Y12 + VMOVDQU 672(CX), Y0 + VMOVDQU 704(CX), Y1 + VMOVDQU 736(CX), Y2 + VMOVDQU 768(CX), Y3 + VMOVSLDUP Y9, Y4 + VPBLENDD $0xaa, Y4, Y7, Y4 + VPSRLQ $0x20, Y7, Y7 + VPBLENDD $0xaa, Y9, Y7, Y9 + VMOVDQA Y4, Y7 + VMOVSLDUP Y10, Y4 + VPBLENDD $0xaa, Y4, Y8, Y4 + VPSRLQ $0x20, Y8, Y8 + VPBLENDD $0xaa, Y10, Y8, Y10 + VMOVDQA Y4, Y8 + VMOVSLDUP Y13, Y4 + VPBLENDD $0xaa, Y4, Y11, Y4 + VPSRLQ $0x20, Y11, Y11 + VPBLENDD $0xaa, Y13, Y11, Y13 + VMOVDQA Y4, Y11 + VMOVSLDUP Y14, Y4 + VPBLENDD $0xaa, Y4, Y12, Y4 + VPSRLQ $0x20, Y12, Y12 + VPBLENDD $0xaa, Y14, Y12, Y14 + VMOVDQA Y4, Y12 + VPMULLW Y8, Y0, Y4 + VPMULLW Y10, Y0, Y5 + VPMULLW Y12, Y2, Y6 + VPMULLW Y14, Y2, Y0 + VPMULHW Y8, Y1, Y8 + VPMULHW Y10, Y1, Y10 + VPMULHW Y12, Y3, Y12 + VPMULHW Y14, Y3, Y14 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPMULHW Y6, Y15, Y6 + VPMULHW Y0, Y15, Y0 + VPSUBW Y4, Y8, Y4 + VPSUBW Y5, Y10, Y5 + VPSUBW Y6, Y12, Y6 + VPSUBW Y0, Y14, Y0 + VPSUBW Y4, Y7, Y8 + VPSUBW Y5, Y9, Y10 + VPSUBW Y6, Y11, Y12 + VPSUBW Y0, Y13, Y14 + VPADDW Y4, Y7, Y7 + VPADDW Y5, Y9, Y9 + VPADDW Y6, Y11, Y11 + VPADDW Y0, Y13, Y13 + VMOVDQU 928(CX), Y0 + VMOVDQU 960(CX), Y1 + VMOVDQU 992(CX), Y2 + VMOVDQU 1024(CX), Y3 + VPSLLD $0x10, Y8, Y4 + VPBLENDW $0xaa, Y4, Y7, Y4 + VPSRLD $0x10, Y7, Y7 + VPBLENDW $0xaa, Y8, Y7, Y8 + VMOVDQA Y4, Y7 + VPSLLD $0x10, Y10, Y4 + VPBLENDW $0xaa, Y4, Y9, Y4 + VPSRLD $0x10, Y9, Y9 + VPBLENDW $0xaa, Y10, Y9, Y10 + VMOVDQA Y4, Y9 + VPSLLD $0x10, Y12, Y4 + VPBLENDW $0xaa, Y4, Y11, Y4 + VPSRLD $0x10, Y11, Y11 + VPBLENDW $0xaa, Y12, Y11, Y12 + VMOVDQA Y4, Y11 + VPSLLD $0x10, Y14, Y4 + VPBLENDW $0xaa, Y4, Y13, Y4 + VPSRLD $0x10, Y13, Y13 + VPBLENDW $0xaa, Y14, Y13, Y14 + VMOVDQA Y4, Y13 + VPMULLW Y9, Y0, Y4 + VPMULLW Y10, Y0, Y5 + VPMULLW Y13, Y2, Y6 + VPMULLW Y14, Y2, Y0 + VPMULHW Y9, Y1, Y9 + VPMULHW Y10, Y1, Y10 + VPMULHW Y13, Y3, Y13 + VPMULHW Y14, Y3, Y14 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPMULHW Y6, Y15, Y6 + VPMULHW Y0, Y15, Y0 + VPSUBW Y4, Y9, Y4 + VPSUBW Y5, Y10, Y5 + VPSUBW Y6, Y13, Y6 + VPSUBW Y0, Y14, Y0 + VPSUBW Y4, Y7, Y9 + VPSUBW Y5, Y8, Y10 + VPSUBW Y6, Y11, Y13 + VPSUBW Y0, Y12, Y14 + VPADDW Y4, Y7, Y7 + VPADDW Y5, Y8, Y8 + VPADDW Y6, Y11, Y11 + VPADDW Y0, Y12, Y12 + VMOVDQU Y7, 256(AX) + VMOVDQU Y8, 288(AX) + VMOVDQU Y9, 320(AX) + VMOVDQU Y10, 352(AX) + VMOVDQU Y11, 384(AX) + VMOVDQU Y12, 416(AX) + VMOVDQU Y13, 448(AX) + VMOVDQU Y14, 480(AX) + RET + +// func invNttAVX2(p *[256]int16) +// Requires: AVX, AVX2 +TEXT ·invNttAVX2(SB), NOSPLIT, $0-8 + MOVQ p+0(FP), AX + LEAQ ·ZetasAVX2+0(SB), CX + MOVL $0x00000d01, DX + VMOVD DX, X0 + VPBROADCASTW X0, Y15 + VMOVDQU (AX), Y7 + VMOVDQU 32(AX), Y8 + VMOVDQU 64(AX), Y9 + VMOVDQU 96(AX), Y10 + VMOVDQU 128(AX), Y11 + VMOVDQU 160(AX), Y12 + VMOVDQU 192(AX), Y13 + VMOVDQU 224(AX), Y14 + VMOVDQU 1056(CX), Y0 + VMOVDQU 1088(CX), Y1 + VMOVDQU 1120(CX), Y2 + VMOVDQU 1152(CX), Y3 + VPSUBW Y7, Y9, Y4 + VPSUBW Y8, Y10, Y5 + VPSUBW Y11, Y13, Y6 + VPADDW Y7, Y9, Y7 + VPADDW Y8, Y10, Y8 + VPADDW Y11, Y13, Y11 + VPMULLW Y4, Y0, Y9 + VPMULLW Y5, Y0, Y10 + VPSUBW Y12, Y14, Y0 + VPMULLW Y6, Y2, Y13 + VPADDW Y12, Y14, Y12 + VPMULLW Y0, Y2, Y14 + VPMULHW Y4, Y1, Y4 + VPMULHW Y5, Y1, Y5 + VPMULHW Y6, Y3, Y6 + VPMULHW Y0, Y3, Y0 + VPMULHW Y9, Y15, Y9 + VPMULHW Y10, Y15, Y10 + VPMULHW Y13, Y15, Y13 + VPMULHW Y14, Y15, Y14 + VPSUBW Y9, Y4, Y9 + VPSUBW Y10, Y5, Y10 + VPSUBW Y13, Y6, Y13 + VPSUBW Y14, Y0, Y14 + VMOVDQU 1312(CX), Y0 + VMOVDQU 1344(CX), Y1 + VMOVDQU 1376(CX), Y2 + VMOVDQU 1408(CX), Y3 + VPSLLD $0x10, Y8, Y4 + VPBLENDW $0xaa, Y4, Y7, Y4 + VPSRLD $0x10, Y7, Y7 + VPBLENDW $0xaa, Y8, Y7, Y8 + VMOVDQA Y4, Y7 + VPSLLD $0x10, Y10, Y4 + VPBLENDW $0xaa, Y4, Y9, Y4 + VPSRLD $0x10, Y9, Y9 + VPBLENDW $0xaa, Y10, Y9, Y10 + VMOVDQA Y4, Y9 + VPSLLD $0x10, Y12, Y4 + VPBLENDW $0xaa, Y4, Y11, Y4 + VPSRLD $0x10, Y11, Y11 + VPBLENDW $0xaa, Y12, Y11, Y12 + VMOVDQA Y4, Y11 + VPSLLD $0x10, Y14, Y4 + VPBLENDW $0xaa, Y4, Y13, Y4 + VPSRLD $0x10, Y13, Y13 + VPBLENDW $0xaa, Y14, Y13, Y14 + VMOVDQA Y4, Y13 + VPSUBW Y7, Y8, Y4 + VPSUBW Y9, Y10, Y5 + VPSUBW Y11, Y12, Y6 + VPADDW Y7, Y8, Y7 + VPADDW Y9, Y10, Y9 + VPADDW Y11, Y12, Y11 + VPMULLW Y4, Y0, Y8 + VPMULLW Y5, Y0, Y10 + VPSUBW Y13, Y14, Y0 + VPMULLW Y6, Y2, Y12 + VPADDW Y13, Y14, Y13 + VPMULLW Y0, Y2, Y14 + VPMULHW Y4, Y1, Y4 + VPMULHW Y5, Y1, Y5 + VPMULHW Y6, Y3, Y6 + VPMULHW Y0, Y3, Y0 + VPMULHW Y8, Y15, Y8 + VPMULHW Y10, Y15, Y10 + VPMULHW Y12, Y15, Y12 + VPMULHW Y14, Y15, Y14 + VPSUBW Y8, Y4, Y8 + VPSUBW Y10, Y5, Y10 + VPSUBW Y12, Y6, Y12 + VPSUBW Y14, Y0, Y14 + VMOVDQU 1568(CX), Y0 + VMOVDQU 1600(CX), Y1 + VMOVDQU 1632(CX), Y2 + VMOVDQU 1664(CX), Y3 + VMOVSLDUP Y9, Y4 + VPBLENDD $0xaa, Y4, Y7, Y4 + VPSRLQ $0x20, Y7, Y7 + VPBLENDD $0xaa, Y9, Y7, Y9 + VMOVDQA Y4, Y7 + VMOVSLDUP Y10, Y4 + VPBLENDD $0xaa, Y4, Y8, Y4 + VPSRLQ $0x20, Y8, Y8 + VPBLENDD $0xaa, Y10, Y8, Y10 + VMOVDQA Y4, Y8 + VMOVSLDUP Y13, Y4 + VPBLENDD $0xaa, Y4, Y11, Y4 + VPSRLQ $0x20, Y11, Y11 + VPBLENDD $0xaa, Y13, Y11, Y13 + VMOVDQA Y4, Y11 + VMOVSLDUP Y14, Y4 + VPBLENDD $0xaa, Y4, Y12, Y4 + VPSRLQ $0x20, Y12, Y12 + VPBLENDD $0xaa, Y14, Y12, Y14 + VMOVDQA Y4, Y12 + VPSUBW Y7, Y9, Y4 + VPSUBW Y8, Y10, Y5 + VPSUBW Y11, Y13, Y6 + VPADDW Y7, Y9, Y7 + VPADDW Y8, Y10, Y8 + VPADDW Y11, Y13, Y11 + VPMULLW Y4, Y0, Y9 + VPMULLW Y5, Y0, Y10 + VPSUBW Y12, Y14, Y0 + VPMULLW Y6, Y2, Y13 + VPADDW Y12, Y14, Y12 + VPMULLW Y0, Y2, Y14 + VPMULHW Y4, Y1, Y4 + VPMULHW Y5, Y1, Y5 + VPMULHW Y6, Y3, Y6 + VPMULHW Y0, Y3, Y0 + VPMULHW Y9, Y15, Y9 + VPMULHW Y10, Y15, Y10 + VPMULHW Y13, Y15, Y13 + VPMULHW Y14, Y15, Y14 + VPSUBW Y9, Y4, Y9 + VPSUBW Y10, Y5, Y10 + VPSUBW Y13, Y6, Y13 + VPSUBW Y14, Y0, Y14 + MOVL $0x00004ebf, DX + VMOVD DX, X0 + VPBROADCASTW X0, Y4 + VPMULHW Y4, Y7, Y5 + VPSRAW $0x0a, Y5, Y5 + VPMULLW Y15, Y5, Y5 + VPSUBW Y5, Y7, Y7 + VPMULHW Y4, Y11, Y5 + VPSRAW $0x0a, Y5, Y5 + VPMULLW Y15, Y5, Y5 + VPSUBW Y5, Y11, Y11 + VMOVDQU 1824(CX), Y0 + VMOVDQU 1856(CX), Y1 + VMOVDQU 1888(CX), Y2 + VMOVDQU 1920(CX), Y3 + VPUNPCKLQDQ Y8, Y7, Y4 + VPUNPCKHQDQ Y8, Y7, Y8 + VMOVDQA Y4, Y7 + VPUNPCKLQDQ Y10, Y9, Y4 + VPUNPCKHQDQ Y10, Y9, Y10 + VMOVDQA Y4, Y9 + VPUNPCKLQDQ Y12, Y11, Y4 + VPUNPCKHQDQ Y12, Y11, Y12 + VMOVDQA Y4, Y11 + VPUNPCKLQDQ Y14, Y13, Y4 + VPUNPCKHQDQ Y14, Y13, Y14 + VMOVDQA Y4, Y13 + VPSUBW Y7, Y8, Y4 + VPSUBW Y9, Y10, Y5 + VPSUBW Y11, Y12, Y6 + VPADDW Y7, Y8, Y7 + VPADDW Y9, Y10, Y9 + VPADDW Y11, Y12, Y11 + VPMULLW Y4, Y0, Y8 + VPMULLW Y5, Y0, Y10 + VPSUBW Y13, Y14, Y0 + VPMULLW Y6, Y2, Y12 + VPADDW Y13, Y14, Y13 + VPMULLW Y0, Y2, Y14 + VPMULHW Y4, Y1, Y4 + VPMULHW Y5, Y1, Y5 + VPMULHW Y6, Y3, Y6 + VPMULHW Y0, Y3, Y0 + VPMULHW Y8, Y15, Y8 + VPMULHW Y10, Y15, Y10 + VPMULHW Y12, Y15, Y12 + VPMULHW Y14, Y15, Y14 + VPSUBW Y8, Y4, Y8 + VPSUBW Y10, Y5, Y10 + VPSUBW Y12, Y6, Y12 + VPSUBW Y14, Y0, Y14 + VPBROADCASTW 2080(CX), Y0 + VPBROADCASTW 2082(CX), Y1 + VPBROADCASTW 2084(CX), Y2 + VPBROADCASTW 2086(CX), Y3 + VPERM2I128 $0x20, Y9, Y7, Y4 + VPERM2I128 $0x31, Y9, Y7, Y9 + VMOVDQA Y4, Y7 + VPERM2I128 $0x20, Y10, Y8, Y4 + VPERM2I128 $0x31, Y10, Y8, Y10 + VMOVDQA Y4, Y8 + VPERM2I128 $0x20, Y13, Y11, Y4 + VPERM2I128 $0x31, Y13, Y11, Y13 + VMOVDQA Y4, Y11 + VPERM2I128 $0x20, Y14, Y12, Y4 + VPERM2I128 $0x31, Y14, Y12, Y14 + VMOVDQA Y4, Y12 + VPSUBW Y7, Y9, Y4 + VPSUBW Y8, Y10, Y5 + VPSUBW Y11, Y13, Y6 + VPADDW Y7, Y9, Y7 + VPADDW Y8, Y10, Y8 + VPADDW Y11, Y13, Y11 + VPMULLW Y4, Y0, Y9 + VPMULLW Y5, Y0, Y10 + VPSUBW Y12, Y14, Y0 + VPMULLW Y6, Y2, Y13 + VPADDW Y12, Y14, Y12 + VPMULLW Y0, Y2, Y14 + VPMULHW Y4, Y1, Y4 + VPMULHW Y5, Y1, Y5 + VPMULHW Y6, Y3, Y6 + VPMULHW Y0, Y3, Y0 + VPMULHW Y9, Y15, Y9 + VPMULHW Y10, Y15, Y10 + VPMULHW Y13, Y15, Y13 + VPMULHW Y14, Y15, Y14 + VPSUBW Y9, Y4, Y9 + VPSUBW Y10, Y5, Y10 + VPSUBW Y13, Y6, Y13 + VPSUBW Y14, Y0, Y14 + MOVL $0x00004ebf, DX + VMOVD DX, X0 + VPBROADCASTW X0, Y4 + VPMULHW Y4, Y7, Y5 + VPSRAW $0x0a, Y5, Y5 + VPMULLW Y15, Y5, Y5 + VPSUBW Y5, Y7, Y7 + VPMULHW Y4, Y11, Y5 + VPSRAW $0x0a, Y5, Y5 + VPMULLW Y15, Y5, Y5 + VPSUBW Y5, Y11, Y11 + VPBROADCASTW 2096(CX), Y0 + VPBROADCASTW 2098(CX), Y1 + VPSUBW Y7, Y11, Y4 + VPSUBW Y8, Y12, Y5 + VPSUBW Y9, Y13, Y6 + VPADDW Y7, Y11, Y7 + VPADDW Y8, Y12, Y8 + VPADDW Y9, Y13, Y9 + VPMULLW Y4, Y0, Y11 + VPMULLW Y5, Y0, Y12 + VPSUBW Y10, Y14, Y2 + VPMULLW Y6, Y0, Y13 + VPADDW Y10, Y14, Y10 + VPMULLW Y2, Y0, Y14 + VPMULHW Y4, Y1, Y4 + VPMULHW Y5, Y1, Y5 + VPMULHW Y6, Y1, Y6 + VPMULHW Y2, Y1, Y2 + VPMULHW Y11, Y15, Y11 + VPMULHW Y12, Y15, Y12 + VPMULHW Y13, Y15, Y13 + VPMULHW Y14, Y15, Y14 + VPSUBW Y11, Y4, Y11 + VPSUBW Y12, Y5, Y12 + VPSUBW Y13, Y6, Y13 + VPSUBW Y14, Y2, Y14 + VMOVDQU Y7, (AX) + VMOVDQU Y8, 32(AX) + VMOVDQU Y9, 64(AX) + VMOVDQU Y10, 96(AX) + VMOVDQU Y11, 128(AX) + VMOVDQU Y12, 160(AX) + VMOVDQU Y13, 192(AX) + VMOVDQU Y14, 224(AX) + VMOVDQU 256(AX), Y7 + VMOVDQU 288(AX), Y8 + VMOVDQU 320(AX), Y9 + VMOVDQU 352(AX), Y10 + VMOVDQU 384(AX), Y11 + VMOVDQU 416(AX), Y12 + VMOVDQU 448(AX), Y13 + VMOVDQU 480(AX), Y14 + VMOVDQU 1184(CX), Y0 + VMOVDQU 1216(CX), Y1 + VMOVDQU 1248(CX), Y2 + VMOVDQU 1280(CX), Y3 + VPSUBW Y7, Y9, Y4 + VPSUBW Y8, Y10, Y5 + VPSUBW Y11, Y13, Y6 + VPADDW Y7, Y9, Y7 + VPADDW Y8, Y10, Y8 + VPADDW Y11, Y13, Y11 + VPMULLW Y4, Y0, Y9 + VPMULLW Y5, Y0, Y10 + VPSUBW Y12, Y14, Y0 + VPMULLW Y6, Y2, Y13 + VPADDW Y12, Y14, Y12 + VPMULLW Y0, Y2, Y14 + VPMULHW Y4, Y1, Y4 + VPMULHW Y5, Y1, Y5 + VPMULHW Y6, Y3, Y6 + VPMULHW Y0, Y3, Y0 + VPMULHW Y9, Y15, Y9 + VPMULHW Y10, Y15, Y10 + VPMULHW Y13, Y15, Y13 + VPMULHW Y14, Y15, Y14 + VPSUBW Y9, Y4, Y9 + VPSUBW Y10, Y5, Y10 + VPSUBW Y13, Y6, Y13 + VPSUBW Y14, Y0, Y14 + VMOVDQU 1440(CX), Y0 + VMOVDQU 1472(CX), Y1 + VMOVDQU 1504(CX), Y2 + VMOVDQU 1536(CX), Y3 + VPSLLD $0x10, Y8, Y4 + VPBLENDW $0xaa, Y4, Y7, Y4 + VPSRLD $0x10, Y7, Y7 + VPBLENDW $0xaa, Y8, Y7, Y8 + VMOVDQA Y4, Y7 + VPSLLD $0x10, Y10, Y4 + VPBLENDW $0xaa, Y4, Y9, Y4 + VPSRLD $0x10, Y9, Y9 + VPBLENDW $0xaa, Y10, Y9, Y10 + VMOVDQA Y4, Y9 + VPSLLD $0x10, Y12, Y4 + VPBLENDW $0xaa, Y4, Y11, Y4 + VPSRLD $0x10, Y11, Y11 + VPBLENDW $0xaa, Y12, Y11, Y12 + VMOVDQA Y4, Y11 + VPSLLD $0x10, Y14, Y4 + VPBLENDW $0xaa, Y4, Y13, Y4 + VPSRLD $0x10, Y13, Y13 + VPBLENDW $0xaa, Y14, Y13, Y14 + VMOVDQA Y4, Y13 + VPSUBW Y7, Y8, Y4 + VPSUBW Y9, Y10, Y5 + VPSUBW Y11, Y12, Y6 + VPADDW Y7, Y8, Y7 + VPADDW Y9, Y10, Y9 + VPADDW Y11, Y12, Y11 + VPMULLW Y4, Y0, Y8 + VPMULLW Y5, Y0, Y10 + VPSUBW Y13, Y14, Y0 + VPMULLW Y6, Y2, Y12 + VPADDW Y13, Y14, Y13 + VPMULLW Y0, Y2, Y14 + VPMULHW Y4, Y1, Y4 + VPMULHW Y5, Y1, Y5 + VPMULHW Y6, Y3, Y6 + VPMULHW Y0, Y3, Y0 + VPMULHW Y8, Y15, Y8 + VPMULHW Y10, Y15, Y10 + VPMULHW Y12, Y15, Y12 + VPMULHW Y14, Y15, Y14 + VPSUBW Y8, Y4, Y8 + VPSUBW Y10, Y5, Y10 + VPSUBW Y12, Y6, Y12 + VPSUBW Y14, Y0, Y14 + VMOVDQU 1696(CX), Y0 + VMOVDQU 1728(CX), Y1 + VMOVDQU 1760(CX), Y2 + VMOVDQU 1792(CX), Y3 + VMOVSLDUP Y9, Y4 + VPBLENDD $0xaa, Y4, Y7, Y4 + VPSRLQ $0x20, Y7, Y7 + VPBLENDD $0xaa, Y9, Y7, Y9 + VMOVDQA Y4, Y7 + VMOVSLDUP Y10, Y4 + VPBLENDD $0xaa, Y4, Y8, Y4 + VPSRLQ $0x20, Y8, Y8 + VPBLENDD $0xaa, Y10, Y8, Y10 + VMOVDQA Y4, Y8 + VMOVSLDUP Y13, Y4 + VPBLENDD $0xaa, Y4, Y11, Y4 + VPSRLQ $0x20, Y11, Y11 + VPBLENDD $0xaa, Y13, Y11, Y13 + VMOVDQA Y4, Y11 + VMOVSLDUP Y14, Y4 + VPBLENDD $0xaa, Y4, Y12, Y4 + VPSRLQ $0x20, Y12, Y12 + VPBLENDD $0xaa, Y14, Y12, Y14 + VMOVDQA Y4, Y12 + VPSUBW Y7, Y9, Y4 + VPSUBW Y8, Y10, Y5 + VPSUBW Y11, Y13, Y6 + VPADDW Y7, Y9, Y7 + VPADDW Y8, Y10, Y8 + VPADDW Y11, Y13, Y11 + VPMULLW Y4, Y0, Y9 + VPMULLW Y5, Y0, Y10 + VPSUBW Y12, Y14, Y0 + VPMULLW Y6, Y2, Y13 + VPADDW Y12, Y14, Y12 + VPMULLW Y0, Y2, Y14 + VPMULHW Y4, Y1, Y4 + VPMULHW Y5, Y1, Y5 + VPMULHW Y6, Y3, Y6 + VPMULHW Y0, Y3, Y0 + VPMULHW Y9, Y15, Y9 + VPMULHW Y10, Y15, Y10 + VPMULHW Y13, Y15, Y13 + VPMULHW Y14, Y15, Y14 + VPSUBW Y9, Y4, Y9 + VPSUBW Y10, Y5, Y10 + VPSUBW Y13, Y6, Y13 + VPSUBW Y14, Y0, Y14 + MOVL $0x00004ebf, DX + VMOVD DX, X0 + VPBROADCASTW X0, Y4 + VPMULHW Y4, Y7, Y5 + VPSRAW $0x0a, Y5, Y5 + VPMULLW Y15, Y5, Y5 + VPSUBW Y5, Y7, Y7 + VPMULHW Y4, Y11, Y5 + VPSRAW $0x0a, Y5, Y5 + VPMULLW Y15, Y5, Y5 + VPSUBW Y5, Y11, Y11 + VMOVDQU 1952(CX), Y0 + VMOVDQU 1984(CX), Y1 + VMOVDQU 2016(CX), Y2 + VMOVDQU 2048(CX), Y3 + VPUNPCKLQDQ Y8, Y7, Y4 + VPUNPCKHQDQ Y8, Y7, Y8 + VMOVDQA Y4, Y7 + VPUNPCKLQDQ Y10, Y9, Y4 + VPUNPCKHQDQ Y10, Y9, Y10 + VMOVDQA Y4, Y9 + VPUNPCKLQDQ Y12, Y11, Y4 + VPUNPCKHQDQ Y12, Y11, Y12 + VMOVDQA Y4, Y11 + VPUNPCKLQDQ Y14, Y13, Y4 + VPUNPCKHQDQ Y14, Y13, Y14 + VMOVDQA Y4, Y13 + VPSUBW Y7, Y8, Y4 + VPSUBW Y9, Y10, Y5 + VPSUBW Y11, Y12, Y6 + VPADDW Y7, Y8, Y7 + VPADDW Y9, Y10, Y9 + VPADDW Y11, Y12, Y11 + VPMULLW Y4, Y0, Y8 + VPMULLW Y5, Y0, Y10 + VPSUBW Y13, Y14, Y0 + VPMULLW Y6, Y2, Y12 + VPADDW Y13, Y14, Y13 + VPMULLW Y0, Y2, Y14 + VPMULHW Y4, Y1, Y4 + VPMULHW Y5, Y1, Y5 + VPMULHW Y6, Y3, Y6 + VPMULHW Y0, Y3, Y0 + VPMULHW Y8, Y15, Y8 + VPMULHW Y10, Y15, Y10 + VPMULHW Y12, Y15, Y12 + VPMULHW Y14, Y15, Y14 + VPSUBW Y8, Y4, Y8 + VPSUBW Y10, Y5, Y10 + VPSUBW Y12, Y6, Y12 + VPSUBW Y14, Y0, Y14 + VPBROADCASTW 2088(CX), Y0 + VPBROADCASTW 2090(CX), Y1 + VPBROADCASTW 2092(CX), Y2 + VPBROADCASTW 2094(CX), Y3 + VPERM2I128 $0x20, Y9, Y7, Y4 + VPERM2I128 $0x31, Y9, Y7, Y9 + VMOVDQA Y4, Y7 + VPERM2I128 $0x20, Y10, Y8, Y4 + VPERM2I128 $0x31, Y10, Y8, Y10 + VMOVDQA Y4, Y8 + VPERM2I128 $0x20, Y13, Y11, Y4 + VPERM2I128 $0x31, Y13, Y11, Y13 + VMOVDQA Y4, Y11 + VPERM2I128 $0x20, Y14, Y12, Y4 + VPERM2I128 $0x31, Y14, Y12, Y14 + VMOVDQA Y4, Y12 + VPSUBW Y7, Y9, Y4 + VPSUBW Y8, Y10, Y5 + VPSUBW Y11, Y13, Y6 + VPADDW Y7, Y9, Y7 + VPADDW Y8, Y10, Y8 + VPADDW Y11, Y13, Y11 + VPMULLW Y4, Y0, Y9 + VPMULLW Y5, Y0, Y10 + VPSUBW Y12, Y14, Y0 + VPMULLW Y6, Y2, Y13 + VPADDW Y12, Y14, Y12 + VPMULLW Y0, Y2, Y14 + VPMULHW Y4, Y1, Y4 + VPMULHW Y5, Y1, Y5 + VPMULHW Y6, Y3, Y6 + VPMULHW Y0, Y3, Y0 + VPMULHW Y9, Y15, Y9 + VPMULHW Y10, Y15, Y10 + VPMULHW Y13, Y15, Y13 + VPMULHW Y14, Y15, Y14 + VPSUBW Y9, Y4, Y9 + VPSUBW Y10, Y5, Y10 + VPSUBW Y13, Y6, Y13 + VPSUBW Y14, Y0, Y14 + MOVL $0x00004ebf, DX + VMOVD DX, X0 + VPBROADCASTW X0, Y4 + VPMULHW Y4, Y7, Y5 + VPSRAW $0x0a, Y5, Y5 + VPMULLW Y15, Y5, Y5 + VPSUBW Y5, Y7, Y7 + VPMULHW Y4, Y11, Y5 + VPSRAW $0x0a, Y5, Y5 + VPMULLW Y15, Y5, Y5 + VPSUBW Y5, Y11, Y11 + VPBROADCASTW 2100(CX), Y0 + VPBROADCASTW 2102(CX), Y1 + VPSUBW Y7, Y11, Y4 + VPSUBW Y8, Y12, Y5 + VPSUBW Y9, Y13, Y6 + VPADDW Y7, Y11, Y7 + VPADDW Y8, Y12, Y8 + VPADDW Y9, Y13, Y9 + VPMULLW Y4, Y0, Y11 + VPMULLW Y5, Y0, Y12 + VPSUBW Y10, Y14, Y2 + VPMULLW Y6, Y0, Y13 + VPADDW Y10, Y14, Y10 + VPMULLW Y2, Y0, Y14 + VPMULHW Y4, Y1, Y4 + VPMULHW Y5, Y1, Y5 + VPMULHW Y6, Y1, Y6 + VPMULHW Y2, Y1, Y2 + VPMULHW Y11, Y15, Y11 + VPMULHW Y12, Y15, Y12 + VPMULHW Y13, Y15, Y13 + VPMULHW Y14, Y15, Y14 + VPSUBW Y11, Y4, Y11 + VPSUBW Y12, Y5, Y12 + VPSUBW Y13, Y6, Y13 + VPSUBW Y14, Y2, Y14 + VMOVDQU Y7, 256(AX) + VMOVDQU Y8, 288(AX) + VMOVDQU Y9, 320(AX) + VMOVDQU Y10, 352(AX) + VMOVDQU Y11, 384(AX) + VMOVDQU Y12, 416(AX) + VMOVDQU Y13, 448(AX) + VMOVDQU Y14, 480(AX) + VPBROADCASTW 2104(CX), Y0 + VPBROADCASTW 2106(CX), Y1 + VMOVDQU (AX), Y7 + VMOVDQU 32(AX), Y8 + VMOVDQU 64(AX), Y9 + VMOVDQU 96(AX), Y10 + VMOVDQU 256(AX), Y11 + VMOVDQU 288(AX), Y12 + VMOVDQU 320(AX), Y13 + VMOVDQU 352(AX), Y14 + VPSUBW Y7, Y11, Y2 + VPSUBW Y8, Y12, Y3 + VPSUBW Y9, Y13, Y4 + VPADDW Y7, Y11, Y7 + VPADDW Y8, Y12, Y8 + VPADDW Y9, Y13, Y9 + VPMULLW Y2, Y0, Y11 + VPMULLW Y3, Y0, Y12 + VPSUBW Y10, Y14, Y5 + VPMULLW Y4, Y0, Y13 + VPADDW Y10, Y14, Y10 + VPMULLW Y5, Y0, Y14 + VPMULHW Y2, Y1, Y2 + VPMULHW Y3, Y1, Y3 + VPMULHW Y4, Y1, Y4 + VPMULHW Y5, Y1, Y5 + VPMULHW Y11, Y15, Y11 + VPMULHW Y12, Y15, Y12 + VPMULHW Y13, Y15, Y13 + VPMULHW Y14, Y15, Y14 + VPSUBW Y11, Y2, Y11 + VPSUBW Y12, Y3, Y12 + VPSUBW Y13, Y4, Y13 + VPSUBW Y14, Y5, Y14 + MOVL $0xffffd8a1, DX + VMOVD DX, X0 + VPBROADCASTW X0, Y0 + MOVL $0x000005a1, DX + VMOVD DX, X1 + VPBROADCASTW X1, Y1 + VPMULLW Y7, Y0, Y2 + VPMULLW Y8, Y0, Y3 + VPMULLW Y9, Y0, Y4 + VPMULLW Y10, Y0, Y5 + VPMULHW Y7, Y1, Y7 + VPMULHW Y8, Y1, Y8 + VPMULHW Y9, Y1, Y9 + VPMULHW Y10, Y1, Y10 + VPMULHW Y2, Y15, Y2 + VPMULHW Y3, Y15, Y3 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPSUBW Y2, Y7, Y7 + VPSUBW Y3, Y8, Y8 + VPSUBW Y4, Y9, Y9 + VPSUBW Y5, Y10, Y10 + VPMULLW Y11, Y0, Y2 + VPMULLW Y12, Y0, Y3 + VPMULLW Y13, Y0, Y4 + VPMULLW Y14, Y0, Y5 + VPMULHW Y11, Y1, Y11 + VPMULHW Y12, Y1, Y12 + VPMULHW Y13, Y1, Y13 + VPMULHW Y14, Y1, Y14 + VPMULHW Y2, Y15, Y2 + VPMULHW Y3, Y15, Y3 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPSUBW Y2, Y11, Y11 + VPSUBW Y3, Y12, Y12 + VPSUBW Y4, Y13, Y13 + VPSUBW Y5, Y14, Y14 + VMOVDQU Y7, (AX) + VMOVDQU Y8, 32(AX) + VMOVDQU Y9, 64(AX) + VMOVDQU Y10, 96(AX) + VMOVDQU Y11, 256(AX) + VMOVDQU Y12, 288(AX) + VMOVDQU Y13, 320(AX) + VMOVDQU Y14, 352(AX) + VPBROADCASTW 2104(CX), Y0 + VPBROADCASTW 2106(CX), Y1 + VMOVDQU 128(AX), Y7 + VMOVDQU 160(AX), Y8 + VMOVDQU 192(AX), Y9 + VMOVDQU 224(AX), Y10 + VMOVDQU 384(AX), Y11 + VMOVDQU 416(AX), Y12 + VMOVDQU 448(AX), Y13 + VMOVDQU 480(AX), Y14 + VPSUBW Y7, Y11, Y2 + VPSUBW Y8, Y12, Y3 + VPSUBW Y9, Y13, Y4 + VPADDW Y7, Y11, Y7 + VPADDW Y8, Y12, Y8 + VPADDW Y9, Y13, Y9 + VPMULLW Y2, Y0, Y11 + VPMULLW Y3, Y0, Y12 + VPSUBW Y10, Y14, Y5 + VPMULLW Y4, Y0, Y13 + VPADDW Y10, Y14, Y10 + VPMULLW Y5, Y0, Y14 + VPMULHW Y2, Y1, Y2 + VPMULHW Y3, Y1, Y3 + VPMULHW Y4, Y1, Y4 + VPMULHW Y5, Y1, Y5 + VPMULHW Y11, Y15, Y11 + VPMULHW Y12, Y15, Y12 + VPMULHW Y13, Y15, Y13 + VPMULHW Y14, Y15, Y14 + VPSUBW Y11, Y2, Y11 + VPSUBW Y12, Y3, Y12 + VPSUBW Y13, Y4, Y13 + VPSUBW Y14, Y5, Y14 + MOVL $0xffffd8a1, CX + VMOVD CX, X0 + VPBROADCASTW X0, Y0 + MOVL $0x000005a1, CX + VMOVD CX, X1 + VPBROADCASTW X1, Y1 + VPMULLW Y7, Y0, Y2 + VPMULLW Y8, Y0, Y3 + VPMULLW Y9, Y0, Y4 + VPMULLW Y10, Y0, Y5 + VPMULHW Y7, Y1, Y7 + VPMULHW Y8, Y1, Y8 + VPMULHW Y9, Y1, Y9 + VPMULHW Y10, Y1, Y10 + VPMULHW Y2, Y15, Y2 + VPMULHW Y3, Y15, Y3 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPSUBW Y2, Y7, Y7 + VPSUBW Y3, Y8, Y8 + VPSUBW Y4, Y9, Y9 + VPSUBW Y5, Y10, Y10 + VPMULLW Y11, Y0, Y2 + VPMULLW Y12, Y0, Y3 + VPMULLW Y13, Y0, Y4 + VPMULLW Y14, Y0, Y5 + VPMULHW Y11, Y1, Y11 + VPMULHW Y12, Y1, Y12 + VPMULHW Y13, Y1, Y13 + VPMULHW Y14, Y1, Y14 + VPMULHW Y2, Y15, Y2 + VPMULHW Y3, Y15, Y3 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPSUBW Y2, Y11, Y11 + VPSUBW Y3, Y12, Y12 + VPSUBW Y4, Y13, Y13 + VPSUBW Y5, Y14, Y14 + VMOVDQU Y7, 128(AX) + VMOVDQU Y8, 160(AX) + VMOVDQU Y9, 192(AX) + VMOVDQU Y10, 224(AX) + VMOVDQU Y11, 384(AX) + VMOVDQU Y12, 416(AX) + VMOVDQU Y13, 448(AX) + VMOVDQU Y14, 480(AX) + RET + +// func mulHatAVX2(p *[256]int16, a *[256]int16, b *[256]int16) +// Requires: AVX, AVX2 +TEXT ·mulHatAVX2(SB), NOSPLIT, $8-24 + MOVQ p+0(FP), AX + MOVQ a+8(FP), CX + MOVQ b+16(FP), DX + LEAQ ·ZetasAVX2+0(SB), BX + MOVL $0xfffff301, BP + VMOVD BP, X0 + VPBROADCASTW X0, Y14 + MOVL $0x00000d01, BP + VMOVD BP, X0 + VPBROADCASTW X0, Y15 + VMOVDQU (CX), Y0 + VMOVDQU 32(CX), Y1 + VMOVDQU 64(CX), Y2 + VMOVDQU 96(CX), Y3 + VMOVDQU (DX), Y4 + VMOVDQU 32(DX), Y5 + VMOVDQU 64(DX), Y6 + VMOVDQU 96(DX), Y7 + VPMULLW Y1, Y5, Y8 + VPMULLW Y0, Y4, Y9 + VPMULLW Y0, Y5, Y10 + VPMULLW Y1, Y4, Y11 + VPMULLW Y8, Y14, Y8 + VPMULLW Y9, Y14, Y9 + VPMULLW Y10, Y14, Y10 + VPMULLW Y11, Y14, Y11 + VPMULHW Y1, Y5, Y12 + VPMULHW Y0, Y4, Y13 + VPMULHW Y0, Y5, Y0 + VPMULHW Y1, Y4, Y1 + VMOVDQA Y12, Y4 + VMOVDQA Y13, Y5 + VPMULHW Y8, Y15, Y8 + VPMULHW Y9, Y15, Y9 + VPMULHW Y10, Y15, Y10 + VPMULHW Y11, Y15, Y11 + VPSUBW Y8, Y4, Y4 + VPSUBW Y9, Y5, Y5 + VPSUBW Y10, Y0, Y0 + VPSUBW Y11, Y1, Y1 + VMOVDQU 800(BX), Y12 + VMOVDQU 832(BX), Y13 + VPMULLW Y4, Y12, Y8 + VPMULHW Y4, Y13, Y4 + VPMULHW Y8, Y15, Y8 + VPSUBW Y8, Y4, Y4 + VPADDW Y4, Y5, Y4 + VPADDW Y0, Y1, Y5 + VPMULLW Y3, Y7, Y8 + VPMULLW Y2, Y6, Y9 + VPMULLW Y2, Y7, Y10 + VPMULLW Y3, Y6, Y11 + VPMULLW Y8, Y14, Y8 + VPMULLW Y9, Y14, Y9 + VPMULLW Y10, Y14, Y10 + VPMULLW Y11, Y14, Y11 + VPMULHW Y3, Y7, Y12 + VPMULHW Y2, Y6, Y13 + VPMULHW Y2, Y7, Y2 + VPMULHW Y3, Y6, Y3 + VMOVDQA Y12, Y6 + VMOVDQA Y13, Y7 + VPMULHW Y8, Y15, Y8 + VPMULHW Y9, Y15, Y9 + VPMULHW Y10, Y15, Y10 + VPMULHW Y11, Y15, Y11 + VPSUBW Y8, Y6, Y6 + VPSUBW Y9, Y7, Y7 + VPSUBW Y10, Y2, Y2 + VPSUBW Y11, Y3, Y3 + VMOVDQU 800(BX), Y12 + VMOVDQU 832(BX), Y13 + VPMULLW Y6, Y12, Y8 + VPMULHW Y6, Y13, Y6 + VPMULHW Y8, Y15, Y8 + VPSUBW Y8, Y6, Y6 + VPSUBW Y6, Y7, Y6 + VPADDW Y2, Y3, Y7 + VMOVDQU Y4, (AX) + VMOVDQU Y5, 32(AX) + VMOVDQU Y6, 64(AX) + VMOVDQU Y7, 96(AX) + VMOVDQU 128(CX), Y0 + VMOVDQU 160(CX), Y1 + VMOVDQU 192(CX), Y2 + VMOVDQU 224(CX), Y3 + VMOVDQU 128(DX), Y4 + VMOVDQU 160(DX), Y5 + VMOVDQU 192(DX), Y6 + VMOVDQU 224(DX), Y7 + VPMULLW Y1, Y5, Y8 + VPMULLW Y0, Y4, Y9 + VPMULLW Y0, Y5, Y10 + VPMULLW Y1, Y4, Y11 + VPMULLW Y8, Y14, Y8 + VPMULLW Y9, Y14, Y9 + VPMULLW Y10, Y14, Y10 + VPMULLW Y11, Y14, Y11 + VPMULHW Y1, Y5, Y12 + VPMULHW Y0, Y4, Y13 + VPMULHW Y0, Y5, Y0 + VPMULHW Y1, Y4, Y1 + VMOVDQA Y12, Y4 + VMOVDQA Y13, Y5 + VPMULHW Y8, Y15, Y8 + VPMULHW Y9, Y15, Y9 + VPMULHW Y10, Y15, Y10 + VPMULHW Y11, Y15, Y11 + VPSUBW Y8, Y4, Y4 + VPSUBW Y9, Y5, Y5 + VPSUBW Y10, Y0, Y0 + VPSUBW Y11, Y1, Y1 + VMOVDQU 864(BX), Y12 + VMOVDQU 896(BX), Y13 + VPMULLW Y4, Y12, Y8 + VPMULHW Y4, Y13, Y4 + VPMULHW Y8, Y15, Y8 + VPSUBW Y8, Y4, Y4 + VPADDW Y4, Y5, Y4 + VPADDW Y0, Y1, Y5 + VPMULLW Y3, Y7, Y8 + VPMULLW Y2, Y6, Y9 + VPMULLW Y2, Y7, Y10 + VPMULLW Y3, Y6, Y11 + VPMULLW Y8, Y14, Y8 + VPMULLW Y9, Y14, Y9 + VPMULLW Y10, Y14, Y10 + VPMULLW Y11, Y14, Y11 + VPMULHW Y3, Y7, Y12 + VPMULHW Y2, Y6, Y13 + VPMULHW Y2, Y7, Y2 + VPMULHW Y3, Y6, Y3 + VMOVDQA Y12, Y6 + VMOVDQA Y13, Y7 + VPMULHW Y8, Y15, Y8 + VPMULHW Y9, Y15, Y9 + VPMULHW Y10, Y15, Y10 + VPMULHW Y11, Y15, Y11 + VPSUBW Y8, Y6, Y6 + VPSUBW Y9, Y7, Y7 + VPSUBW Y10, Y2, Y2 + VPSUBW Y11, Y3, Y3 + VMOVDQU 864(BX), Y12 + VMOVDQU 896(BX), Y13 + VPMULLW Y6, Y12, Y8 + VPMULHW Y6, Y13, Y6 + VPMULHW Y8, Y15, Y8 + VPSUBW Y8, Y6, Y6 + VPSUBW Y6, Y7, Y6 + VPADDW Y2, Y3, Y7 + VMOVDQU Y4, 128(AX) + VMOVDQU Y5, 160(AX) + VMOVDQU Y6, 192(AX) + VMOVDQU Y7, 224(AX) + VMOVDQU 256(CX), Y0 + VMOVDQU 288(CX), Y1 + VMOVDQU 320(CX), Y2 + VMOVDQU 352(CX), Y3 + VMOVDQU 256(DX), Y4 + VMOVDQU 288(DX), Y5 + VMOVDQU 320(DX), Y6 + VMOVDQU 352(DX), Y7 + VPMULLW Y1, Y5, Y8 + VPMULLW Y0, Y4, Y9 + VPMULLW Y0, Y5, Y10 + VPMULLW Y1, Y4, Y11 + VPMULLW Y8, Y14, Y8 + VPMULLW Y9, Y14, Y9 + VPMULLW Y10, Y14, Y10 + VPMULLW Y11, Y14, Y11 + VPMULHW Y1, Y5, Y12 + VPMULHW Y0, Y4, Y13 + VPMULHW Y0, Y5, Y0 + VPMULHW Y1, Y4, Y1 + VMOVDQA Y12, Y4 + VMOVDQA Y13, Y5 + VPMULHW Y8, Y15, Y8 + VPMULHW Y9, Y15, Y9 + VPMULHW Y10, Y15, Y10 + VPMULHW Y11, Y15, Y11 + VPSUBW Y8, Y4, Y4 + VPSUBW Y9, Y5, Y5 + VPSUBW Y10, Y0, Y0 + VPSUBW Y11, Y1, Y1 + VMOVDQU 928(BX), Y12 + VMOVDQU 960(BX), Y13 + VPMULLW Y4, Y12, Y8 + VPMULHW Y4, Y13, Y4 + VPMULHW Y8, Y15, Y8 + VPSUBW Y8, Y4, Y4 + VPADDW Y4, Y5, Y4 + VPADDW Y0, Y1, Y5 + VPMULLW Y3, Y7, Y8 + VPMULLW Y2, Y6, Y9 + VPMULLW Y2, Y7, Y10 + VPMULLW Y3, Y6, Y11 + VPMULLW Y8, Y14, Y8 + VPMULLW Y9, Y14, Y9 + VPMULLW Y10, Y14, Y10 + VPMULLW Y11, Y14, Y11 + VPMULHW Y3, Y7, Y12 + VPMULHW Y2, Y6, Y13 + VPMULHW Y2, Y7, Y2 + VPMULHW Y3, Y6, Y3 + VMOVDQA Y12, Y6 + VMOVDQA Y13, Y7 + VPMULHW Y8, Y15, Y8 + VPMULHW Y9, Y15, Y9 + VPMULHW Y10, Y15, Y10 + VPMULHW Y11, Y15, Y11 + VPSUBW Y8, Y6, Y6 + VPSUBW Y9, Y7, Y7 + VPSUBW Y10, Y2, Y2 + VPSUBW Y11, Y3, Y3 + VMOVDQU 928(BX), Y12 + VMOVDQU 960(BX), Y13 + VPMULLW Y6, Y12, Y8 + VPMULHW Y6, Y13, Y6 + VPMULHW Y8, Y15, Y8 + VPSUBW Y8, Y6, Y6 + VPSUBW Y6, Y7, Y6 + VPADDW Y2, Y3, Y7 + VMOVDQU Y4, 256(AX) + VMOVDQU Y5, 288(AX) + VMOVDQU Y6, 320(AX) + VMOVDQU Y7, 352(AX) + VMOVDQU 384(CX), Y0 + VMOVDQU 416(CX), Y1 + VMOVDQU 448(CX), Y2 + VMOVDQU 480(CX), Y3 + VMOVDQU 384(DX), Y4 + VMOVDQU 416(DX), Y5 + VMOVDQU 448(DX), Y6 + VMOVDQU 480(DX), Y7 + VPMULLW Y1, Y5, Y8 + VPMULLW Y0, Y4, Y9 + VPMULLW Y0, Y5, Y10 + VPMULLW Y1, Y4, Y11 + VPMULLW Y8, Y14, Y8 + VPMULLW Y9, Y14, Y9 + VPMULLW Y10, Y14, Y10 + VPMULLW Y11, Y14, Y11 + VPMULHW Y1, Y5, Y12 + VPMULHW Y0, Y4, Y13 + VPMULHW Y0, Y5, Y0 + VPMULHW Y1, Y4, Y1 + VMOVDQA Y12, Y4 + VMOVDQA Y13, Y5 + VPMULHW Y8, Y15, Y8 + VPMULHW Y9, Y15, Y9 + VPMULHW Y10, Y15, Y10 + VPMULHW Y11, Y15, Y11 + VPSUBW Y8, Y4, Y4 + VPSUBW Y9, Y5, Y5 + VPSUBW Y10, Y0, Y0 + VPSUBW Y11, Y1, Y1 + VMOVDQU 992(BX), Y12 + VMOVDQU 1024(BX), Y13 + VPMULLW Y4, Y12, Y8 + VPMULHW Y4, Y13, Y4 + VPMULHW Y8, Y15, Y8 + VPSUBW Y8, Y4, Y4 + VPADDW Y4, Y5, Y4 + VPADDW Y0, Y1, Y5 + VPMULLW Y3, Y7, Y8 + VPMULLW Y2, Y6, Y9 + VPMULLW Y2, Y7, Y10 + VPMULLW Y3, Y6, Y11 + VPMULLW Y8, Y14, Y8 + VPMULLW Y9, Y14, Y9 + VPMULLW Y10, Y14, Y10 + VPMULLW Y11, Y14, Y11 + VPMULHW Y3, Y7, Y12 + VPMULHW Y2, Y6, Y13 + VPMULHW Y2, Y7, Y2 + VPMULHW Y3, Y6, Y3 + VMOVDQA Y12, Y6 + VMOVDQA Y13, Y7 + VPMULHW Y8, Y15, Y8 + VPMULHW Y9, Y15, Y9 + VPMULHW Y10, Y15, Y10 + VPMULHW Y11, Y15, Y11 + VPSUBW Y8, Y6, Y6 + VPSUBW Y9, Y7, Y7 + VPSUBW Y10, Y2, Y2 + VPSUBW Y11, Y3, Y3 + VMOVDQU 992(BX), Y12 + VMOVDQU 1024(BX), Y13 + VPMULLW Y6, Y12, Y8 + VPMULHW Y6, Y13, Y6 + VPMULHW Y8, Y15, Y8 + VPSUBW Y8, Y6, Y6 + VPSUBW Y6, Y7, Y6 + VPADDW Y2, Y3, Y7 + VMOVDQU Y4, 384(AX) + VMOVDQU Y5, 416(AX) + VMOVDQU Y6, 448(AX) + VMOVDQU Y7, 480(AX) + RET + +// func detangleAVX2(p *[256]int16) +// Requires: AVX, AVX2 +TEXT ·detangleAVX2(SB), NOSPLIT, $0-8 + MOVQ p+0(FP), AX + VMOVDQU (AX), Y0 + VMOVDQU 32(AX), Y1 + VMOVDQU 64(AX), Y2 + VMOVDQU 96(AX), Y3 + VMOVDQU 128(AX), Y4 + VMOVDQU 160(AX), Y5 + VMOVDQU 192(AX), Y6 + VMOVDQU 224(AX), Y7 + VPSLLD $0x10, Y1, Y8 + VPBLENDW $0xaa, Y8, Y0, Y8 + VPSRLD $0x10, Y0, Y0 + VPBLENDW $0xaa, Y1, Y0, Y1 + VMOVDQA Y8, Y0 + VPSLLD $0x10, Y3, Y8 + VPBLENDW $0xaa, Y8, Y2, Y8 + VPSRLD $0x10, Y2, Y2 + VPBLENDW $0xaa, Y3, Y2, Y3 + VMOVDQA Y8, Y2 + VPSLLD $0x10, Y5, Y8 + VPBLENDW $0xaa, Y8, Y4, Y8 + VPSRLD $0x10, Y4, Y4 + VPBLENDW $0xaa, Y5, Y4, Y5 + VMOVDQA Y8, Y4 + VPSLLD $0x10, Y7, Y8 + VPBLENDW $0xaa, Y8, Y6, Y8 + VPSRLD $0x10, Y6, Y6 + VPBLENDW $0xaa, Y7, Y6, Y7 + VMOVDQA Y8, Y6 + VMOVSLDUP Y2, Y8 + VPBLENDD $0xaa, Y8, Y0, Y8 + VPSRLQ $0x20, Y0, Y0 + VPBLENDD $0xaa, Y2, Y0, Y2 + VMOVDQA Y8, Y0 + VMOVSLDUP Y3, Y8 + VPBLENDD $0xaa, Y8, Y1, Y8 + VPSRLQ $0x20, Y1, Y1 + VPBLENDD $0xaa, Y3, Y1, Y3 + VMOVDQA Y8, Y1 + VMOVSLDUP Y6, Y8 + VPBLENDD $0xaa, Y8, Y4, Y8 + VPSRLQ $0x20, Y4, Y4 + VPBLENDD $0xaa, Y6, Y4, Y6 + VMOVDQA Y8, Y4 + VMOVSLDUP Y7, Y8 + VPBLENDD $0xaa, Y8, Y5, Y8 + VPSRLQ $0x20, Y5, Y5 + VPBLENDD $0xaa, Y7, Y5, Y7 + VMOVDQA Y8, Y5 + VPUNPCKLQDQ Y1, Y0, Y8 + VPUNPCKHQDQ Y1, Y0, Y1 + VMOVDQA Y8, Y0 + VPUNPCKLQDQ Y3, Y2, Y8 + VPUNPCKHQDQ Y3, Y2, Y3 + VMOVDQA Y8, Y2 + VPUNPCKLQDQ Y5, Y4, Y8 + VPUNPCKHQDQ Y5, Y4, Y5 + VMOVDQA Y8, Y4 + VPUNPCKLQDQ Y7, Y6, Y8 + VPUNPCKHQDQ Y7, Y6, Y7 + VMOVDQA Y8, Y6 + VPERM2I128 $0x20, Y2, Y0, Y8 + VPERM2I128 $0x31, Y2, Y0, Y2 + VMOVDQA Y8, Y0 + VPERM2I128 $0x20, Y3, Y1, Y8 + VPERM2I128 $0x31, Y3, Y1, Y3 + VMOVDQA Y8, Y1 + VPERM2I128 $0x20, Y6, Y4, Y8 + VPERM2I128 $0x31, Y6, Y4, Y6 + VMOVDQA Y8, Y4 + VPERM2I128 $0x20, Y7, Y5, Y8 + VPERM2I128 $0x31, Y7, Y5, Y7 + VMOVDQA Y8, Y5 + VMOVDQU Y0, (AX) + VMOVDQU Y1, 32(AX) + VMOVDQU Y2, 64(AX) + VMOVDQU Y3, 96(AX) + VMOVDQU Y4, 128(AX) + VMOVDQU Y5, 160(AX) + VMOVDQU Y6, 192(AX) + VMOVDQU Y7, 224(AX) + VMOVDQU 256(AX), Y0 + VMOVDQU 288(AX), Y1 + VMOVDQU 320(AX), Y2 + VMOVDQU 352(AX), Y3 + VMOVDQU 384(AX), Y4 + VMOVDQU 416(AX), Y5 + VMOVDQU 448(AX), Y6 + VMOVDQU 480(AX), Y7 + VPSLLD $0x10, Y1, Y8 + VPBLENDW $0xaa, Y8, Y0, Y8 + VPSRLD $0x10, Y0, Y0 + VPBLENDW $0xaa, Y1, Y0, Y1 + VMOVDQA Y8, Y0 + VPSLLD $0x10, Y3, Y8 + VPBLENDW $0xaa, Y8, Y2, Y8 + VPSRLD $0x10, Y2, Y2 + VPBLENDW $0xaa, Y3, Y2, Y3 + VMOVDQA Y8, Y2 + VPSLLD $0x10, Y5, Y8 + VPBLENDW $0xaa, Y8, Y4, Y8 + VPSRLD $0x10, Y4, Y4 + VPBLENDW $0xaa, Y5, Y4, Y5 + VMOVDQA Y8, Y4 + VPSLLD $0x10, Y7, Y8 + VPBLENDW $0xaa, Y8, Y6, Y8 + VPSRLD $0x10, Y6, Y6 + VPBLENDW $0xaa, Y7, Y6, Y7 + VMOVDQA Y8, Y6 + VMOVSLDUP Y2, Y8 + VPBLENDD $0xaa, Y8, Y0, Y8 + VPSRLQ $0x20, Y0, Y0 + VPBLENDD $0xaa, Y2, Y0, Y2 + VMOVDQA Y8, Y0 + VMOVSLDUP Y3, Y8 + VPBLENDD $0xaa, Y8, Y1, Y8 + VPSRLQ $0x20, Y1, Y1 + VPBLENDD $0xaa, Y3, Y1, Y3 + VMOVDQA Y8, Y1 + VMOVSLDUP Y6, Y8 + VPBLENDD $0xaa, Y8, Y4, Y8 + VPSRLQ $0x20, Y4, Y4 + VPBLENDD $0xaa, Y6, Y4, Y6 + VMOVDQA Y8, Y4 + VMOVSLDUP Y7, Y8 + VPBLENDD $0xaa, Y8, Y5, Y8 + VPSRLQ $0x20, Y5, Y5 + VPBLENDD $0xaa, Y7, Y5, Y7 + VMOVDQA Y8, Y5 + VPUNPCKLQDQ Y1, Y0, Y8 + VPUNPCKHQDQ Y1, Y0, Y1 + VMOVDQA Y8, Y0 + VPUNPCKLQDQ Y3, Y2, Y8 + VPUNPCKHQDQ Y3, Y2, Y3 + VMOVDQA Y8, Y2 + VPUNPCKLQDQ Y5, Y4, Y8 + VPUNPCKHQDQ Y5, Y4, Y5 + VMOVDQA Y8, Y4 + VPUNPCKLQDQ Y7, Y6, Y8 + VPUNPCKHQDQ Y7, Y6, Y7 + VMOVDQA Y8, Y6 + VPERM2I128 $0x20, Y2, Y0, Y8 + VPERM2I128 $0x31, Y2, Y0, Y2 + VMOVDQA Y8, Y0 + VPERM2I128 $0x20, Y3, Y1, Y8 + VPERM2I128 $0x31, Y3, Y1, Y3 + VMOVDQA Y8, Y1 + VPERM2I128 $0x20, Y6, Y4, Y8 + VPERM2I128 $0x31, Y6, Y4, Y6 + VMOVDQA Y8, Y4 + VPERM2I128 $0x20, Y7, Y5, Y8 + VPERM2I128 $0x31, Y7, Y5, Y7 + VMOVDQA Y8, Y5 + VMOVDQU Y0, 256(AX) + VMOVDQU Y1, 288(AX) + VMOVDQU Y2, 320(AX) + VMOVDQU Y3, 352(AX) + VMOVDQU Y4, 384(AX) + VMOVDQU Y5, 416(AX) + VMOVDQU Y6, 448(AX) + VMOVDQU Y7, 480(AX) + RET + +// func tangleAVX2(p *[256]int16) +// Requires: AVX, AVX2 +TEXT ·tangleAVX2(SB), NOSPLIT, $0-8 + MOVQ p+0(FP), AX + VMOVDQU (AX), Y0 + VMOVDQU 32(AX), Y1 + VMOVDQU 64(AX), Y2 + VMOVDQU 96(AX), Y3 + VMOVDQU 128(AX), Y4 + VMOVDQU 160(AX), Y5 + VMOVDQU 192(AX), Y6 + VMOVDQU 224(AX), Y7 + VPERM2I128 $0x20, Y2, Y0, Y8 + VPERM2I128 $0x31, Y2, Y0, Y2 + VMOVDQA Y8, Y0 + VPERM2I128 $0x20, Y3, Y1, Y8 + VPERM2I128 $0x31, Y3, Y1, Y3 + VMOVDQA Y8, Y1 + VPERM2I128 $0x20, Y6, Y4, Y8 + VPERM2I128 $0x31, Y6, Y4, Y6 + VMOVDQA Y8, Y4 + VPERM2I128 $0x20, Y7, Y5, Y8 + VPERM2I128 $0x31, Y7, Y5, Y7 + VMOVDQA Y8, Y5 + VPUNPCKLQDQ Y1, Y0, Y8 + VPUNPCKHQDQ Y1, Y0, Y1 + VMOVDQA Y8, Y0 + VPUNPCKLQDQ Y3, Y2, Y8 + VPUNPCKHQDQ Y3, Y2, Y3 + VMOVDQA Y8, Y2 + VPUNPCKLQDQ Y5, Y4, Y8 + VPUNPCKHQDQ Y5, Y4, Y5 + VMOVDQA Y8, Y4 + VPUNPCKLQDQ Y7, Y6, Y8 + VPUNPCKHQDQ Y7, Y6, Y7 + VMOVDQA Y8, Y6 + VMOVSLDUP Y2, Y8 + VPBLENDD $0xaa, Y8, Y0, Y8 + VPSRLQ $0x20, Y0, Y0 + VPBLENDD $0xaa, Y2, Y0, Y2 + VMOVDQA Y8, Y0 + VMOVSLDUP Y3, Y8 + VPBLENDD $0xaa, Y8, Y1, Y8 + VPSRLQ $0x20, Y1, Y1 + VPBLENDD $0xaa, Y3, Y1, Y3 + VMOVDQA Y8, Y1 + VMOVSLDUP Y6, Y8 + VPBLENDD $0xaa, Y8, Y4, Y8 + VPSRLQ $0x20, Y4, Y4 + VPBLENDD $0xaa, Y6, Y4, Y6 + VMOVDQA Y8, Y4 + VMOVSLDUP Y7, Y8 + VPBLENDD $0xaa, Y8, Y5, Y8 + VPSRLQ $0x20, Y5, Y5 + VPBLENDD $0xaa, Y7, Y5, Y7 + VMOVDQA Y8, Y5 + VPSLLD $0x10, Y1, Y8 + VPBLENDW $0xaa, Y8, Y0, Y8 + VPSRLD $0x10, Y0, Y0 + VPBLENDW $0xaa, Y1, Y0, Y1 + VMOVDQA Y8, Y0 + VPSLLD $0x10, Y3, Y8 + VPBLENDW $0xaa, Y8, Y2, Y8 + VPSRLD $0x10, Y2, Y2 + VPBLENDW $0xaa, Y3, Y2, Y3 + VMOVDQA Y8, Y2 + VPSLLD $0x10, Y5, Y8 + VPBLENDW $0xaa, Y8, Y4, Y8 + VPSRLD $0x10, Y4, Y4 + VPBLENDW $0xaa, Y5, Y4, Y5 + VMOVDQA Y8, Y4 + VPSLLD $0x10, Y7, Y8 + VPBLENDW $0xaa, Y8, Y6, Y8 + VPSRLD $0x10, Y6, Y6 + VPBLENDW $0xaa, Y7, Y6, Y7 + VMOVDQA Y8, Y6 + VMOVDQU Y0, (AX) + VMOVDQU Y1, 32(AX) + VMOVDQU Y2, 64(AX) + VMOVDQU Y3, 96(AX) + VMOVDQU Y4, 128(AX) + VMOVDQU Y5, 160(AX) + VMOVDQU Y6, 192(AX) + VMOVDQU Y7, 224(AX) + VMOVDQU 256(AX), Y0 + VMOVDQU 288(AX), Y1 + VMOVDQU 320(AX), Y2 + VMOVDQU 352(AX), Y3 + VMOVDQU 384(AX), Y4 + VMOVDQU 416(AX), Y5 + VMOVDQU 448(AX), Y6 + VMOVDQU 480(AX), Y7 + VPERM2I128 $0x20, Y2, Y0, Y8 + VPERM2I128 $0x31, Y2, Y0, Y2 + VMOVDQA Y8, Y0 + VPERM2I128 $0x20, Y3, Y1, Y8 + VPERM2I128 $0x31, Y3, Y1, Y3 + VMOVDQA Y8, Y1 + VPERM2I128 $0x20, Y6, Y4, Y8 + VPERM2I128 $0x31, Y6, Y4, Y6 + VMOVDQA Y8, Y4 + VPERM2I128 $0x20, Y7, Y5, Y8 + VPERM2I128 $0x31, Y7, Y5, Y7 + VMOVDQA Y8, Y5 + VPUNPCKLQDQ Y1, Y0, Y8 + VPUNPCKHQDQ Y1, Y0, Y1 + VMOVDQA Y8, Y0 + VPUNPCKLQDQ Y3, Y2, Y8 + VPUNPCKHQDQ Y3, Y2, Y3 + VMOVDQA Y8, Y2 + VPUNPCKLQDQ Y5, Y4, Y8 + VPUNPCKHQDQ Y5, Y4, Y5 + VMOVDQA Y8, Y4 + VPUNPCKLQDQ Y7, Y6, Y8 + VPUNPCKHQDQ Y7, Y6, Y7 + VMOVDQA Y8, Y6 + VMOVSLDUP Y2, Y8 + VPBLENDD $0xaa, Y8, Y0, Y8 + VPSRLQ $0x20, Y0, Y0 + VPBLENDD $0xaa, Y2, Y0, Y2 + VMOVDQA Y8, Y0 + VMOVSLDUP Y3, Y8 + VPBLENDD $0xaa, Y8, Y1, Y8 + VPSRLQ $0x20, Y1, Y1 + VPBLENDD $0xaa, Y3, Y1, Y3 + VMOVDQA Y8, Y1 + VMOVSLDUP Y6, Y8 + VPBLENDD $0xaa, Y8, Y4, Y8 + VPSRLQ $0x20, Y4, Y4 + VPBLENDD $0xaa, Y6, Y4, Y6 + VMOVDQA Y8, Y4 + VMOVSLDUP Y7, Y8 + VPBLENDD $0xaa, Y8, Y5, Y8 + VPSRLQ $0x20, Y5, Y5 + VPBLENDD $0xaa, Y7, Y5, Y7 + VMOVDQA Y8, Y5 + VPSLLD $0x10, Y1, Y8 + VPBLENDW $0xaa, Y8, Y0, Y8 + VPSRLD $0x10, Y0, Y0 + VPBLENDW $0xaa, Y1, Y0, Y1 + VMOVDQA Y8, Y0 + VPSLLD $0x10, Y3, Y8 + VPBLENDW $0xaa, Y8, Y2, Y8 + VPSRLD $0x10, Y2, Y2 + VPBLENDW $0xaa, Y3, Y2, Y3 + VMOVDQA Y8, Y2 + VPSLLD $0x10, Y5, Y8 + VPBLENDW $0xaa, Y8, Y4, Y8 + VPSRLD $0x10, Y4, Y4 + VPBLENDW $0xaa, Y5, Y4, Y5 + VMOVDQA Y8, Y4 + VPSLLD $0x10, Y7, Y8 + VPBLENDW $0xaa, Y8, Y6, Y8 + VPSRLD $0x10, Y6, Y6 + VPBLENDW $0xaa, Y7, Y6, Y7 + VMOVDQA Y8, Y6 + VMOVDQU Y0, 256(AX) + VMOVDQU Y1, 288(AX) + VMOVDQU Y2, 320(AX) + VMOVDQU Y3, 352(AX) + VMOVDQU Y4, 384(AX) + VMOVDQU Y5, 416(AX) + VMOVDQU Y6, 448(AX) + VMOVDQU Y7, 480(AX) + RET + +// func barrettReduceAVX2(p *[256]int16) +// Requires: AVX, AVX2 +TEXT ·barrettReduceAVX2(SB), NOSPLIT, $0-8 + MOVQ p+0(FP), AX + MOVL $0x00000d01, CX + VMOVD CX, X0 + VPBROADCASTW X0, Y9 + MOVL $0x00004ebf, CX + VMOVD CX, X0 + VPBROADCASTW X0, Y8 + VMOVDQU (AX), Y0 + VMOVDQU 32(AX), Y1 + VMOVDQU 64(AX), Y2 + VMOVDQU 96(AX), Y3 + VPMULHW Y8, Y0, Y4 + VPMULHW Y8, Y1, Y5 + VPMULHW Y8, Y2, Y6 + VPMULHW Y8, Y3, Y7 + VPSRAW $0x0a, Y4, Y4 + VPSRAW $0x0a, Y5, Y5 + VPSRAW $0x0a, Y6, Y6 + VPSRAW $0x0a, Y7, Y7 + VPMULLW Y9, Y4, Y4 + VPMULLW Y9, Y5, Y5 + VPMULLW Y9, Y6, Y6 + VPMULLW Y9, Y7, Y7 + VPSUBW Y4, Y0, Y0 + VPSUBW Y5, Y1, Y1 + VPSUBW Y6, Y2, Y2 + VPSUBW Y7, Y3, Y3 + VMOVDQU Y0, (AX) + VMOVDQU Y1, 32(AX) + VMOVDQU Y2, 64(AX) + VMOVDQU Y3, 96(AX) + VMOVDQU 128(AX), Y0 + VMOVDQU 160(AX), Y1 + VMOVDQU 192(AX), Y2 + VMOVDQU 224(AX), Y3 + VPMULHW Y8, Y0, Y4 + VPMULHW Y8, Y1, Y5 + VPMULHW Y8, Y2, Y6 + VPMULHW Y8, Y3, Y7 + VPSRAW $0x0a, Y4, Y4 + VPSRAW $0x0a, Y5, Y5 + VPSRAW $0x0a, Y6, Y6 + VPSRAW $0x0a, Y7, Y7 + VPMULLW Y9, Y4, Y4 + VPMULLW Y9, Y5, Y5 + VPMULLW Y9, Y6, Y6 + VPMULLW Y9, Y7, Y7 + VPSUBW Y4, Y0, Y0 + VPSUBW Y5, Y1, Y1 + VPSUBW Y6, Y2, Y2 + VPSUBW Y7, Y3, Y3 + VMOVDQU Y0, 128(AX) + VMOVDQU Y1, 160(AX) + VMOVDQU Y2, 192(AX) + VMOVDQU Y3, 224(AX) + VMOVDQU 256(AX), Y0 + VMOVDQU 288(AX), Y1 + VMOVDQU 320(AX), Y2 + VMOVDQU 352(AX), Y3 + VPMULHW Y8, Y0, Y4 + VPMULHW Y8, Y1, Y5 + VPMULHW Y8, Y2, Y6 + VPMULHW Y8, Y3, Y7 + VPSRAW $0x0a, Y4, Y4 + VPSRAW $0x0a, Y5, Y5 + VPSRAW $0x0a, Y6, Y6 + VPSRAW $0x0a, Y7, Y7 + VPMULLW Y9, Y4, Y4 + VPMULLW Y9, Y5, Y5 + VPMULLW Y9, Y6, Y6 + VPMULLW Y9, Y7, Y7 + VPSUBW Y4, Y0, Y0 + VPSUBW Y5, Y1, Y1 + VPSUBW Y6, Y2, Y2 + VPSUBW Y7, Y3, Y3 + VMOVDQU Y0, 256(AX) + VMOVDQU Y1, 288(AX) + VMOVDQU Y2, 320(AX) + VMOVDQU Y3, 352(AX) + VMOVDQU 384(AX), Y0 + VMOVDQU 416(AX), Y1 + VMOVDQU 448(AX), Y2 + VMOVDQU 480(AX), Y3 + VPMULHW Y8, Y0, Y4 + VPMULHW Y8, Y1, Y5 + VPMULHW Y8, Y2, Y6 + VPMULHW Y8, Y3, Y7 + VPSRAW $0x0a, Y4, Y4 + VPSRAW $0x0a, Y5, Y5 + VPSRAW $0x0a, Y6, Y6 + VPSRAW $0x0a, Y7, Y7 + VPMULLW Y9, Y4, Y4 + VPMULLW Y9, Y5, Y5 + VPMULLW Y9, Y6, Y6 + VPMULLW Y9, Y7, Y7 + VPSUBW Y4, Y0, Y0 + VPSUBW Y5, Y1, Y1 + VPSUBW Y6, Y2, Y2 + VPSUBW Y7, Y3, Y3 + VMOVDQU Y0, 384(AX) + VMOVDQU Y1, 416(AX) + VMOVDQU Y2, 448(AX) + VMOVDQU Y3, 480(AX) + RET + +// func normalizeAVX2(p *[256]int16) +// Requires: AVX, AVX2 +TEXT ·normalizeAVX2(SB), NOSPLIT, $0-8 + MOVQ p+0(FP), AX + MOVL $0x00000d01, CX + VMOVD CX, X0 + VPBROADCASTW X0, Y9 + MOVL $0x00004ebf, CX + VMOVD CX, X0 + VPBROADCASTW X0, Y8 + VMOVDQU (AX), Y0 + VMOVDQU 32(AX), Y1 + VMOVDQU 64(AX), Y2 + VMOVDQU 96(AX), Y3 + VPMULHW Y8, Y0, Y4 + VPMULHW Y8, Y1, Y5 + VPMULHW Y8, Y2, Y6 + VPMULHW Y8, Y3, Y7 + VPSRAW $0x0a, Y4, Y4 + VPSRAW $0x0a, Y5, Y5 + VPSRAW $0x0a, Y6, Y6 + VPSRAW $0x0a, Y7, Y7 + VPMULLW Y9, Y4, Y4 + VPMULLW Y9, Y5, Y5 + VPMULLW Y9, Y6, Y6 + VPMULLW Y9, Y7, Y7 + VPSUBW Y4, Y0, Y0 + VPSUBW Y5, Y1, Y1 + VPSUBW Y6, Y2, Y2 + VPSUBW Y7, Y3, Y3 + VPSUBW Y9, Y0, Y0 + VPSUBW Y9, Y1, Y1 + VPSUBW Y9, Y2, Y2 + VPSUBW Y9, Y3, Y3 + VPSRAW $0x0f, Y0, Y4 + VPSRAW $0x0f, Y1, Y5 + VPSRAW $0x0f, Y2, Y6 + VPSRAW $0x0f, Y3, Y7 + VPAND Y4, Y9, Y4 + VPAND Y5, Y9, Y5 + VPAND Y6, Y9, Y6 + VPAND Y7, Y9, Y7 + VPADDW Y0, Y4, Y0 + VPADDW Y1, Y5, Y1 + VPADDW Y2, Y6, Y2 + VPADDW Y3, Y7, Y3 + VMOVDQU Y0, (AX) + VMOVDQU Y1, 32(AX) + VMOVDQU Y2, 64(AX) + VMOVDQU Y3, 96(AX) + VMOVDQU 128(AX), Y0 + VMOVDQU 160(AX), Y1 + VMOVDQU 192(AX), Y2 + VMOVDQU 224(AX), Y3 + VPMULHW Y8, Y0, Y4 + VPMULHW Y8, Y1, Y5 + VPMULHW Y8, Y2, Y6 + VPMULHW Y8, Y3, Y7 + VPSRAW $0x0a, Y4, Y4 + VPSRAW $0x0a, Y5, Y5 + VPSRAW $0x0a, Y6, Y6 + VPSRAW $0x0a, Y7, Y7 + VPMULLW Y9, Y4, Y4 + VPMULLW Y9, Y5, Y5 + VPMULLW Y9, Y6, Y6 + VPMULLW Y9, Y7, Y7 + VPSUBW Y4, Y0, Y0 + VPSUBW Y5, Y1, Y1 + VPSUBW Y6, Y2, Y2 + VPSUBW Y7, Y3, Y3 + VPSUBW Y9, Y0, Y0 + VPSUBW Y9, Y1, Y1 + VPSUBW Y9, Y2, Y2 + VPSUBW Y9, Y3, Y3 + VPSRAW $0x0f, Y0, Y4 + VPSRAW $0x0f, Y1, Y5 + VPSRAW $0x0f, Y2, Y6 + VPSRAW $0x0f, Y3, Y7 + VPAND Y4, Y9, Y4 + VPAND Y5, Y9, Y5 + VPAND Y6, Y9, Y6 + VPAND Y7, Y9, Y7 + VPADDW Y0, Y4, Y0 + VPADDW Y1, Y5, Y1 + VPADDW Y2, Y6, Y2 + VPADDW Y3, Y7, Y3 + VMOVDQU Y0, 128(AX) + VMOVDQU Y1, 160(AX) + VMOVDQU Y2, 192(AX) + VMOVDQU Y3, 224(AX) + VMOVDQU 256(AX), Y0 + VMOVDQU 288(AX), Y1 + VMOVDQU 320(AX), Y2 + VMOVDQU 352(AX), Y3 + VPMULHW Y8, Y0, Y4 + VPMULHW Y8, Y1, Y5 + VPMULHW Y8, Y2, Y6 + VPMULHW Y8, Y3, Y7 + VPSRAW $0x0a, Y4, Y4 + VPSRAW $0x0a, Y5, Y5 + VPSRAW $0x0a, Y6, Y6 + VPSRAW $0x0a, Y7, Y7 + VPMULLW Y9, Y4, Y4 + VPMULLW Y9, Y5, Y5 + VPMULLW Y9, Y6, Y6 + VPMULLW Y9, Y7, Y7 + VPSUBW Y4, Y0, Y0 + VPSUBW Y5, Y1, Y1 + VPSUBW Y6, Y2, Y2 + VPSUBW Y7, Y3, Y3 + VPSUBW Y9, Y0, Y0 + VPSUBW Y9, Y1, Y1 + VPSUBW Y9, Y2, Y2 + VPSUBW Y9, Y3, Y3 + VPSRAW $0x0f, Y0, Y4 + VPSRAW $0x0f, Y1, Y5 + VPSRAW $0x0f, Y2, Y6 + VPSRAW $0x0f, Y3, Y7 + VPAND Y4, Y9, Y4 + VPAND Y5, Y9, Y5 + VPAND Y6, Y9, Y6 + VPAND Y7, Y9, Y7 + VPADDW Y0, Y4, Y0 + VPADDW Y1, Y5, Y1 + VPADDW Y2, Y6, Y2 + VPADDW Y3, Y7, Y3 + VMOVDQU Y0, 256(AX) + VMOVDQU Y1, 288(AX) + VMOVDQU Y2, 320(AX) + VMOVDQU Y3, 352(AX) + VMOVDQU 384(AX), Y0 + VMOVDQU 416(AX), Y1 + VMOVDQU 448(AX), Y2 + VMOVDQU 480(AX), Y3 + VPMULHW Y8, Y0, Y4 + VPMULHW Y8, Y1, Y5 + VPMULHW Y8, Y2, Y6 + VPMULHW Y8, Y3, Y7 + VPSRAW $0x0a, Y4, Y4 + VPSRAW $0x0a, Y5, Y5 + VPSRAW $0x0a, Y6, Y6 + VPSRAW $0x0a, Y7, Y7 + VPMULLW Y9, Y4, Y4 + VPMULLW Y9, Y5, Y5 + VPMULLW Y9, Y6, Y6 + VPMULLW Y9, Y7, Y7 + VPSUBW Y4, Y0, Y0 + VPSUBW Y5, Y1, Y1 + VPSUBW Y6, Y2, Y2 + VPSUBW Y7, Y3, Y3 + VPSUBW Y9, Y0, Y0 + VPSUBW Y9, Y1, Y1 + VPSUBW Y9, Y2, Y2 + VPSUBW Y9, Y3, Y3 + VPSRAW $0x0f, Y0, Y4 + VPSRAW $0x0f, Y1, Y5 + VPSRAW $0x0f, Y2, Y6 + VPSRAW $0x0f, Y3, Y7 + VPAND Y4, Y9, Y4 + VPAND Y5, Y9, Y5 + VPAND Y6, Y9, Y6 + VPAND Y7, Y9, Y7 + VPADDW Y0, Y4, Y0 + VPADDW Y1, Y5, Y1 + VPADDW Y2, Y6, Y2 + VPADDW Y3, Y7, Y3 + VMOVDQU Y0, 384(AX) + VMOVDQU Y1, 416(AX) + VMOVDQU Y2, 448(AX) + VMOVDQU Y3, 480(AX) + RET diff --git a/vendor/github.com/cloudflare/circl/pke/kyber/internal/common/field.go b/vendor/github.com/cloudflare/circl/pke/kyber/internal/common/field.go new file mode 100644 index 00000000..33744dff --- /dev/null +++ b/vendor/github.com/cloudflare/circl/pke/kyber/internal/common/field.go @@ -0,0 +1,74 @@ +package common + +// Given -2¹⁵ q ≤ x < 2¹⁵ q, returns -q < y < q with x 2⁻¹⁶ = y (mod q). +func montReduce(x int32) int16 { + // This is Montgomery reduction with R=2¹⁶. + // + // Note gcd(2¹⁶, q) = 1 as q is prime. Write q' := 62209 = q⁻¹ mod R. + // First we compute + // + // m := ((x mod R) q') mod R + // = x q' mod R + // = int16(x q') + // = int16(int32(x) * int32(q')) + // + // Note that x q' might be as big as 2³² and could overflow the int32 + // multiplication in the last line. However for any int32s a and b, + // we have int32(int64(a)*int64(b)) = int32(a*b) and so the result is ok. + m := int16(x * 62209) + + // Note that x - m q is divisable by R; indeed modulo R we have + // + // x - m q ≡ x - x q' q ≡ x - x q⁻¹ q ≡ x - x = 0. + // + // We return y := (x - m q) / R. Note that y is indeed correct as + // modulo q we have + // + // y ≡ x R⁻¹ - m q R⁻¹ = x R⁻¹ + // + // and as both 2¹⁵ q ≤ m q, x < 2¹⁵ q, we have + // 2¹⁶ q ≤ x - m q < 2¹⁶ and so q ≤ (x - m q) / R < q as desired. + return int16(uint32(x-int32(m)*int32(Q)) >> 16) +} + +// Given any x, returns x R mod q where R=2¹⁶. +func toMont(x int16) int16 { + // Note |1353 x| ≤ 1353 2¹⁵ ≤ 13318 q ≤ 2¹⁵ q and so we're within + // the bounds of montReduce. + return montReduce(int32(x) * 1353) // 1353 = R² mod q. +} + +// Given any x, compute 0 ≤ y ≤ q with x = y (mod q). +// +// Beware: we might have barrettReduce(x) = q ≠ 0 for some x. In fact, +// this happens if and only if x = -nq for some positive integer n. +func barrettReduce(x int16) int16 { + // This is standard Barrett reduction. + // + // For any x we have x mod q = x - ⌊x/q⌋ q. We will use 20159/2²⁶ as + // an approximation of 1/q. Note that 0 ≤ 20159/2²⁶ - 1/q ≤ 0.135/2²⁶ + // and so | x 20156/2²⁶ - x/q | ≤ 2⁻¹⁰ for |x| ≤ 2¹⁶. For all x + // not a multiple of q, the number x/q is further than 1/q from any integer + // and so ⌊x 20156/2²⁶⌋ = ⌊x/q⌋. If x is a multiple of q and x is positive, + // then x 20156/2²⁶ is larger than x/q so ⌊x 20156/2²⁶⌋ = ⌊x/q⌋ as well. + // Finally, if x is negative multiple of q, then ⌊x 20156/2²⁶⌋ = ⌊x/q⌋-1. + // Thus + // [ q if x=-nq for pos. integer n + // x - ⌊x 20156/2²⁶⌋ q = [ + // [ x mod q otherwise + // + // To compute actually compute this, note that + // + // ⌊x 20156/2²⁶⌋ = (20159 x) >> 26. + return x - int16((int32(x)*20159)>>26)*Q +} + +// Returns x if x < q and x - q otherwise. Assumes x ≥ -29439. +func csubq(x int16) int16 { + x -= Q // no overflow due to assumption x ≥ -29439. + // If x is positive, then x >> 15 = 0. If x is negative, + // then uint16(x >> 15) = 2¹⁶-1. So this will add back in q + // if x was smaller than q. + x += (x >> 15) & Q + return x +} diff --git a/vendor/github.com/cloudflare/circl/pke/kyber/internal/common/generic.go b/vendor/github.com/cloudflare/circl/pke/kyber/internal/common/generic.go new file mode 100644 index 00000000..2b742b95 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/pke/kyber/internal/common/generic.go @@ -0,0 +1,77 @@ +//go:build !amd64 +// +build !amd64 + +package common + +// Sets p to a + b. Does not normalize coefficients. +func (p *Poly) Add(a, b *Poly) { + p.addGeneric(a, b) +} + +// Sets p to a - b. Does not normalize coefficients. +func (p *Poly) Sub(a, b *Poly) { + p.subGeneric(a, b) +} + +// Executes an in-place forward "NTT" on p. +// +// Assumes the coefficients are in absolute value ≤q. The resulting +// coefficients are in absolute value ≤7q. If the input is in Montgomery +// form, then the result is in Montgomery form and so (by linearity of the NTT) +// if the input is in regular form, then the result is also in regular form. +// The order of coefficients will be "tangled". These can be put back into +// their proper order by calling Detangle(). +func (p *Poly) NTT() { + p.nttGeneric() +} + +// Executes an in-place inverse "NTT" on p and multiply by the Montgomery +// factor R. +// +// Requires coefficients to be in "tangled" order, see Tangle(). +// Assumes the coefficients are in absolute value ≤q. The resulting +// coefficients are in absolute value ≤q. If the input is in Montgomery +// form, then the result is in Montgomery form and so (by linearity) +// if the input is in regular form, then the result is also in regular form. +func (p *Poly) InvNTT() { + p.invNTTGeneric() +} + +// Sets p to the "pointwise" multiplication of a and b. +// +// That is: InvNTT(p) = InvNTT(a) * InvNTT(b). Assumes a and b are in +// Montgomery form. Products between coefficients of a and b must be strictly +// bounded in absolute value by 2¹⁵q. p will be in Montgomery form and +// bounded in absolute value by 2q. +// +// Requires a and b to be in "tangled" order, see Tangle(). p will be in +// tangled order as well. +func (p *Poly) MulHat(a, b *Poly) { + p.mulHatGeneric(a, b) +} + +// Puts p into the right form to be used with (among others) InvNTT(). +func (p *Poly) Tangle() { + // In the generic implementation there is no advantage to using a + // different order, so we use the standard order everywhere. +} + +// Puts p back into standard form. +func (p *Poly) Detangle() { + // In the generic implementation there is no advantage to using a + // different order, so we use the standard order everywhere. +} + +// Almost normalizes coefficients. +// +// Ensures each coefficient is in {0, …, q}. +func (p *Poly) BarrettReduce() { + p.barrettReduceGeneric() +} + +// Normalizes coefficients. +// +// Ensures each coefficient is in {0, …, q-1}. +func (p *Poly) Normalize() { + p.normalizeGeneric() +} diff --git a/vendor/github.com/cloudflare/circl/pke/kyber/internal/common/ntt.go b/vendor/github.com/cloudflare/circl/pke/kyber/internal/common/ntt.go new file mode 100644 index 00000000..c1abaf23 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/pke/kyber/internal/common/ntt.go @@ -0,0 +1,193 @@ +package common + +// Zetas lists precomputed powers of the primitive root of unity in +// Montgomery representation used for the NTT: +// +// Zetas[i] = ζᵇʳᵛ⁽ⁱ⁾ R mod q +// +// where ζ = 17, brv(i) is the bitreversal of a 7-bit number and R=2¹⁶ mod q. +// +// The following Python code generates the Zetas arrays: +// +// q = 13*2**8 + 1; zeta = 17 +// R = 2**16 % q # Montgomery const. +// def brv(x): return int(''.join(reversed(bin(x)[2:].zfill(7))),2) +// print([(pow(zeta, brv(i), q)*R)%q for i in range(128)]) +var Zetas = [128]int16{ + 2285, 2571, 2970, 1812, 1493, 1422, 287, 202, 3158, 622, 1577, 182, + 962, 2127, 1855, 1468, 573, 2004, 264, 383, 2500, 1458, 1727, 3199, + 2648, 1017, 732, 608, 1787, 411, 3124, 1758, 1223, 652, 2777, 1015, + 2036, 1491, 3047, 1785, 516, 3321, 3009, 2663, 1711, 2167, 126, + 1469, 2476, 3239, 3058, 830, 107, 1908, 3082, 2378, 2931, 961, 1821, + 2604, 448, 2264, 677, 2054, 2226, 430, 555, 843, 2078, 871, 1550, + 105, 422, 587, 177, 3094, 3038, 2869, 1574, 1653, 3083, 778, 1159, + 3182, 2552, 1483, 2727, 1119, 1739, 644, 2457, 349, 418, 329, 3173, + 3254, 817, 1097, 603, 610, 1322, 2044, 1864, 384, 2114, 3193, 1218, + 1994, 2455, 220, 2142, 1670, 2144, 1799, 2051, 794, 1819, 2475, + 2459, 478, 3221, 3021, 996, 991, 958, 1869, 1522, 1628, +} + +// InvNTTReductions keeps track of which coefficients to apply Barrett +// reduction to in Poly.InvNTT(). +// +// Generated in a lazily: once a butterfly is computed which is about to +// overflow the int16, the largest coefficient is reduced. If that is +// not enough, the other coefficient is reduced as well. +// +// This is actually optimal, as proven in https://eprint.iacr.org/2020/1377.pdf +var InvNTTReductions = [...]int{ + -1, // after layer 1 + -1, // after layer 2 + 16, 17, 48, 49, 80, 81, 112, 113, 144, 145, 176, 177, 208, 209, 240, + 241, -1, // after layer 3 + 0, 1, 32, 33, 34, 35, 64, 65, 96, 97, 98, 99, 128, 129, 160, 161, 162, 163, + 192, 193, 224, 225, 226, 227, -1, // after layer 4 + 2, 3, 66, 67, 68, 69, 70, 71, 130, 131, 194, 195, 196, 197, 198, + 199, -1, // after layer 5 + 4, 5, 6, 7, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, + 143, -1, // after layer 6 + -1, // after layer 7 +} + +// Executes an in-place forward "NTT" on p. +// +// Assumes the coefficients are in absolute value ≤q. The resulting +// coefficients are in absolute value ≤7q. If the input is in Montgomery +// form, then the result is in Montgomery form and so (by linearity of the NTT) +// if the input is in regular form, then the result is also in regular form. +// The order of coefficients will be "tangled". These can be put back into +// their proper order by calling Detangle(). +func (p *Poly) nttGeneric() { + // Note that ℤ_q does not have a primitive 512ᵗʰ root of unity (as 512 + // does not divide into q-1) and so we cannot do a regular NTT. ℤ_q + // does have a primitive 256ᵗʰ root of unity, the smallest of which + // is ζ := 17. + // + // Recall that our base ring R := ℤ_q[x] / (x²⁵⁶ + 1). The polynomial + // x²⁵⁶+1 will not split completely (as its roots would be 512ᵗʰ roots + // of unity.) However, it does split almost (using ζ¹²⁸ = -1): + // + // x²⁵⁶ + 1 = (x²)¹²⁸ - ζ¹²⁸ + // = ((x²)⁶⁴ - ζ⁶⁴)((x²)⁶⁴ + ζ⁶⁴) + // = ((x²)³² - ζ³²)((x²)³² + ζ³²)((x²)³² - ζ⁹⁶)((x²)³² + ζ⁹⁶) + // ⋮ + // = (x² - ζ)(x² + ζ)(x² - ζ⁶⁵)(x² + ζ⁶⁵) … (x² + ζ¹²⁷) + // + // Note that the powers of ζ that appear (from the second line down) are + // in binary + // + // 0100000 1100000 + // 0010000 1010000 0110000 1110000 + // 0001000 1001000 0101000 1101000 0011000 1011000 0111000 1111000 + // … + // + // That is: brv(2), brv(3), brv(4), …, where brv(x) denotes the 7-bit + // bitreversal of x. These powers of ζ are given by the Zetas array. + // + // The polynomials x² ± ζⁱ are irreducible and coprime, hence by + // the Chinese Remainder Theorem we know + // + // ℤ_q[x]/(x²⁵⁶+1) → ℤ_q[x]/(x²-ζ) x … x ℤ_q[x]/(x²+ζ¹²⁷) + // + // given by a ↦ ( a mod x²-ζ, …, a mod x²+ζ¹²⁷ ) + // is an isomorphism, which is the "NTT". It can be efficiently computed by + // + // + // a ↦ ( a mod (x²)⁶⁴ - ζ⁶⁴, a mod (x²)⁶⁴ + ζ⁶⁴ ) + // ↦ ( a mod (x²)³² - ζ³², a mod (x²)³² + ζ³², + // a mod (x²)⁹⁶ - ζ⁹⁶, a mod (x²)⁹⁶ + ζ⁹⁶ ) + // + // et cetera + // + // If N was 8 then this can be pictured in the following diagram: + // + // https://cnx.org/resources/17ee4dfe517a6adda05377b25a00bf6e6c93c334/File0026.png + // + // Each cross is a Cooley-Tukey butterfly: it's the map + // + // (a, b) ↦ (a + ζb, a - ζb) + // + // for the appropriate power ζ for that column and row group. + + k := 0 // Index into Zetas + + // l runs effectively over the columns in the diagram above; it is half the + // height of a row group, i.e. the number of butterflies in each row group. + // In the diagram above it would be 4, 2, 1. + for l := N / 2; l > 1; l >>= 1 { + // On the nᵗʰ iteration of the l-loop, the absolute value of the + // coefficients are bounded by nq. + + // offset effectively loops over the row groups in this column; it is + // the first row in the row group. + for offset := 0; offset < N-l; offset += 2 * l { + k++ + zeta := int32(Zetas[k]) + + // j loops over each butterfly in the row group. + for j := offset; j < offset+l; j++ { + t := montReduce(zeta * int32(p[j+l])) + p[j+l] = p[j] - t + p[j] += t + } + } + } +} + +// Executes an in-place inverse "NTT" on p and multiply by the Montgomery +// factor R. +// +// Requires coefficients to be in "tangled" order, see Tangle(). +// Assumes the coefficients are in absolute value ≤q. The resulting +// coefficients are in absolute value ≤q. If the input is in Montgomery +// form, then the result is in Montgomery form and so (by linearity) +// if the input is in regular form, then the result is also in regular form. +func (p *Poly) invNTTGeneric() { + k := 127 // Index into Zetas + r := -1 // Index into InvNTTReductions. + + // We basically do the oppposite of NTT, but postpone dividing by 2 in the + // inverse of the Cooley-Tukey butterfly and accumulate that into a big + // division by 2⁷ at the end. See the comments in the NTT() function. + + for l := 2; l < N; l <<= 1 { + for offset := 0; offset < N-l; offset += 2 * l { + // As we're inverting, we need powers of ζ⁻¹ (instead of ζ). + // To be precise, we need ζᵇʳᵛ⁽ᵏ⁾⁻¹²⁸. However, as ζ⁻¹²⁸ = -1, + // we can use the existing Zetas table instead of + // keeping a separate InvZetas table as in Dilithium. + + minZeta := int32(Zetas[k]) + k-- + + for j := offset; j < offset+l; j++ { + // Gentleman-Sande butterfly: (a, b) ↦ (a + b, ζ(a-b)) + t := p[j+l] - p[j] + p[j] += p[j+l] + p[j+l] = montReduce(minZeta * int32(t)) + + // Note that if we had |a| < αq and |b| < βq before the + // butterfly, then now we have |a| < (α+β)q and |b| < q. + } + } + + // We let the InvNTTReductions instruct us which coefficients to + // Barrett reduce. See TestInvNTTReductions, which tests whether + // there is an overflow. + for { + r++ + i := InvNTTReductions[r] + if i < 0 { + break + } + p[i] = barrettReduce(p[i]) + } + } + + for j := 0; j < N; j++ { + // Note 1441 = (128)⁻¹ R². The coefficients are bounded by 9q, so + // as 1441 * 9 ≈ 2¹⁴ < 2¹⁵, we're within the required bounds + // for montReduce(). + p[j] = montReduce(1441 * int32(p[j])) + } +} diff --git a/vendor/github.com/cloudflare/circl/pke/kyber/internal/common/params.go b/vendor/github.com/cloudflare/circl/pke/kyber/internal/common/params.go new file mode 100644 index 00000000..f04d1aaa --- /dev/null +++ b/vendor/github.com/cloudflare/circl/pke/kyber/internal/common/params.go @@ -0,0 +1,22 @@ +package common + +import ( + "github.com/cloudflare/circl/pke/kyber/internal/common/params" +) + +const ( + // Q is the parameter q ≡ 3329 = 2¹¹ + 2¹⁰ + 2⁸ + 1. + Q = params.Q + + // N is the parameter N: the length of the polynomials + N = params.N + + // PolySize is the size of a packed polynomial. + PolySize = params.PolySize + + // PlaintextSize is the size of the plaintext + PlaintextSize = params.PlaintextSize + + // Eta2 is the parameter η₂ + Eta2 = params.Eta2 +) diff --git a/vendor/github.com/cloudflare/circl/pke/kyber/internal/common/params/params.go b/vendor/github.com/cloudflare/circl/pke/kyber/internal/common/params/params.go new file mode 100644 index 00000000..f7fe31ab --- /dev/null +++ b/vendor/github.com/cloudflare/circl/pke/kyber/internal/common/params/params.go @@ -0,0 +1,21 @@ +package params + +// We put these parameters in a separate package so that the Go code, +// such as asm/src.go, that generates assembler can import it. + +const ( + // Q is the parameter q ≡ 3329 = 2¹¹ + 2¹⁰ + 2⁸ + 1. + Q int16 = 3329 + + // N is the parameter N: the length of the polynomials + N int = 256 + + // PolySize is the size of a packed polynomial. + PolySize int = 384 + + // PlaintextSize is the size of the plaintext + PlaintextSize = 32 + + // Eta2 is the parameter η₂ + Eta2 = 2 +) diff --git a/vendor/github.com/cloudflare/circl/pke/kyber/internal/common/poly.go b/vendor/github.com/cloudflare/circl/pke/kyber/internal/common/poly.go new file mode 100644 index 00000000..f6842152 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/pke/kyber/internal/common/poly.go @@ -0,0 +1,324 @@ +package common + +// An element of our base ring R which are polynomials over ℤ_q +// modulo the equation Xᴺ = -1, where q=3329 and N=256. +// +// This type is also used to store NTT-transformed polynomials, +// see Poly.NTT(). +// +// Coefficients aren't always reduced. See Normalize(). +type Poly [N]int16 + +// Sets p to a + b. Does not normalize coefficients. +func (p *Poly) addGeneric(a, b *Poly) { + for i := 0; i < N; i++ { + p[i] = a[i] + b[i] + } +} + +// Sets p to a - b. Does not normalize coefficients. +func (p *Poly) subGeneric(a, b *Poly) { + for i := 0; i < N; i++ { + p[i] = a[i] - b[i] + } +} + +// Almost normalizes coefficients. +// +// Ensures each coefficient is in {0, …, q}. +func (p *Poly) barrettReduceGeneric() { + for i := 0; i < N; i++ { + p[i] = barrettReduce(p[i]) + } +} + +// Normalizes coefficients. +// +// Ensures each coefficient is in {0, …, q-1}. +func (p *Poly) normalizeGeneric() { + for i := 0; i < N; i++ { + p[i] = csubq(barrettReduce(p[i])) + } +} + +// Multiplies p in-place by the Montgomery factor 2¹⁶. +// +// Coefficients of p can be artbitray. Resulting coefficients are bounded +// in absolute value by q. +func (p *Poly) ToMont() { + for i := 0; i < N; i++ { + p[i] = toMont(p[i]) + } +} + +// Sets p to the "pointwise" multiplication of a and b. +// +// That is: InvNTT(p) = InvNTT(a) * InvNTT(b). Assumes a and b are in +// Montgomery form. Products between coefficients of a and b must be strictly +// bounded in absolute value by 2¹⁵q. p will be in Montgomery form and +// bounded in absolute value by 2q. +// +// Requires a and b to be in "tangled" order, see Tangle(). p will be in +// tangled order as well. +func (p *Poly) mulHatGeneric(a, b *Poly) { + // Recall from the discussion in NTT(), that a transformed polynomial is + // an element of ℤ_q[x]/(x²-ζ) x … x ℤ_q[x]/(x²+ζ¹²⁷); + // that is: 128 degree-one polynomials instead of simply 256 elements + // from ℤ_q as in the regular NTT. So instead of pointwise multiplication, + // we multiply the 128 pairs of degree-one polynomials modulo the + // right equation: + // + // (a₁ + a₂x)(b₁ + b₂x) = a₁b₁ + a₂b₂ζ' + (a₁b₂ + a₂b₁)x, + // + // where ζ' is the appropriate power of ζ. + + k := 64 + for i := 0; i < N; i += 4 { + zeta := int32(Zetas[k]) + k++ + + p0 := montReduce(int32(a[i+1]) * int32(b[i+1])) + p0 = montReduce(int32(p0) * zeta) + p0 += montReduce(int32(a[i]) * int32(b[i])) + + p1 := montReduce(int32(a[i]) * int32(b[i+1])) + p1 += montReduce(int32(a[i+1]) * int32(b[i])) + + p[i] = p0 + p[i+1] = p1 + + p2 := montReduce(int32(a[i+3]) * int32(b[i+3])) + p2 = -montReduce(int32(p2) * zeta) + p2 += montReduce(int32(a[i+2]) * int32(b[i+2])) + + p3 := montReduce(int32(a[i+2]) * int32(b[i+3])) + p3 += montReduce(int32(a[i+3]) * int32(b[i+2])) + + p[i+2] = p2 + p[i+3] = p3 + } +} + +// Packs p into buf. buf should be of length PolySize. +// +// Assumes p is normalized (and not just Barrett reduced) and "tangled", +// see Tangle(). +func (p *Poly) Pack(buf []byte) { + q := *p + q.Detangle() + for i := 0; i < 128; i++ { + t0 := q[2*i] + t1 := q[2*i+1] + buf[3*i] = byte(t0) + buf[3*i+1] = byte(t0>>8) | byte(t1<<4) + buf[3*i+2] = byte(t1 >> 4) + } +} + +// Unpacks p from buf. +// +// buf should be of length PolySize. p will be "tangled", see Detangle(). +// +// p will not be normalized; instead 0 ≤ p[i] < 4096. +func (p *Poly) Unpack(buf []byte) { + for i := 0; i < 128; i++ { + p[2*i] = int16(buf[3*i]) | ((int16(buf[3*i+1]) << 8) & 0xfff) + p[2*i+1] = int16(buf[3*i+1]>>4) | (int16(buf[3*i+2]) << 4) + } + p.Tangle() +} + +// Set p to Decompress_q(m, 1). +// +// p will be normalized. m has to be of PlaintextSize. +func (p *Poly) DecompressMessage(m []byte) { + // Decompress_q(x, 1) = ⌈xq/2⌋ = ⌊xq/2+½⌋ = (xq+1) >> 1 and so + // Decompress_q(0, 1) = 0 and Decompress_q(1, 1) = (q+1)/2. + for i := 0; i < 32; i++ { + for j := 0; j < 8; j++ { + bit := (m[i] >> uint(j)) & 1 + + // Set coefficient to either 0 or (q+1)/2 depending on the bit. + p[8*i+j] = -int16(bit) & ((Q + 1) / 2) + } + } +} + +// Writes Compress_q(p, 1) to m. +// +// Assumes p is normalized. m has to be of length at least PlaintextSize. +func (p *Poly) CompressMessageTo(m []byte) { + // Compress_q(x, 1) is 1 on {833, …, 2496} and zero elsewhere. + for i := 0; i < 32; i++ { + m[i] = 0 + for j := 0; j < 8; j++ { + x := 1664 - p[8*i+j] + // With the previous substitution, we want to return 1 if + // and only if x is in {831, …, -832}. + x = (x >> 15) ^ x + // Note (x >> 15)ˣ if x≥0 and -x-1 otherwise. Thus now we want + // to return 1 iff x ≤ 831, ie. x - 832 < 0. + x -= 832 + m[i] |= ((byte(x >> 15)) & 1) << uint(j) + } + } +} + +// Set p to Decompress_q(m, 1). +// +// Assumes d is in {3, 4, 5, 10, 11}. p will be normalized. +func (p *Poly) Decompress(m []byte, d int) { + // Decompress_q(x, d) = ⌈(q/2ᵈ)x⌋ + // = ⌊(q/2ᵈ)x+½⌋ + // = ⌊(qx + 2ᵈ⁻¹)/2ᵈ⌋ + // = (qx + (1<<(d-1))) >> d + switch d { + case 4: + for i := 0; i < N/2; i++ { + p[2*i] = int16(((1 << 3) + + uint32(m[i]&15)*uint32(Q)) >> 4) + p[2*i+1] = int16(((1 << 3) + + uint32(m[i]>>4)*uint32(Q)) >> 4) + } + case 5: + var t [8]uint16 + idx := 0 + for i := 0; i < N/8; i++ { + t[0] = uint16(m[idx]) + t[1] = (uint16(m[idx]) >> 5) | (uint16(m[idx+1] << 3)) + t[2] = uint16(m[idx+1]) >> 2 + t[3] = (uint16(m[idx+1]) >> 7) | (uint16(m[idx+2] << 1)) + t[4] = (uint16(m[idx+2]) >> 4) | (uint16(m[idx+3] << 4)) + t[5] = uint16(m[idx+3]) >> 1 + t[6] = (uint16(m[idx+3]) >> 6) | (uint16(m[idx+4] << 2)) + t[7] = uint16(m[idx+4]) >> 3 + + for j := 0; j < 8; j++ { + p[8*i+j] = int16(((1 << 4) + + uint32(t[j]&((1<<5)-1))*uint32(Q)) >> 5) + } + + idx += 5 + } + + case 10: + var t [4]uint16 + idx := 0 + for i := 0; i < N/4; i++ { + t[0] = uint16(m[idx]) | (uint16(m[idx+1]) << 8) + t[1] = (uint16(m[idx+1]) >> 2) | (uint16(m[idx+2]) << 6) + t[2] = (uint16(m[idx+2]) >> 4) | (uint16(m[idx+3]) << 4) + t[3] = (uint16(m[idx+3]) >> 6) | (uint16(m[idx+4]) << 2) + + for j := 0; j < 4; j++ { + p[4*i+j] = int16(((1 << 9) + + uint32(t[j]&((1<<10)-1))*uint32(Q)) >> 10) + } + + idx += 5 + } + case 11: + var t [8]uint16 + idx := 0 + for i := 0; i < N/8; i++ { + t[0] = uint16(m[idx]) | (uint16(m[idx+1]) << 8) + t[1] = (uint16(m[idx+1]) >> 3) | (uint16(m[idx+2]) << 5) + t[2] = (uint16(m[idx+2]) >> 6) | (uint16(m[idx+3]) << 2) | (uint16(m[idx+4]) << 10) + t[3] = (uint16(m[idx+4]) >> 1) | (uint16(m[idx+5]) << 7) + t[4] = (uint16(m[idx+5]) >> 4) | (uint16(m[idx+6]) << 4) + t[5] = (uint16(m[idx+6]) >> 7) | (uint16(m[idx+7]) << 1) | (uint16(m[idx+8]) << 9) + t[6] = (uint16(m[idx+8]) >> 2) | (uint16(m[idx+9]) << 6) + t[7] = (uint16(m[idx+9]) >> 5) | (uint16(m[idx+10]) << 3) + + for j := 0; j < 8; j++ { + p[8*i+j] = int16(((1 << 10) + + uint32(t[j]&((1<<11)-1))*uint32(Q)) >> 11) + } + + idx += 11 + } + default: + panic("unsupported d") + } +} + +// Writes Compress_q(p, d) to m. +// +// Assumes p is normalized and d is in {3, 4, 5, 10, 11}. +func (p *Poly) CompressTo(m []byte, d int) { + // Compress_q(x, d) = ⌈(2ᵈ/q)x⌋ mod⁺ 2ᵈ + // = ⌊(2ᵈ/q)x+½⌋ mod⁺ 2ᵈ + // = ⌊((x << d) + q/2) / q⌋ mod⁺ 2ᵈ + // = DIV((x << d) + q/2, q) & ((1<>3) | byte(t[2]<<2) | byte(t[3]<<7) + m[idx+2] = byte(t[3]>>1) | byte(t[4]<<4) + m[idx+3] = byte(t[4]>>4) | byte(t[5]<<1) | byte(t[6]<<6) + m[idx+4] = byte(t[6]>>2) | byte(t[7]<<3) + idx += 5 + } + + case 10: + var t [4]uint16 + idx := 0 + for i := 0; i < N/4; i++ { + for j := 0; j < 4; j++ { + t[j] = uint16(((uint32(p[4*i+j])<<10)+uint32(Q)/2)/ + uint32(Q)) & ((1 << 10) - 1) + } + m[idx] = byte(t[0]) + m[idx+1] = byte(t[0]>>8) | byte(t[1]<<2) + m[idx+2] = byte(t[1]>>6) | byte(t[2]<<4) + m[idx+3] = byte(t[2]>>4) | byte(t[3]<<6) + m[idx+4] = byte(t[3] >> 2) + idx += 5 + } + case 11: + var t [8]uint16 + idx := 0 + for i := 0; i < N/8; i++ { + for j := 0; j < 8; j++ { + t[j] = uint16(((uint32(p[8*i+j])<<11)+uint32(Q)/2)/ + uint32(Q)) & ((1 << 11) - 1) + } + m[idx] = byte(t[0]) + m[idx+1] = byte(t[0]>>8) | byte(t[1]<<3) + m[idx+2] = byte(t[1]>>5) | byte(t[2]<<6) + m[idx+3] = byte(t[2] >> 2) + m[idx+4] = byte(t[2]>>10) | byte(t[3]<<1) + m[idx+5] = byte(t[3]>>7) | byte(t[4]<<4) + m[idx+6] = byte(t[4]>>4) | byte(t[5]<<7) + m[idx+7] = byte(t[5] >> 1) + m[idx+8] = byte(t[5]>>9) | byte(t[6]<<2) + m[idx+9] = byte(t[6]>>6) | byte(t[7]<<5) + m[idx+10] = byte(t[7] >> 3) + idx += 11 + } + default: + panic("unsupported d") + } +} diff --git a/vendor/github.com/cloudflare/circl/pke/kyber/internal/common/sample.go b/vendor/github.com/cloudflare/circl/pke/kyber/internal/common/sample.go new file mode 100644 index 00000000..1f15f32c --- /dev/null +++ b/vendor/github.com/cloudflare/circl/pke/kyber/internal/common/sample.go @@ -0,0 +1,236 @@ +package common + +import ( + "encoding/binary" + + "github.com/cloudflare/circl/internal/sha3" + "github.com/cloudflare/circl/simd/keccakf1600" +) + +// DeriveX4Available indicates whether the system supports the quick fourway +// sampling variants like PolyDeriveUniformX4. +var DeriveX4Available = keccakf1600.IsEnabledX4() + +// Samples p from a centered binomial distribution with given η. +// +// Essentially CBD_η(PRF(seed, nonce)) from the specification. +func (p *Poly) DeriveNoise(seed []byte, nonce uint8, eta int) { + switch eta { + case 2: + p.DeriveNoise2(seed, nonce) + case 3: + p.DeriveNoise3(seed, nonce) + default: + panic("unsupported eta") + } +} + +// Sample p from a centered binomial distribution with n=6 and p=½ - that is: +// coefficients are in {-3, -2, -1, 0, 1, 2, 3} with probabilities {1/64, 3/32, +// 15/64, 5/16, 16/64, 3/32, 1/64}. +func (p *Poly) DeriveNoise3(seed []byte, nonce uint8) { + keySuffix := [1]byte{nonce} + h := sha3.NewShake256() + _, _ = h.Write(seed[:]) + _, _ = h.Write(keySuffix[:]) + + // The distribution at hand is exactly the same as that + // of (a₁ + a₂ + a₃) - (b₁ + b₂+b₃) where a_i,b_i~U(1). Thus we need + // 6 bits per coefficients, thus 192 bytes of input entropy. + + // We add two extra zero bytes in the buffer to be able to read 8 bytes + // at the same time (while using only 6.) + var buf [192 + 2]byte + _, _ = h.Read(buf[:192]) + + for i := 0; i < 32; i++ { + // t is interpreted as a₁ + 2a₂ + 4a₃ + 8b₁ + 16b₂ + …. + t := binary.LittleEndian.Uint64(buf[6*i:]) + + d := t & 0x249249249249 // a₁ + 8b₁ + … + d += (t >> 1) & 0x249249249249 // a₁ + a₂ + 8(b₁ + b₂) + … + d += (t >> 2) & 0x249249249249 // a₁ + a₂ + a₃ + 4(b₁ + b₂ + b₃) + … + + for j := 0; j < 8; j++ { + a := int16(d) & 0x7 // a₁ + a₂ + a₃ + d >>= 3 + b := int16(d) & 0x7 // b₁ + b₂ + b₃ + d >>= 3 + p[8*i+j] = a - b + } + } +} + +// Sample p from a centered binomial distribution with n=4 and p=½ - that is: +// coefficients are in {-2, -1, 0, 1, 2} with probabilities {1/16, 1/4, +// 3/8, 1/4, 1/16}. +func (p *Poly) DeriveNoise2(seed []byte, nonce uint8) { + keySuffix := [1]byte{nonce} + h := sha3.NewShake256() + _, _ = h.Write(seed[:]) + _, _ = h.Write(keySuffix[:]) + + // The distribution at hand is exactly the same as that + // of (a + a') - (b + b') where a,a',b,b'~U(1). Thus we need 4 bits per + // coefficients, thus 128 bytes of input entropy. + + var buf [128]byte + _, _ = h.Read(buf[:]) + + for i := 0; i < 16; i++ { + // t is interpreted as a + 2a' + 4b + 8b' + …. + t := binary.LittleEndian.Uint64(buf[8*i:]) + + d := t & 0x5555555555555555 // a + 4b + … + d += (t >> 1) & 0x5555555555555555 // a+a' + 4(b + b') + … + + for j := 0; j < 16; j++ { + a := int16(d) & 0x3 + d >>= 2 + b := int16(d) & 0x3 + d >>= 2 + p[16*i+j] = a - b + } + } +} + +// For each i, sample ps[i] uniformly from the given seed for coordinates +// xs[i] and ys[i]. ps[i] may be nil and is ignored in that case. +// +// Can only be called when DeriveX4Available is true. +func PolyDeriveUniformX4(ps [4]*Poly, seed *[32]byte, xs, ys [4]uint8) { + var perm keccakf1600.StateX4 + state := perm.Initialize() + + // Absorb the seed in the four states + for i := 0; i < 4; i++ { + v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) + for j := 0; j < 4; j++ { + state[i*4+j] = v + } + } + + // Absorb the coordinates, the SHAKE128 domain separator (0b1111), the + // start of the padding (0b…001) and the end of the padding 0b100…. + // Recall that the rate of SHAKE128 is 168; ie. 21 uint64s. + for j := 0; j < 4; j++ { + state[4*4+j] = uint64(xs[j]) | (uint64(ys[j]) << 8) | (0x1f << 16) + state[20*4+j] = 0x80 << 56 + } + + var idx [4]int // indices into ps + for j := 0; j < 4; j++ { + if ps[j] == nil { + idx[j] = N // mark nil polynomials as completed + } + } + + done := false + for !done { + // Applies KeccaK-f[1600] to state to get the next 21 uint64s of each of + // the four SHAKE128 streams. + perm.Permute() + + done = true + + PolyLoop: + for j := 0; j < 4; j++ { + if idx[j] == N { + continue + } + for i := 0; i < 7; i++ { + var t [16]uint16 + + v1 := state[i*3*4+j] + v2 := state[(i*3+1)*4+j] + v3 := state[(i*3+2)*4+j] + + t[0] = uint16(v1) & 0xfff + t[1] = uint16(v1>>12) & 0xfff + t[2] = uint16(v1>>24) & 0xfff + t[3] = uint16(v1>>36) & 0xfff + t[4] = uint16(v1>>48) & 0xfff + t[5] = uint16((v1>>60)|(v2<<4)) & 0xfff + + t[6] = uint16(v2>>8) & 0xfff + t[7] = uint16(v2>>20) & 0xfff + t[8] = uint16(v2>>32) & 0xfff + t[9] = uint16(v2>>44) & 0xfff + t[10] = uint16((v2>>56)|(v3<<8)) & 0xfff + + t[11] = uint16(v3>>4) & 0xfff + t[12] = uint16(v3>>16) & 0xfff + t[13] = uint16(v3>>28) & 0xfff + t[14] = uint16(v3>>40) & 0xfff + t[15] = uint16(v3>>52) & 0xfff + + for k := 0; k < 16; k++ { + if t[k] < uint16(Q) { + ps[j][idx[j]] = int16(t[k]) + idx[j]++ + if idx[j] == N { + continue PolyLoop + } + } + } + } + + done = false + } + } + + for i := 0; i < 4; i++ { + if ps[i] != nil { + ps[i].Tangle() + } + } +} + +// Sample p uniformly from the given seed and x and y coordinates. +// +// Coefficients are reduced and will be in "tangled" order. See Tangle(). +func (p *Poly) DeriveUniform(seed *[32]byte, x, y uint8) { + var seedSuffix [2]byte + var buf [168]byte // rate of SHAKE-128 + + seedSuffix[0] = x + seedSuffix[1] = y + + h := sha3.NewShake128() + _, _ = h.Write(seed[:]) + _, _ = h.Write(seedSuffix[:]) + + i := 0 + for { + _, _ = h.Read(buf[:]) + + for j := 0; j < 168; j += 3 { + t1 := (uint16(buf[j]) | (uint16(buf[j+1]) << 8)) & 0xfff + t2 := (uint16(buf[j+1]>>4) | (uint16(buf[j+2]) << 4)) & 0xfff + + if t1 < uint16(Q) { + p[i] = int16(t1) + i++ + + if i == N { + break + } + } + + if t2 < uint16(Q) { + p[i] = int16(t2) + i++ + + if i == N { + break + } + } + } + + if i == N { + break + } + } + + p.Tangle() +} diff --git a/vendor/github.com/cloudflare/circl/pke/kyber/internal/common/stubs_amd64.go b/vendor/github.com/cloudflare/circl/pke/kyber/internal/common/stubs_amd64.go new file mode 100644 index 00000000..dd869993 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/pke/kyber/internal/common/stubs_amd64.go @@ -0,0 +1,33 @@ +// Code generated by command: go run src.go -out ../amd64.s -stubs ../stubs_amd64.go -pkg common. DO NOT EDIT. + +//go:build amd64 +// +build amd64 + +package common + +//go:noescape +func addAVX2(p *[256]int16, a *[256]int16, b *[256]int16) + +//go:noescape +func subAVX2(p *[256]int16, a *[256]int16, b *[256]int16) + +//go:noescape +func nttAVX2(p *[256]int16) + +//go:noescape +func invNttAVX2(p *[256]int16) + +//go:noescape +func mulHatAVX2(p *[256]int16, a *[256]int16, b *[256]int16) + +//go:noescape +func detangleAVX2(p *[256]int16) + +//go:noescape +func tangleAVX2(p *[256]int16) + +//go:noescape +func barrettReduceAVX2(p *[256]int16) + +//go:noescape +func normalizeAVX2(p *[256]int16) diff --git a/vendor/github.com/cloudflare/circl/pke/kyber/kyber1024/internal/cpapke.go b/vendor/github.com/cloudflare/circl/pke/kyber/kyber1024/internal/cpapke.go new file mode 100644 index 00000000..01ef88b2 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/pke/kyber/kyber1024/internal/cpapke.go @@ -0,0 +1,176 @@ +// Code generated from kyber512/internal/cpapke.go by gen.go + +package internal + +import ( + "github.com/cloudflare/circl/internal/sha3" + "github.com/cloudflare/circl/pke/kyber/internal/common" +) + +// A Kyber.CPAPKE private key. +type PrivateKey struct { + sh Vec // NTT(s), normalized +} + +// A Kyber.CPAPKE public key. +type PublicKey struct { + rho [32]byte // ρ, the seed for the matrix A + th Vec // NTT(t), normalized + + // cached values + aT Mat // the matrix Aᵀ +} + +// Packs the private key to buf. +func (sk *PrivateKey) Pack(buf []byte) { + sk.sh.Pack(buf) +} + +// Unpacks the private key from buf. +func (sk *PrivateKey) Unpack(buf []byte) { + sk.sh.Unpack(buf) + sk.sh.Normalize() +} + +// Packs the public key to buf. +func (pk *PublicKey) Pack(buf []byte) { + pk.th.Pack(buf) + copy(buf[K*common.PolySize:], pk.rho[:]) +} + +// Unpacks the public key from buf. +func (pk *PublicKey) Unpack(buf []byte) { + pk.th.Unpack(buf) + pk.th.Normalize() + copy(pk.rho[:], buf[K*common.PolySize:]) + pk.aT.Derive(&pk.rho, true) +} + +// Derives a new Kyber.CPAPKE keypair from the given seed. +func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { + var pk PublicKey + var sk PrivateKey + + var expandedSeed [64]byte + + h := sha3.New512() + _, _ = h.Write(seed) + + // This writes hash into expandedSeed. Yes, this is idiomatic Go. + _, _ = h.Read(expandedSeed[:]) + + copy(pk.rho[:], expandedSeed[:32]) + sigma := expandedSeed[32:] // σ, the noise seed + + pk.aT.Derive(&pk.rho, false) // Expand ρ to matrix A; we'll transpose later + + var eh Vec + sk.sh.DeriveNoise(sigma, 0, Eta1) // Sample secret vector s + sk.sh.NTT() + sk.sh.Normalize() + + eh.DeriveNoise(sigma, K, Eta1) // Sample blind e + eh.NTT() + + // Next, we compute t = A s + e. + for i := 0; i < K; i++ { + // Note that coefficients of s are bounded by q and those of A + // are bounded by 4.5q and so their product is bounded by 2¹⁵q + // as required for multiplication. + PolyDotHat(&pk.th[i], &pk.aT[i], &sk.sh) + + // A and s were not in Montgomery form, so the Montgomery + // multiplications in the inner product added a factor R⁻¹ which + // we'll cancel out now. This will also ensure the coefficients of + // t are bounded in absolute value by q. + pk.th[i].ToMont() + } + + pk.th.Add(&pk.th, &eh) // bounded by 8q. + pk.th.Normalize() + pk.aT.Transpose() + + return &pk, &sk +} + +// Decrypts ciphertext ct meant for private key sk to plaintext pt. +func (sk *PrivateKey) DecryptTo(pt, ct []byte) { + var u Vec + var v, m common.Poly + + u.Decompress(ct, DU) + v.Decompress(ct[K*compressedPolySize(DU):], DV) + + // Compute m = v - + u.NTT() + PolyDotHat(&m, &sk.sh, &u) + m.BarrettReduce() + m.InvNTT() + m.Sub(&v, &m) + m.Normalize() + + // Compress polynomial m to original message + m.CompressMessageTo(pt) +} + +// Encrypts message pt for the public key to ciphertext ct using randomness +// from seed. +// +// seed has to be of length SeedSize, pt of PlaintextSize and ct of +// CiphertextSize. +func (pk *PublicKey) EncryptTo(ct, pt, seed []byte) { + var rh, e1, u Vec + var e2, v, m common.Poly + + // Sample r, e₁ and e₂ from B_η + rh.DeriveNoise(seed, 0, Eta1) + rh.NTT() + rh.BarrettReduce() + + e1.DeriveNoise(seed, K, common.Eta2) + e2.DeriveNoise(seed, 2*K, common.Eta2) + + // Next we compute u = Aᵀ r + e₁. First Aᵀ. + for i := 0; i < K; i++ { + // Note that coefficients of r are bounded by q and those of Aᵀ + // are bounded by 4.5q and so their product is bounded by 2¹⁵q + // as required for multiplication. + PolyDotHat(&u[i], &pk.aT[i], &rh) + } + + u.BarrettReduce() + + // Aᵀ and r were not in Montgomery form, so the Montgomery + // multiplications in the inner product added a factor R⁻¹ which + // the InvNTT cancels out. + u.InvNTT() + + u.Add(&u, &e1) // u = Aᵀ r + e₁ + + // Next compute v = + e₂ + Decompress_q(m, 1). + PolyDotHat(&v, &pk.th, &rh) + v.BarrettReduce() + v.InvNTT() + + m.DecompressMessage(pt) + v.Add(&v, &m) + v.Add(&v, &e2) // v = + e₂ + Decompress_q(m, 1) + + // Pack ciphertext + u.Normalize() + v.Normalize() + + u.CompressTo(ct, DU) + v.CompressTo(ct[K*compressedPolySize(DU):], DV) +} + +// Returns whether sk equals other. +func (sk *PrivateKey) Equal(other *PrivateKey) bool { + ret := int16(0) + for i := 0; i < K; i++ { + for j := 0; j < common.N; j++ { + ret |= sk.sh[i][j] ^ other.sh[i][j] + } + } + return ret == 0 +} diff --git a/vendor/github.com/cloudflare/circl/pke/kyber/kyber1024/internal/mat.go b/vendor/github.com/cloudflare/circl/pke/kyber/kyber1024/internal/mat.go new file mode 100644 index 00000000..e8a35aff --- /dev/null +++ b/vendor/github.com/cloudflare/circl/pke/kyber/kyber1024/internal/mat.go @@ -0,0 +1,85 @@ +// Code generated from kyber512/internal/mat.go by gen.go + +package internal + +import ( + "github.com/cloudflare/circl/pke/kyber/internal/common" +) + +// A k by k matrix of polynomials. +type Mat [K]Vec + +// Expands the given seed to the corresponding matrix A or its transpose Aᵀ. +func (m *Mat) Derive(seed *[32]byte, transpose bool) { + if !common.DeriveX4Available { + if transpose { + for i := 0; i < K; i++ { + for j := 0; j < K; j++ { + m[i][j].DeriveUniform(seed, uint8(i), uint8(j)) + } + } + } else { + for i := 0; i < K; i++ { + for j := 0; j < K; j++ { + m[i][j].DeriveUniform(seed, uint8(j), uint8(i)) + } + } + } + return + } + + var ps [4]*common.Poly + var xs [4]uint8 + var ys [4]uint8 + x := uint8(0) + y := uint8(0) + + for x != K { + idx := 0 + for ; idx < 4; idx++ { + ps[idx] = &m[x][y] + + if transpose { + xs[idx] = x + ys[idx] = y + } else { + xs[idx] = y + ys[idx] = x + } + + y++ + if y == K { + x++ + y = 0 + + if x == K { + if idx == 0 { + // If there is just one left, then a plain DeriveUniform + // is quicker than the X4 variant. + ps[0].DeriveUniform(seed, xs[0], ys[0]) + return + } + + for idx++; idx < 4; idx++ { + ps[idx] = nil + } + + break + } + } + } + + common.PolyDeriveUniformX4(ps, seed, xs, ys) + } +} + +// Tranposes A in place. +func (m *Mat) Transpose() { + for i := 0; i < K-1; i++ { + for j := i + 1; j < K; j++ { + t := m[i][j] + m[i][j] = m[j][i] + m[j][i] = t + } + } +} diff --git a/vendor/github.com/cloudflare/circl/pke/kyber/kyber1024/internal/params.go b/vendor/github.com/cloudflare/circl/pke/kyber/kyber1024/internal/params.go new file mode 100644 index 00000000..669b0eda --- /dev/null +++ b/vendor/github.com/cloudflare/circl/pke/kyber/kyber1024/internal/params.go @@ -0,0 +1,21 @@ +// Code generated from params.templ.go. DO NOT EDIT. + +package internal + +import ( + "github.com/cloudflare/circl/pke/kyber/internal/common" +) + +const ( + K = 4 + Eta1 = 2 + DU = 11 + DV = 5 + PublicKeySize = 32 + K*common.PolySize + + PrivateKeySize = K * common.PolySize + + PlaintextSize = common.PlaintextSize + SeedSize = 32 + CiphertextSize = 1568 +) diff --git a/vendor/github.com/cloudflare/circl/pke/kyber/kyber1024/internal/vec.go b/vendor/github.com/cloudflare/circl/pke/kyber/kyber1024/internal/vec.go new file mode 100644 index 00000000..6681895a --- /dev/null +++ b/vendor/github.com/cloudflare/circl/pke/kyber/kyber1024/internal/vec.go @@ -0,0 +1,125 @@ +// Code generated from kyber512/internal/vec.go by gen.go + +package internal + +import ( + "github.com/cloudflare/circl/pke/kyber/internal/common" +) + +// A vector of K polynomials +type Vec [K]common.Poly + +// Samples v[i] from a centered binomial distribution with given η, +// seed and nonce+i. +// +// Essentially CBD_η(PRF(seed, nonce+i)) from the specification. +func (v *Vec) DeriveNoise(seed []byte, nonce uint8, eta int) { + for i := 0; i < K; i++ { + v[i].DeriveNoise(seed, nonce+uint8(i), eta) + } +} + +// Sets p to the inner product of a and b using "pointwise" multiplication. +// +// See MulHat() and NTT() for a description of the multiplication. +// Assumes a and b are in Montgomery form. p will be in Montgomery form, +// and its coefficients will be bounded in absolute value by 2kq. +// If a and b are not in Montgomery form, then the action is the same +// as "pointwise" multiplication followed by multiplying by R⁻¹, the inverse +// of the Montgomery factor. +func PolyDotHat(p *common.Poly, a, b *Vec) { + var t common.Poly + *p = common.Poly{} // set p to zero + for i := 0; i < K; i++ { + t.MulHat(&a[i], &b[i]) + p.Add(&t, p) + } +} + +// Almost normalizes coefficients in-place. +// +// Ensures each coefficient is in {0, …, q}. +func (v *Vec) BarrettReduce() { + for i := 0; i < K; i++ { + v[i].BarrettReduce() + } +} + +// Normalizes coefficients in-place. +// +// Ensures each coefficient is in {0, …, q-1}. +func (v *Vec) Normalize() { + for i := 0; i < K; i++ { + v[i].Normalize() + } +} + +// Applies in-place inverse NTT(). See Poly.InvNTT() for assumptions. +func (v *Vec) InvNTT() { + for i := 0; i < K; i++ { + v[i].InvNTT() + } +} + +// Applies in-place forward NTT(). See Poly.NTT() for assumptions. +func (v *Vec) NTT() { + for i := 0; i < K; i++ { + v[i].NTT() + } +} + +// Sets v to a + b. +func (v *Vec) Add(a, b *Vec) { + for i := 0; i < K; i++ { + v[i].Add(&a[i], &b[i]) + } +} + +// Packs v into buf, which must be of length K*PolySize. +func (v *Vec) Pack(buf []byte) { + for i := 0; i < K; i++ { + v[i].Pack(buf[common.PolySize*i:]) + } +} + +// Unpacks v from buf which must be of length K*PolySize. +func (v *Vec) Unpack(buf []byte) { + for i := 0; i < K; i++ { + v[i].Unpack(buf[common.PolySize*i:]) + } +} + +// Writes Compress_q(v, d) to m. +// +// Assumes v is normalized and d is in {3, 4, 5, 10, 11}. +func (v *Vec) CompressTo(m []byte, d int) { + size := compressedPolySize(d) + for i := 0; i < K; i++ { + v[i].CompressTo(m[size*i:], d) + } +} + +// Set v to Decompress_q(m, 1). +// +// Assumes d is in {3, 4, 5, 10, 11}. v will be normalized. +func (v *Vec) Decompress(m []byte, d int) { + size := compressedPolySize(d) + for i := 0; i < K; i++ { + v[i].Decompress(m[size*i:], d) + } +} + +// ⌈(256 d)/8⌉ +func compressedPolySize(d int) int { + switch d { + case 4: + return 128 + case 5: + return 160 + case 10: + return 320 + case 11: + return 352 + } + panic("unsupported d") +} diff --git a/vendor/github.com/cloudflare/circl/pke/kyber/kyber1024/kyber.go b/vendor/github.com/cloudflare/circl/pke/kyber/kyber1024/kyber.go new file mode 100644 index 00000000..fb5911fa --- /dev/null +++ b/vendor/github.com/cloudflare/circl/pke/kyber/kyber1024/kyber.go @@ -0,0 +1,145 @@ +// Code generated from modePkg.templ.go. DO NOT EDIT. + +// kyber1024 implements the IND-CPA-secure Public Key Encryption +// scheme Kyber1024.CPAPKE as submitted to round 3 of the NIST PQC competition +// and described in +// +// https://pq-crystals.org/kyber/data/kyber-specification-round3.pdf +package kyber1024 + +import ( + cryptoRand "crypto/rand" + "io" + + "github.com/cloudflare/circl/pke/kyber/kyber1024/internal" +) + +const ( + // Size of seed for NewKeyFromSeed + KeySeedSize = internal.SeedSize + + // Size of seed for EncryptTo + EncryptionSeedSize = internal.SeedSize + + // Size of a packed PublicKey + PublicKeySize = internal.PublicKeySize + + // Size of a packed PrivateKey + PrivateKeySize = internal.PrivateKeySize + + // Size of a ciphertext + CiphertextSize = internal.CiphertextSize + + // Size of a plaintext + PlaintextSize = internal.PlaintextSize +) + +// PublicKey is the type of Kyber1024.CPAPKE public key +type PublicKey internal.PublicKey + +// PrivateKey is the type of Kyber1024.CPAPKE private key +type PrivateKey internal.PrivateKey + +// GenerateKey generates a public/private key pair using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { + var seed [KeySeedSize]byte + if rand == nil { + rand = cryptoRand.Reader + } + _, err := io.ReadFull(rand, seed[:]) + if err != nil { + return nil, nil, err + } + pk, sk := internal.NewKeyFromSeed(seed[:]) + return (*PublicKey)(pk), (*PrivateKey)(sk), nil +} + +// NewKeyFromSeed derives a public/private key pair using the given seed. +// +// Panics if seed is not of length KeySeedSize. +func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { + if len(seed) != KeySeedSize { + panic("seed must be of length KeySeedSize") + } + pk, sk := internal.NewKeyFromSeed(seed) + return (*PublicKey)(pk), (*PrivateKey)(sk) +} + +// EncryptTo encrypts message pt for the public key and writes the ciphertext +// to ct using randomness from seed. +// +// This function panics if the lengths of pt, seed, and ct are not +// PlaintextSize, EncryptionSeedSize, and CiphertextSize respectively. +func (pk *PublicKey) EncryptTo(ct []byte, pt []byte, seed []byte) { + if len(pt) != PlaintextSize { + panic("pt must be of length PlaintextSize") + } + if len(ct) != CiphertextSize { + panic("ct must be of length CiphertextSize") + } + if len(seed) != EncryptionSeedSize { + panic("seed must be of length EncryptionSeedSize") + } + (*internal.PublicKey)(pk).EncryptTo(ct, pt, seed) +} + +// DecryptTo decrypts message ct for the private key and writes the +// plaintext to pt. +// +// This function panics if the lengths of ct and pt are not +// CiphertextSize and PlaintextSize respectively. +func (sk *PrivateKey) DecryptTo(pt []byte, ct []byte) { + if len(pt) != PlaintextSize { + panic("pt must be of length PlaintextSize") + } + if len(ct) != CiphertextSize { + panic("ct must be of length CiphertextSize") + } + (*internal.PrivateKey)(sk).DecryptTo(pt, ct) +} + +// Packs pk into the given buffer. +// +// Panics if buf is not of length PublicKeySize. +func (pk *PublicKey) Pack(buf []byte) { + if len(buf) != PublicKeySize { + panic("buf must be of size PublicKeySize") + } + (*internal.PublicKey)(pk).Pack(buf) +} + +// Packs sk into the given buffer. +// +// Panics if buf is not of length PrivateKeySize. +func (sk *PrivateKey) Pack(buf []byte) { + if len(buf) != PrivateKeySize { + panic("buf must be of size PrivateKeySize") + } + (*internal.PrivateKey)(sk).Pack(buf) +} + +// Unpacks pk from the given buffer. +// +// Panics if buf is not of length PublicKeySize. +func (pk *PublicKey) Unpack(buf []byte) { + if len(buf) != PublicKeySize { + panic("buf must be of size PublicKeySize") + } + (*internal.PublicKey)(pk).Unpack(buf) +} + +// Unpacks sk from the given buffer. +// +// Panics if buf is not of length PrivateKeySize. +func (sk *PrivateKey) Unpack(buf []byte) { + if len(buf) != PrivateKeySize { + panic("buf must be of size PrivateKeySize") + } + (*internal.PrivateKey)(sk).Unpack(buf) +} + +// Returns whether the two private keys are equal. +func (sk *PrivateKey) Equal(other *PrivateKey) bool { + return (*internal.PrivateKey)(sk).Equal((*internal.PrivateKey)(other)) +} diff --git a/vendor/github.com/cloudflare/circl/pke/kyber/kyber512/internal/cpapke.go b/vendor/github.com/cloudflare/circl/pke/kyber/kyber512/internal/cpapke.go new file mode 100644 index 00000000..80ab2501 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/pke/kyber/kyber512/internal/cpapke.go @@ -0,0 +1,174 @@ +package internal + +import ( + "github.com/cloudflare/circl/internal/sha3" + "github.com/cloudflare/circl/pke/kyber/internal/common" +) + +// A Kyber.CPAPKE private key. +type PrivateKey struct { + sh Vec // NTT(s), normalized +} + +// A Kyber.CPAPKE public key. +type PublicKey struct { + rho [32]byte // ρ, the seed for the matrix A + th Vec // NTT(t), normalized + + // cached values + aT Mat // the matrix Aᵀ +} + +// Packs the private key to buf. +func (sk *PrivateKey) Pack(buf []byte) { + sk.sh.Pack(buf) +} + +// Unpacks the private key from buf. +func (sk *PrivateKey) Unpack(buf []byte) { + sk.sh.Unpack(buf) + sk.sh.Normalize() +} + +// Packs the public key to buf. +func (pk *PublicKey) Pack(buf []byte) { + pk.th.Pack(buf) + copy(buf[K*common.PolySize:], pk.rho[:]) +} + +// Unpacks the public key from buf. +func (pk *PublicKey) Unpack(buf []byte) { + pk.th.Unpack(buf) + pk.th.Normalize() + copy(pk.rho[:], buf[K*common.PolySize:]) + pk.aT.Derive(&pk.rho, true) +} + +// Derives a new Kyber.CPAPKE keypair from the given seed. +func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { + var pk PublicKey + var sk PrivateKey + + var expandedSeed [64]byte + + h := sha3.New512() + _, _ = h.Write(seed) + + // This writes hash into expandedSeed. Yes, this is idiomatic Go. + _, _ = h.Read(expandedSeed[:]) + + copy(pk.rho[:], expandedSeed[:32]) + sigma := expandedSeed[32:] // σ, the noise seed + + pk.aT.Derive(&pk.rho, false) // Expand ρ to matrix A; we'll transpose later + + var eh Vec + sk.sh.DeriveNoise(sigma, 0, Eta1) // Sample secret vector s + sk.sh.NTT() + sk.sh.Normalize() + + eh.DeriveNoise(sigma, K, Eta1) // Sample blind e + eh.NTT() + + // Next, we compute t = A s + e. + for i := 0; i < K; i++ { + // Note that coefficients of s are bounded by q and those of A + // are bounded by 4.5q and so their product is bounded by 2¹⁵q + // as required for multiplication. + PolyDotHat(&pk.th[i], &pk.aT[i], &sk.sh) + + // A and s were not in Montgomery form, so the Montgomery + // multiplications in the inner product added a factor R⁻¹ which + // we'll cancel out now. This will also ensure the coefficients of + // t are bounded in absolute value by q. + pk.th[i].ToMont() + } + + pk.th.Add(&pk.th, &eh) // bounded by 8q. + pk.th.Normalize() + pk.aT.Transpose() + + return &pk, &sk +} + +// Decrypts ciphertext ct meant for private key sk to plaintext pt. +func (sk *PrivateKey) DecryptTo(pt, ct []byte) { + var u Vec + var v, m common.Poly + + u.Decompress(ct, DU) + v.Decompress(ct[K*compressedPolySize(DU):], DV) + + // Compute m = v - + u.NTT() + PolyDotHat(&m, &sk.sh, &u) + m.BarrettReduce() + m.InvNTT() + m.Sub(&v, &m) + m.Normalize() + + // Compress polynomial m to original message + m.CompressMessageTo(pt) +} + +// Encrypts message pt for the public key to ciphertext ct using randomness +// from seed. +// +// seed has to be of length SeedSize, pt of PlaintextSize and ct of +// CiphertextSize. +func (pk *PublicKey) EncryptTo(ct, pt, seed []byte) { + var rh, e1, u Vec + var e2, v, m common.Poly + + // Sample r, e₁ and e₂ from B_η + rh.DeriveNoise(seed, 0, Eta1) + rh.NTT() + rh.BarrettReduce() + + e1.DeriveNoise(seed, K, common.Eta2) + e2.DeriveNoise(seed, 2*K, common.Eta2) + + // Next we compute u = Aᵀ r + e₁. First Aᵀ. + for i := 0; i < K; i++ { + // Note that coefficients of r are bounded by q and those of Aᵀ + // are bounded by 4.5q and so their product is bounded by 2¹⁵q + // as required for multiplication. + PolyDotHat(&u[i], &pk.aT[i], &rh) + } + + u.BarrettReduce() + + // Aᵀ and r were not in Montgomery form, so the Montgomery + // multiplications in the inner product added a factor R⁻¹ which + // the InvNTT cancels out. + u.InvNTT() + + u.Add(&u, &e1) // u = Aᵀ r + e₁ + + // Next compute v = + e₂ + Decompress_q(m, 1). + PolyDotHat(&v, &pk.th, &rh) + v.BarrettReduce() + v.InvNTT() + + m.DecompressMessage(pt) + v.Add(&v, &m) + v.Add(&v, &e2) // v = + e₂ + Decompress_q(m, 1) + + // Pack ciphertext + u.Normalize() + v.Normalize() + + u.CompressTo(ct, DU) + v.CompressTo(ct[K*compressedPolySize(DU):], DV) +} + +// Returns whether sk equals other. +func (sk *PrivateKey) Equal(other *PrivateKey) bool { + ret := int16(0) + for i := 0; i < K; i++ { + for j := 0; j < common.N; j++ { + ret |= sk.sh[i][j] ^ other.sh[i][j] + } + } + return ret == 0 +} diff --git a/vendor/github.com/cloudflare/circl/pke/kyber/kyber512/internal/mat.go b/vendor/github.com/cloudflare/circl/pke/kyber/kyber512/internal/mat.go new file mode 100644 index 00000000..9871a774 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/pke/kyber/kyber512/internal/mat.go @@ -0,0 +1,83 @@ +package internal + +import ( + "github.com/cloudflare/circl/pke/kyber/internal/common" +) + +// A k by k matrix of polynomials. +type Mat [K]Vec + +// Expands the given seed to the corresponding matrix A or its transpose Aᵀ. +func (m *Mat) Derive(seed *[32]byte, transpose bool) { + if !common.DeriveX4Available { + if transpose { + for i := 0; i < K; i++ { + for j := 0; j < K; j++ { + m[i][j].DeriveUniform(seed, uint8(i), uint8(j)) + } + } + } else { + for i := 0; i < K; i++ { + for j := 0; j < K; j++ { + m[i][j].DeriveUniform(seed, uint8(j), uint8(i)) + } + } + } + return + } + + var ps [4]*common.Poly + var xs [4]uint8 + var ys [4]uint8 + x := uint8(0) + y := uint8(0) + + for x != K { + idx := 0 + for ; idx < 4; idx++ { + ps[idx] = &m[x][y] + + if transpose { + xs[idx] = x + ys[idx] = y + } else { + xs[idx] = y + ys[idx] = x + } + + y++ + if y == K { + x++ + y = 0 + + if x == K { + if idx == 0 { + // If there is just one left, then a plain DeriveUniform + // is quicker than the X4 variant. + ps[0].DeriveUniform(seed, xs[0], ys[0]) + return + } + + for idx++; idx < 4; idx++ { + ps[idx] = nil + } + + break + } + } + } + + common.PolyDeriveUniformX4(ps, seed, xs, ys) + } +} + +// Tranposes A in place. +func (m *Mat) Transpose() { + for i := 0; i < K-1; i++ { + for j := i + 1; j < K; j++ { + t := m[i][j] + m[i][j] = m[j][i] + m[j][i] = t + } + } +} diff --git a/vendor/github.com/cloudflare/circl/pke/kyber/kyber512/internal/params.go b/vendor/github.com/cloudflare/circl/pke/kyber/kyber512/internal/params.go new file mode 100644 index 00000000..0e6df77b --- /dev/null +++ b/vendor/github.com/cloudflare/circl/pke/kyber/kyber512/internal/params.go @@ -0,0 +1,21 @@ +// Code generated from params.templ.go. DO NOT EDIT. + +package internal + +import ( + "github.com/cloudflare/circl/pke/kyber/internal/common" +) + +const ( + K = 2 + Eta1 = 3 + DU = 10 + DV = 4 + PublicKeySize = 32 + K*common.PolySize + + PrivateKeySize = K * common.PolySize + + PlaintextSize = common.PlaintextSize + SeedSize = 32 + CiphertextSize = 768 +) diff --git a/vendor/github.com/cloudflare/circl/pke/kyber/kyber512/internal/vec.go b/vendor/github.com/cloudflare/circl/pke/kyber/kyber512/internal/vec.go new file mode 100644 index 00000000..222f1ca9 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/pke/kyber/kyber512/internal/vec.go @@ -0,0 +1,123 @@ +package internal + +import ( + "github.com/cloudflare/circl/pke/kyber/internal/common" +) + +// A vector of K polynomials +type Vec [K]common.Poly + +// Samples v[i] from a centered binomial distribution with given η, +// seed and nonce+i. +// +// Essentially CBD_η(PRF(seed, nonce+i)) from the specification. +func (v *Vec) DeriveNoise(seed []byte, nonce uint8, eta int) { + for i := 0; i < K; i++ { + v[i].DeriveNoise(seed, nonce+uint8(i), eta) + } +} + +// Sets p to the inner product of a and b using "pointwise" multiplication. +// +// See MulHat() and NTT() for a description of the multiplication. +// Assumes a and b are in Montgomery form. p will be in Montgomery form, +// and its coefficients will be bounded in absolute value by 2kq. +// If a and b are not in Montgomery form, then the action is the same +// as "pointwise" multiplication followed by multiplying by R⁻¹, the inverse +// of the Montgomery factor. +func PolyDotHat(p *common.Poly, a, b *Vec) { + var t common.Poly + *p = common.Poly{} // set p to zero + for i := 0; i < K; i++ { + t.MulHat(&a[i], &b[i]) + p.Add(&t, p) + } +} + +// Almost normalizes coefficients in-place. +// +// Ensures each coefficient is in {0, …, q}. +func (v *Vec) BarrettReduce() { + for i := 0; i < K; i++ { + v[i].BarrettReduce() + } +} + +// Normalizes coefficients in-place. +// +// Ensures each coefficient is in {0, …, q-1}. +func (v *Vec) Normalize() { + for i := 0; i < K; i++ { + v[i].Normalize() + } +} + +// Applies in-place inverse NTT(). See Poly.InvNTT() for assumptions. +func (v *Vec) InvNTT() { + for i := 0; i < K; i++ { + v[i].InvNTT() + } +} + +// Applies in-place forward NTT(). See Poly.NTT() for assumptions. +func (v *Vec) NTT() { + for i := 0; i < K; i++ { + v[i].NTT() + } +} + +// Sets v to a + b. +func (v *Vec) Add(a, b *Vec) { + for i := 0; i < K; i++ { + v[i].Add(&a[i], &b[i]) + } +} + +// Packs v into buf, which must be of length K*PolySize. +func (v *Vec) Pack(buf []byte) { + for i := 0; i < K; i++ { + v[i].Pack(buf[common.PolySize*i:]) + } +} + +// Unpacks v from buf which must be of length K*PolySize. +func (v *Vec) Unpack(buf []byte) { + for i := 0; i < K; i++ { + v[i].Unpack(buf[common.PolySize*i:]) + } +} + +// Writes Compress_q(v, d) to m. +// +// Assumes v is normalized and d is in {3, 4, 5, 10, 11}. +func (v *Vec) CompressTo(m []byte, d int) { + size := compressedPolySize(d) + for i := 0; i < K; i++ { + v[i].CompressTo(m[size*i:], d) + } +} + +// Set v to Decompress_q(m, 1). +// +// Assumes d is in {3, 4, 5, 10, 11}. v will be normalized. +func (v *Vec) Decompress(m []byte, d int) { + size := compressedPolySize(d) + for i := 0; i < K; i++ { + v[i].Decompress(m[size*i:], d) + } +} + +// ⌈(256 d)/8⌉ +func compressedPolySize(d int) int { + switch d { + case 4: + return 128 + case 5: + return 160 + case 10: + return 320 + case 11: + return 352 + } + panic("unsupported d") +} diff --git a/vendor/github.com/cloudflare/circl/pke/kyber/kyber512/kyber.go b/vendor/github.com/cloudflare/circl/pke/kyber/kyber512/kyber.go new file mode 100644 index 00000000..ea924848 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/pke/kyber/kyber512/kyber.go @@ -0,0 +1,145 @@ +// Code generated from modePkg.templ.go. DO NOT EDIT. + +// kyber512 implements the IND-CPA-secure Public Key Encryption +// scheme Kyber512.CPAPKE as submitted to round 3 of the NIST PQC competition +// and described in +// +// https://pq-crystals.org/kyber/data/kyber-specification-round3.pdf +package kyber512 + +import ( + cryptoRand "crypto/rand" + "io" + + "github.com/cloudflare/circl/pke/kyber/kyber512/internal" +) + +const ( + // Size of seed for NewKeyFromSeed + KeySeedSize = internal.SeedSize + + // Size of seed for EncryptTo + EncryptionSeedSize = internal.SeedSize + + // Size of a packed PublicKey + PublicKeySize = internal.PublicKeySize + + // Size of a packed PrivateKey + PrivateKeySize = internal.PrivateKeySize + + // Size of a ciphertext + CiphertextSize = internal.CiphertextSize + + // Size of a plaintext + PlaintextSize = internal.PlaintextSize +) + +// PublicKey is the type of Kyber512.CPAPKE public key +type PublicKey internal.PublicKey + +// PrivateKey is the type of Kyber512.CPAPKE private key +type PrivateKey internal.PrivateKey + +// GenerateKey generates a public/private key pair using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { + var seed [KeySeedSize]byte + if rand == nil { + rand = cryptoRand.Reader + } + _, err := io.ReadFull(rand, seed[:]) + if err != nil { + return nil, nil, err + } + pk, sk := internal.NewKeyFromSeed(seed[:]) + return (*PublicKey)(pk), (*PrivateKey)(sk), nil +} + +// NewKeyFromSeed derives a public/private key pair using the given seed. +// +// Panics if seed is not of length KeySeedSize. +func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { + if len(seed) != KeySeedSize { + panic("seed must be of length KeySeedSize") + } + pk, sk := internal.NewKeyFromSeed(seed) + return (*PublicKey)(pk), (*PrivateKey)(sk) +} + +// EncryptTo encrypts message pt for the public key and writes the ciphertext +// to ct using randomness from seed. +// +// This function panics if the lengths of pt, seed, and ct are not +// PlaintextSize, EncryptionSeedSize, and CiphertextSize respectively. +func (pk *PublicKey) EncryptTo(ct []byte, pt []byte, seed []byte) { + if len(pt) != PlaintextSize { + panic("pt must be of length PlaintextSize") + } + if len(ct) != CiphertextSize { + panic("ct must be of length CiphertextSize") + } + if len(seed) != EncryptionSeedSize { + panic("seed must be of length EncryptionSeedSize") + } + (*internal.PublicKey)(pk).EncryptTo(ct, pt, seed) +} + +// DecryptTo decrypts message ct for the private key and writes the +// plaintext to pt. +// +// This function panics if the lengths of ct and pt are not +// CiphertextSize and PlaintextSize respectively. +func (sk *PrivateKey) DecryptTo(pt []byte, ct []byte) { + if len(pt) != PlaintextSize { + panic("pt must be of length PlaintextSize") + } + if len(ct) != CiphertextSize { + panic("ct must be of length CiphertextSize") + } + (*internal.PrivateKey)(sk).DecryptTo(pt, ct) +} + +// Packs pk into the given buffer. +// +// Panics if buf is not of length PublicKeySize. +func (pk *PublicKey) Pack(buf []byte) { + if len(buf) != PublicKeySize { + panic("buf must be of size PublicKeySize") + } + (*internal.PublicKey)(pk).Pack(buf) +} + +// Packs sk into the given buffer. +// +// Panics if buf is not of length PrivateKeySize. +func (sk *PrivateKey) Pack(buf []byte) { + if len(buf) != PrivateKeySize { + panic("buf must be of size PrivateKeySize") + } + (*internal.PrivateKey)(sk).Pack(buf) +} + +// Unpacks pk from the given buffer. +// +// Panics if buf is not of length PublicKeySize. +func (pk *PublicKey) Unpack(buf []byte) { + if len(buf) != PublicKeySize { + panic("buf must be of size PublicKeySize") + } + (*internal.PublicKey)(pk).Unpack(buf) +} + +// Unpacks sk from the given buffer. +// +// Panics if buf is not of length PrivateKeySize. +func (sk *PrivateKey) Unpack(buf []byte) { + if len(buf) != PrivateKeySize { + panic("buf must be of size PrivateKeySize") + } + (*internal.PrivateKey)(sk).Unpack(buf) +} + +// Returns whether the two private keys are equal. +func (sk *PrivateKey) Equal(other *PrivateKey) bool { + return (*internal.PrivateKey)(sk).Equal((*internal.PrivateKey)(other)) +} diff --git a/vendor/github.com/cloudflare/circl/pke/kyber/kyber768/internal/cpapke.go b/vendor/github.com/cloudflare/circl/pke/kyber/kyber768/internal/cpapke.go new file mode 100644 index 00000000..01ef88b2 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/pke/kyber/kyber768/internal/cpapke.go @@ -0,0 +1,176 @@ +// Code generated from kyber512/internal/cpapke.go by gen.go + +package internal + +import ( + "github.com/cloudflare/circl/internal/sha3" + "github.com/cloudflare/circl/pke/kyber/internal/common" +) + +// A Kyber.CPAPKE private key. +type PrivateKey struct { + sh Vec // NTT(s), normalized +} + +// A Kyber.CPAPKE public key. +type PublicKey struct { + rho [32]byte // ρ, the seed for the matrix A + th Vec // NTT(t), normalized + + // cached values + aT Mat // the matrix Aᵀ +} + +// Packs the private key to buf. +func (sk *PrivateKey) Pack(buf []byte) { + sk.sh.Pack(buf) +} + +// Unpacks the private key from buf. +func (sk *PrivateKey) Unpack(buf []byte) { + sk.sh.Unpack(buf) + sk.sh.Normalize() +} + +// Packs the public key to buf. +func (pk *PublicKey) Pack(buf []byte) { + pk.th.Pack(buf) + copy(buf[K*common.PolySize:], pk.rho[:]) +} + +// Unpacks the public key from buf. +func (pk *PublicKey) Unpack(buf []byte) { + pk.th.Unpack(buf) + pk.th.Normalize() + copy(pk.rho[:], buf[K*common.PolySize:]) + pk.aT.Derive(&pk.rho, true) +} + +// Derives a new Kyber.CPAPKE keypair from the given seed. +func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { + var pk PublicKey + var sk PrivateKey + + var expandedSeed [64]byte + + h := sha3.New512() + _, _ = h.Write(seed) + + // This writes hash into expandedSeed. Yes, this is idiomatic Go. + _, _ = h.Read(expandedSeed[:]) + + copy(pk.rho[:], expandedSeed[:32]) + sigma := expandedSeed[32:] // σ, the noise seed + + pk.aT.Derive(&pk.rho, false) // Expand ρ to matrix A; we'll transpose later + + var eh Vec + sk.sh.DeriveNoise(sigma, 0, Eta1) // Sample secret vector s + sk.sh.NTT() + sk.sh.Normalize() + + eh.DeriveNoise(sigma, K, Eta1) // Sample blind e + eh.NTT() + + // Next, we compute t = A s + e. + for i := 0; i < K; i++ { + // Note that coefficients of s are bounded by q and those of A + // are bounded by 4.5q and so their product is bounded by 2¹⁵q + // as required for multiplication. + PolyDotHat(&pk.th[i], &pk.aT[i], &sk.sh) + + // A and s were not in Montgomery form, so the Montgomery + // multiplications in the inner product added a factor R⁻¹ which + // we'll cancel out now. This will also ensure the coefficients of + // t are bounded in absolute value by q. + pk.th[i].ToMont() + } + + pk.th.Add(&pk.th, &eh) // bounded by 8q. + pk.th.Normalize() + pk.aT.Transpose() + + return &pk, &sk +} + +// Decrypts ciphertext ct meant for private key sk to plaintext pt. +func (sk *PrivateKey) DecryptTo(pt, ct []byte) { + var u Vec + var v, m common.Poly + + u.Decompress(ct, DU) + v.Decompress(ct[K*compressedPolySize(DU):], DV) + + // Compute m = v - + u.NTT() + PolyDotHat(&m, &sk.sh, &u) + m.BarrettReduce() + m.InvNTT() + m.Sub(&v, &m) + m.Normalize() + + // Compress polynomial m to original message + m.CompressMessageTo(pt) +} + +// Encrypts message pt for the public key to ciphertext ct using randomness +// from seed. +// +// seed has to be of length SeedSize, pt of PlaintextSize and ct of +// CiphertextSize. +func (pk *PublicKey) EncryptTo(ct, pt, seed []byte) { + var rh, e1, u Vec + var e2, v, m common.Poly + + // Sample r, e₁ and e₂ from B_η + rh.DeriveNoise(seed, 0, Eta1) + rh.NTT() + rh.BarrettReduce() + + e1.DeriveNoise(seed, K, common.Eta2) + e2.DeriveNoise(seed, 2*K, common.Eta2) + + // Next we compute u = Aᵀ r + e₁. First Aᵀ. + for i := 0; i < K; i++ { + // Note that coefficients of r are bounded by q and those of Aᵀ + // are bounded by 4.5q and so their product is bounded by 2¹⁵q + // as required for multiplication. + PolyDotHat(&u[i], &pk.aT[i], &rh) + } + + u.BarrettReduce() + + // Aᵀ and r were not in Montgomery form, so the Montgomery + // multiplications in the inner product added a factor R⁻¹ which + // the InvNTT cancels out. + u.InvNTT() + + u.Add(&u, &e1) // u = Aᵀ r + e₁ + + // Next compute v = + e₂ + Decompress_q(m, 1). + PolyDotHat(&v, &pk.th, &rh) + v.BarrettReduce() + v.InvNTT() + + m.DecompressMessage(pt) + v.Add(&v, &m) + v.Add(&v, &e2) // v = + e₂ + Decompress_q(m, 1) + + // Pack ciphertext + u.Normalize() + v.Normalize() + + u.CompressTo(ct, DU) + v.CompressTo(ct[K*compressedPolySize(DU):], DV) +} + +// Returns whether sk equals other. +func (sk *PrivateKey) Equal(other *PrivateKey) bool { + ret := int16(0) + for i := 0; i < K; i++ { + for j := 0; j < common.N; j++ { + ret |= sk.sh[i][j] ^ other.sh[i][j] + } + } + return ret == 0 +} diff --git a/vendor/github.com/cloudflare/circl/pke/kyber/kyber768/internal/mat.go b/vendor/github.com/cloudflare/circl/pke/kyber/kyber768/internal/mat.go new file mode 100644 index 00000000..e8a35aff --- /dev/null +++ b/vendor/github.com/cloudflare/circl/pke/kyber/kyber768/internal/mat.go @@ -0,0 +1,85 @@ +// Code generated from kyber512/internal/mat.go by gen.go + +package internal + +import ( + "github.com/cloudflare/circl/pke/kyber/internal/common" +) + +// A k by k matrix of polynomials. +type Mat [K]Vec + +// Expands the given seed to the corresponding matrix A or its transpose Aᵀ. +func (m *Mat) Derive(seed *[32]byte, transpose bool) { + if !common.DeriveX4Available { + if transpose { + for i := 0; i < K; i++ { + for j := 0; j < K; j++ { + m[i][j].DeriveUniform(seed, uint8(i), uint8(j)) + } + } + } else { + for i := 0; i < K; i++ { + for j := 0; j < K; j++ { + m[i][j].DeriveUniform(seed, uint8(j), uint8(i)) + } + } + } + return + } + + var ps [4]*common.Poly + var xs [4]uint8 + var ys [4]uint8 + x := uint8(0) + y := uint8(0) + + for x != K { + idx := 0 + for ; idx < 4; idx++ { + ps[idx] = &m[x][y] + + if transpose { + xs[idx] = x + ys[idx] = y + } else { + xs[idx] = y + ys[idx] = x + } + + y++ + if y == K { + x++ + y = 0 + + if x == K { + if idx == 0 { + // If there is just one left, then a plain DeriveUniform + // is quicker than the X4 variant. + ps[0].DeriveUniform(seed, xs[0], ys[0]) + return + } + + for idx++; idx < 4; idx++ { + ps[idx] = nil + } + + break + } + } + } + + common.PolyDeriveUniformX4(ps, seed, xs, ys) + } +} + +// Tranposes A in place. +func (m *Mat) Transpose() { + for i := 0; i < K-1; i++ { + for j := i + 1; j < K; j++ { + t := m[i][j] + m[i][j] = m[j][i] + m[j][i] = t + } + } +} diff --git a/vendor/github.com/cloudflare/circl/pke/kyber/kyber768/internal/params.go b/vendor/github.com/cloudflare/circl/pke/kyber/kyber768/internal/params.go new file mode 100644 index 00000000..27cdb1ab --- /dev/null +++ b/vendor/github.com/cloudflare/circl/pke/kyber/kyber768/internal/params.go @@ -0,0 +1,21 @@ +// Code generated from params.templ.go. DO NOT EDIT. + +package internal + +import ( + "github.com/cloudflare/circl/pke/kyber/internal/common" +) + +const ( + K = 3 + Eta1 = 2 + DU = 10 + DV = 4 + PublicKeySize = 32 + K*common.PolySize + + PrivateKeySize = K * common.PolySize + + PlaintextSize = common.PlaintextSize + SeedSize = 32 + CiphertextSize = 1088 +) diff --git a/vendor/github.com/cloudflare/circl/pke/kyber/kyber768/internal/vec.go b/vendor/github.com/cloudflare/circl/pke/kyber/kyber768/internal/vec.go new file mode 100644 index 00000000..6681895a --- /dev/null +++ b/vendor/github.com/cloudflare/circl/pke/kyber/kyber768/internal/vec.go @@ -0,0 +1,125 @@ +// Code generated from kyber512/internal/vec.go by gen.go + +package internal + +import ( + "github.com/cloudflare/circl/pke/kyber/internal/common" +) + +// A vector of K polynomials +type Vec [K]common.Poly + +// Samples v[i] from a centered binomial distribution with given η, +// seed and nonce+i. +// +// Essentially CBD_η(PRF(seed, nonce+i)) from the specification. +func (v *Vec) DeriveNoise(seed []byte, nonce uint8, eta int) { + for i := 0; i < K; i++ { + v[i].DeriveNoise(seed, nonce+uint8(i), eta) + } +} + +// Sets p to the inner product of a and b using "pointwise" multiplication. +// +// See MulHat() and NTT() for a description of the multiplication. +// Assumes a and b are in Montgomery form. p will be in Montgomery form, +// and its coefficients will be bounded in absolute value by 2kq. +// If a and b are not in Montgomery form, then the action is the same +// as "pointwise" multiplication followed by multiplying by R⁻¹, the inverse +// of the Montgomery factor. +func PolyDotHat(p *common.Poly, a, b *Vec) { + var t common.Poly + *p = common.Poly{} // set p to zero + for i := 0; i < K; i++ { + t.MulHat(&a[i], &b[i]) + p.Add(&t, p) + } +} + +// Almost normalizes coefficients in-place. +// +// Ensures each coefficient is in {0, …, q}. +func (v *Vec) BarrettReduce() { + for i := 0; i < K; i++ { + v[i].BarrettReduce() + } +} + +// Normalizes coefficients in-place. +// +// Ensures each coefficient is in {0, …, q-1}. +func (v *Vec) Normalize() { + for i := 0; i < K; i++ { + v[i].Normalize() + } +} + +// Applies in-place inverse NTT(). See Poly.InvNTT() for assumptions. +func (v *Vec) InvNTT() { + for i := 0; i < K; i++ { + v[i].InvNTT() + } +} + +// Applies in-place forward NTT(). See Poly.NTT() for assumptions. +func (v *Vec) NTT() { + for i := 0; i < K; i++ { + v[i].NTT() + } +} + +// Sets v to a + b. +func (v *Vec) Add(a, b *Vec) { + for i := 0; i < K; i++ { + v[i].Add(&a[i], &b[i]) + } +} + +// Packs v into buf, which must be of length K*PolySize. +func (v *Vec) Pack(buf []byte) { + for i := 0; i < K; i++ { + v[i].Pack(buf[common.PolySize*i:]) + } +} + +// Unpacks v from buf which must be of length K*PolySize. +func (v *Vec) Unpack(buf []byte) { + for i := 0; i < K; i++ { + v[i].Unpack(buf[common.PolySize*i:]) + } +} + +// Writes Compress_q(v, d) to m. +// +// Assumes v is normalized and d is in {3, 4, 5, 10, 11}. +func (v *Vec) CompressTo(m []byte, d int) { + size := compressedPolySize(d) + for i := 0; i < K; i++ { + v[i].CompressTo(m[size*i:], d) + } +} + +// Set v to Decompress_q(m, 1). +// +// Assumes d is in {3, 4, 5, 10, 11}. v will be normalized. +func (v *Vec) Decompress(m []byte, d int) { + size := compressedPolySize(d) + for i := 0; i < K; i++ { + v[i].Decompress(m[size*i:], d) + } +} + +// ⌈(256 d)/8⌉ +func compressedPolySize(d int) int { + switch d { + case 4: + return 128 + case 5: + return 160 + case 10: + return 320 + case 11: + return 352 + } + panic("unsupported d") +} diff --git a/vendor/github.com/cloudflare/circl/pke/kyber/kyber768/kyber.go b/vendor/github.com/cloudflare/circl/pke/kyber/kyber768/kyber.go new file mode 100644 index 00000000..4cecbb1b --- /dev/null +++ b/vendor/github.com/cloudflare/circl/pke/kyber/kyber768/kyber.go @@ -0,0 +1,145 @@ +// Code generated from modePkg.templ.go. DO NOT EDIT. + +// kyber768 implements the IND-CPA-secure Public Key Encryption +// scheme Kyber768.CPAPKE as submitted to round 3 of the NIST PQC competition +// and described in +// +// https://pq-crystals.org/kyber/data/kyber-specification-round3.pdf +package kyber768 + +import ( + cryptoRand "crypto/rand" + "io" + + "github.com/cloudflare/circl/pke/kyber/kyber768/internal" +) + +const ( + // Size of seed for NewKeyFromSeed + KeySeedSize = internal.SeedSize + + // Size of seed for EncryptTo + EncryptionSeedSize = internal.SeedSize + + // Size of a packed PublicKey + PublicKeySize = internal.PublicKeySize + + // Size of a packed PrivateKey + PrivateKeySize = internal.PrivateKeySize + + // Size of a ciphertext + CiphertextSize = internal.CiphertextSize + + // Size of a plaintext + PlaintextSize = internal.PlaintextSize +) + +// PublicKey is the type of Kyber768.CPAPKE public key +type PublicKey internal.PublicKey + +// PrivateKey is the type of Kyber768.CPAPKE private key +type PrivateKey internal.PrivateKey + +// GenerateKey generates a public/private key pair using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { + var seed [KeySeedSize]byte + if rand == nil { + rand = cryptoRand.Reader + } + _, err := io.ReadFull(rand, seed[:]) + if err != nil { + return nil, nil, err + } + pk, sk := internal.NewKeyFromSeed(seed[:]) + return (*PublicKey)(pk), (*PrivateKey)(sk), nil +} + +// NewKeyFromSeed derives a public/private key pair using the given seed. +// +// Panics if seed is not of length KeySeedSize. +func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { + if len(seed) != KeySeedSize { + panic("seed must be of length KeySeedSize") + } + pk, sk := internal.NewKeyFromSeed(seed) + return (*PublicKey)(pk), (*PrivateKey)(sk) +} + +// EncryptTo encrypts message pt for the public key and writes the ciphertext +// to ct using randomness from seed. +// +// This function panics if the lengths of pt, seed, and ct are not +// PlaintextSize, EncryptionSeedSize, and CiphertextSize respectively. +func (pk *PublicKey) EncryptTo(ct []byte, pt []byte, seed []byte) { + if len(pt) != PlaintextSize { + panic("pt must be of length PlaintextSize") + } + if len(ct) != CiphertextSize { + panic("ct must be of length CiphertextSize") + } + if len(seed) != EncryptionSeedSize { + panic("seed must be of length EncryptionSeedSize") + } + (*internal.PublicKey)(pk).EncryptTo(ct, pt, seed) +} + +// DecryptTo decrypts message ct for the private key and writes the +// plaintext to pt. +// +// This function panics if the lengths of ct and pt are not +// CiphertextSize and PlaintextSize respectively. +func (sk *PrivateKey) DecryptTo(pt []byte, ct []byte) { + if len(pt) != PlaintextSize { + panic("pt must be of length PlaintextSize") + } + if len(ct) != CiphertextSize { + panic("ct must be of length CiphertextSize") + } + (*internal.PrivateKey)(sk).DecryptTo(pt, ct) +} + +// Packs pk into the given buffer. +// +// Panics if buf is not of length PublicKeySize. +func (pk *PublicKey) Pack(buf []byte) { + if len(buf) != PublicKeySize { + panic("buf must be of size PublicKeySize") + } + (*internal.PublicKey)(pk).Pack(buf) +} + +// Packs sk into the given buffer. +// +// Panics if buf is not of length PrivateKeySize. +func (sk *PrivateKey) Pack(buf []byte) { + if len(buf) != PrivateKeySize { + panic("buf must be of size PrivateKeySize") + } + (*internal.PrivateKey)(sk).Pack(buf) +} + +// Unpacks pk from the given buffer. +// +// Panics if buf is not of length PublicKeySize. +func (pk *PublicKey) Unpack(buf []byte) { + if len(buf) != PublicKeySize { + panic("buf must be of size PublicKeySize") + } + (*internal.PublicKey)(pk).Unpack(buf) +} + +// Unpacks sk from the given buffer. +// +// Panics if buf is not of length PrivateKeySize. +func (sk *PrivateKey) Unpack(buf []byte) { + if len(buf) != PrivateKeySize { + panic("buf must be of size PrivateKeySize") + } + (*internal.PrivateKey)(sk).Unpack(buf) +} + +// Returns whether the two private keys are equal. +func (sk *PrivateKey) Equal(other *PrivateKey) bool { + return (*internal.PrivateKey)(sk).Equal((*internal.PrivateKey)(other)) +} diff --git a/vendor/github.com/cloudflare/circl/simd/keccakf1600/f1600x.go b/vendor/github.com/cloudflare/circl/simd/keccakf1600/f1600x.go new file mode 100644 index 00000000..7ce0c2ef --- /dev/null +++ b/vendor/github.com/cloudflare/circl/simd/keccakf1600/f1600x.go @@ -0,0 +1,149 @@ +// Package keccakf1600 provides a two and four-way Keccak-f[1600] permutation in parallel. +// +// Keccak-f[1600] is the permutation underlying several algorithms such as +// Keccak, SHA3 and SHAKE. Running two or four permutations in parallel is +// useful in some scenarios like in hash-based signatures. +// +// # Limitations +// +// Note that not all the architectures support SIMD instructions. This package +// uses AVX2 instructions that are available in some AMD64 architectures +// and NEON instructions that are available in some ARM64 architectures. +// +// For those systems not supporting these, the package still provides the +// expected functionality by means of a generic and slow implementation. +// The recommendation is to beforehand verify IsEnabledX4() and IsEnabledX2() +// to determine if the current system supports the SIMD implementation. +package keccakf1600 + +import ( + "unsafe" + + "github.com/cloudflare/circl/internal/sha3" + "golang.org/x/sys/cpu" +) + +// StateX4 contains state for the four-way permutation including the four +// interleaved [25]uint64 buffers. Call Initialize() before use to initialize +// and get a pointer to the interleaved buffer. +type StateX4 struct { + // Go guarantees a to be aligned on 8 bytes, whereas we need it to be + // aligned on 32 bytes for bet performance. Thus we leave some headroom + // to be able to move the start of the state. + + // 4 x 25 uint64s for the interleaved states and three uint64s headroom + // to fix alignment. + a [103]uint64 + + // Offset into a that is 32 byte aligned. + offset int +} + +// StateX2 contains state for the two-way permutation including the two +// interleaved [25]uint64 buffers. Call Initialize() before use to initialize +// and get a pointer to the interleaved buffer. +type StateX2 struct { + // Go guarantees a to be aligned on 8 bytes, whereas we need it to be + // aligned on 32 bytes for bet performance. Thus we leave some headroom + // to be able to move the start of the state. + + // 2 x 25 uint64s for the interleaved states and three uint64s headroom + // to fix alignment. + a [53]uint64 + + // Offset into a that is 32 byte aligned. + offset int +} + +// IsEnabledX4 returns true if the architecture supports a four-way SIMD +// implementation provided in this package. +func IsEnabledX4() bool { return cpu.X86.HasAVX2 } + +// IsEnabledX2 returns true if the architecture supports a two-way SIMD +// implementation provided in this package. +func IsEnabledX2() bool { + // After Go 1.16 the flag cpu.ARM64.HasSHA3 is no longer exposed. + return false +} + +// Initialize the state and returns the buffer on which the four permutations +// will act: a uint64 slice of length 100. The first permutation will act +// on {a[0], a[4], ..., a[96]}, the second on {a[1], a[5], ..., a[97]}, etc. +func (s *StateX4) Initialize() []uint64 { + rp := unsafe.Pointer(&s.a[0]) + + // uint64s are always aligned by a multiple of 8. Compute the remainder + // of the address modulo 32 divided by 8. + rem := (int(uintptr(rp)&31) >> 3) + + if rem != 0 { + s.offset = 4 - rem + } + + // The slice we return will be aligned on 32 byte boundary. + return s.a[s.offset : s.offset+100] +} + +// Initialize the state and returns the buffer on which the two permutations +// will act: a uint64 slice of length 50. The first permutation will act +// on {a[0], a[2], ..., a[48]} and the second on {a[1], a[3], ..., a[49]}. +func (s *StateX2) Initialize() []uint64 { + rp := unsafe.Pointer(&s.a[0]) + + // uint64s are always aligned by a multiple of 8. Compute the remainder + // of the address modulo 32 divided by 8. + rem := (int(uintptr(rp)&31) >> 3) + + if rem != 0 { + s.offset = 4 - rem + } + + // The slice we return will be aligned on 32 byte boundary. + return s.a[s.offset : s.offset+50] +} + +// Permute performs the four parallel Keccak-f[1600]s interleaved on the slice +// returned from Initialize(). +func (s *StateX4) Permute() { + if IsEnabledX4() { + permuteSIMDx4(s.a[s.offset:]) + } else { + permuteScalarX4(s.a[s.offset:]) // A slower generic implementation. + } +} + +// Permute performs the two parallel Keccak-f[1600]s interleaved on the slice +// returned from Initialize(). +func (s *StateX2) Permute() { + if IsEnabledX2() { + permuteSIMDx2(s.a[s.offset:]) + } else { + permuteScalarX2(s.a[s.offset:]) // A slower generic implementation. + } +} + +func permuteScalarX4(a []uint64) { + var buf [25]uint64 + for i := 0; i < 4; i++ { + for j := 0; j < 25; j++ { + buf[j] = a[4*j+i] + } + sha3.KeccakF1600(&buf) + for j := 0; j < 25; j++ { + a[4*j+i] = buf[j] + } + } +} + +func permuteScalarX2(a []uint64) { + var buf [25]uint64 + for i := 0; i < 2; i++ { + for j := 0; j < 25; j++ { + buf[j] = a[2*j+i] + } + sha3.KeccakF1600(&buf) + for j := 0; j < 25; j++ { + a[2*j+i] = buf[j] + } + } +} diff --git a/vendor/github.com/cloudflare/circl/simd/keccakf1600/f1600x2_arm64.go b/vendor/github.com/cloudflare/circl/simd/keccakf1600/f1600x2_arm64.go new file mode 100644 index 00000000..75461dd7 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/simd/keccakf1600/f1600x2_arm64.go @@ -0,0 +1,13 @@ +//go:build arm64 && go1.16 +// +build arm64,go1.16 + +package keccakf1600 + +import "github.com/cloudflare/circl/internal/sha3" + +func permuteSIMDx2(state []uint64) { f1600x2ARM(&state[0], &sha3.RC) } + +func permuteSIMDx4(state []uint64) { permuteScalarX4(state) } + +//go:noescape +func f1600x2ARM(state *uint64, rc *[24]uint64) diff --git a/vendor/github.com/cloudflare/circl/simd/keccakf1600/f1600x2_arm64.s b/vendor/github.com/cloudflare/circl/simd/keccakf1600/f1600x2_arm64.s new file mode 100644 index 00000000..1e8547f9 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/simd/keccakf1600/f1600x2_arm64.s @@ -0,0 +1,130 @@ +// +build arm64,go1.16 + +// Taken from https://github.com/bwesterb/armed-keccak + +#include "textflag.h" + +// func f1600x2ARM(state *uint64, rc *[24]uint64) +TEXT ·f1600x2ARM(SB), NOSPLIT, $0-16 + MOVD state+0(FP), R0 + MOVD rc+8(FP), R1 + MOVD R0, R2 + MOVD $24, R3 + + VLD1.P 64(R0), [ V0.B16, V1.B16, V2.B16, V3.B16] + VLD1.P 64(R0), [ V4.B16, V5.B16, V6.B16, V7.B16] + VLD1.P 64(R0), [ V8.B16, V9.B16, V10.B16, V11.B16] + VLD1.P 64(R0), [V12.B16, V13.B16, V14.B16, V15.B16] + VLD1.P 64(R0), [V16.B16, V17.B16, V18.B16, V19.B16] + VLD1.P 64(R0), [V20.B16, V21.B16, V22.B16, V23.B16] + VLD1.P (R0), [V24.B16] + +loop: + // Execute theta but without xorring into the state yet. + VEOR3 V10.B16, V5.B16, V0.B16, V25.B16 + VEOR3 V11.B16, V6.B16, V1.B16, V26.B16 + VEOR3 V12.B16, V7.B16, V2.B16, V27.B16 + VEOR3 V13.B16, V8.B16, V3.B16, V28.B16 + VEOR3 V14.B16, V9.B16, V4.B16, V29.B16 + + VEOR3 V20.B16, V15.B16, V25.B16, V25.B16 + VEOR3 V21.B16, V16.B16, V26.B16, V26.B16 + VEOR3 V22.B16, V17.B16, V27.B16, V27.B16 + VEOR3 V23.B16, V18.B16, V28.B16, V28.B16 + VEOR3 V24.B16, V19.B16, V29.B16, V29.B16 + + // Xor parities from step theta into the state at the same time as + // exeuting rho and pi. + VRAX1 V26.D2, V29.D2, V30.D2 + VRAX1 V29.D2, V27.D2, V29.D2 + VRAX1 V27.D2, V25.D2, V27.D2 + VRAX1 V25.D2, V28.D2, V25.D2 + VRAX1 V28.D2, V26.D2, V28.D2 + + VEOR V30.B16, V0.B16, V0.B16 + VMOV V1.B16, V31.B16 + + VXAR $20, V27.D2, V6.D2, V1.D2 + VXAR $44, V25.D2, V9.D2, V6.D2 + VXAR $3 , V28.D2, V22.D2, V9.D2 + VXAR $25, V25.D2, V14.D2, V22.D2 + VXAR $46, V30.D2, V20.D2, V14.D2 + VXAR $2 , V28.D2, V2.D2, V20.D2 + VXAR $21, V28.D2, V12.D2, V2.D2 + VXAR $39, V29.D2, V13.D2, V12.D2 + VXAR $56, V25.D2, V19.D2, V13.D2 + VXAR $8 , V29.D2, V23.D2, V19.D2 + VXAR $23, V30.D2, V15.D2, V23.D2 + VXAR $37, V25.D2, V4.D2, V15.D2 + VXAR $50, V25.D2, V24.D2, V4.D2 + VXAR $62, V27.D2, V21.D2, V24.D2 + VXAR $9 , V29.D2, V8.D2, V21.D2 + VXAR $19, V27.D2, V16.D2, V8.D2 + VXAR $28, V30.D2, V5.D2, V16.D2 + VXAR $36, V29.D2, V3.D2, V5.D2 + VXAR $43, V29.D2, V18.D2, V3.D2 + VXAR $49, V28.D2, V17.D2, V18.D2 + VXAR $54, V27.D2, V11.D2, V17.D2 + VXAR $58, V28.D2, V7.D2, V11.D2 + VXAR $61, V30.D2, V10.D2, V7.D2 + VXAR $63, V27.D2, V31.D2, V10.D2 + + // Chi + VBCAX V1.B16, V2.B16, V0.B16, V25.B16 + VBCAX V2.B16, V3.B16, V1.B16, V26.B16 + VBCAX V3.B16, V4.B16, V2.B16, V2.B16 + VBCAX V4.B16, V0.B16, V3.B16, V3.B16 + VBCAX V0.B16, V1.B16, V4.B16, V4.B16 + VMOV V25.B16, V0.B16 + VMOV V26.B16, V1.B16 + + VBCAX V6.B16, V7.B16, V5.B16, V25.B16 + VBCAX V7.B16, V8.B16, V6.B16, V26.B16 + VBCAX V8.B16, V9.B16, V7.B16, V7.B16 + VBCAX V9.B16, V5.B16, V8.B16, V8.B16 + VBCAX V5.B16, V6.B16, V9.B16, V9.B16 + VMOV V25.B16, V5.B16 + VMOV V26.B16, V6.B16 + + VBCAX V11.B16, V12.B16, V10.B16, V25.B16 + VBCAX V12.B16, V13.B16, V11.B16, V26.B16 + VBCAX V13.B16, V14.B16, V12.B16, V12.B16 + VBCAX V14.B16, V10.B16, V13.B16, V13.B16 + VBCAX V10.B16, V11.B16, V14.B16, V14.B16 + VMOV V25.B16, V10.B16 + VMOV V26.B16, V11.B16 + + VBCAX V16.B16, V17.B16, V15.B16, V25.B16 + VBCAX V17.B16, V18.B16, V16.B16, V26.B16 + VBCAX V18.B16, V19.B16, V17.B16, V17.B16 + VBCAX V19.B16, V15.B16, V18.B16, V18.B16 + VBCAX V15.B16, V16.B16, V19.B16, V19.B16 + VMOV V25.B16, V15.B16 + VMOV V26.B16, V16.B16 + + VBCAX V21.B16, V22.B16, V20.B16, V25.B16 + VBCAX V22.B16, V23.B16, V21.B16, V26.B16 + VBCAX V23.B16, V24.B16, V22.B16, V22.B16 + VBCAX V24.B16, V20.B16, V23.B16, V23.B16 + VBCAX V20.B16, V21.B16, V24.B16, V24.B16 + VMOV V25.B16, V20.B16 + VMOV V26.B16, V21.B16 + + // Iota + VLD1R.P 8(R1), [V25.D2] + VEOR V25.B16, V0.B16, V0.B16 + + SUBS $1, R3, R3 + CBNZ R3, loop + + MOVD R2, R0 + + VST1.P [ V0.B16, V1.B16, V2.B16, V3.B16], 64(R0) + VST1.P [ V4.B16, V5.B16, V6.B16, V7.B16], 64(R0) + VST1.P [ V8.B16, V9.B16, V10.B16, V11.B16], 64(R0) + VST1.P [V12.B16, V13.B16, V14.B16, V15.B16], 64(R0) + VST1.P [V16.B16, V17.B16, V18.B16, V19.B16], 64(R0) + VST1.P [V20.B16, V21.B16, V22.B16, V23.B16], 64(R0) + VST1.P [V24.B16], (R0) + + RET diff --git a/vendor/github.com/cloudflare/circl/simd/keccakf1600/f1600x4_amd64.go b/vendor/github.com/cloudflare/circl/simd/keccakf1600/f1600x4_amd64.go new file mode 100644 index 00000000..ac5c658d --- /dev/null +++ b/vendor/github.com/cloudflare/circl/simd/keccakf1600/f1600x4_amd64.go @@ -0,0 +1,7 @@ +package keccakf1600 + +import "github.com/cloudflare/circl/internal/sha3" + +func permuteSIMDx4(state []uint64) { f1600x4AVX2(&state[0], &sha3.RC) } + +func permuteSIMDx2(state []uint64) { permuteScalarX2(state) } diff --git a/vendor/github.com/cloudflare/circl/simd/keccakf1600/f1600x4_amd64.s b/vendor/github.com/cloudflare/circl/simd/keccakf1600/f1600x4_amd64.s new file mode 100644 index 00000000..194981f1 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/simd/keccakf1600/f1600x4_amd64.s @@ -0,0 +1,894 @@ +// Code generated by command: go run src.go -out ../../f1600x4_amd64.s -stubs ../../f1600x4stubs_amd64.go -pkg keccakf1600. DO NOT EDIT. + +// +build amd64 + +#include "textflag.h" + +// func f1600x4AVX2(state *uint64, rc *[24]uint64) +// Requires: AVX, AVX2 +TEXT ·f1600x4AVX2(SB), NOSPLIT, $0-16 + MOVQ state+0(FP), AX + MOVQ rc+8(FP), CX + MOVQ $0x0000000000000006, DX + +loop: + VMOVDQA (AX), Y0 + VMOVDQA 32(AX), Y1 + VMOVDQA 64(AX), Y2 + VMOVDQA 96(AX), Y3 + VMOVDQA 128(AX), Y4 + VPXOR 160(AX), Y0, Y0 + VPXOR 192(AX), Y1, Y1 + VPXOR 224(AX), Y2, Y2 + VPXOR 256(AX), Y3, Y3 + VPXOR 288(AX), Y4, Y4 + VPXOR 320(AX), Y0, Y0 + VPXOR 352(AX), Y1, Y1 + VPXOR 384(AX), Y2, Y2 + VPXOR 416(AX), Y3, Y3 + VPXOR 448(AX), Y4, Y4 + VPXOR 480(AX), Y0, Y0 + VPXOR 512(AX), Y1, Y1 + VPXOR 544(AX), Y2, Y2 + VPXOR 576(AX), Y3, Y3 + VPXOR 608(AX), Y4, Y4 + VPXOR 640(AX), Y0, Y0 + VPXOR 672(AX), Y1, Y1 + VPXOR 704(AX), Y2, Y2 + VPXOR 736(AX), Y3, Y3 + VPXOR 768(AX), Y4, Y4 + VPSLLQ $0x01, Y1, Y5 + VPSLLQ $0x01, Y2, Y6 + VPSLLQ $0x01, Y3, Y7 + VPSLLQ $0x01, Y4, Y8 + VPSLLQ $0x01, Y0, Y9 + VPSRLQ $0x3f, Y1, Y10 + VPSRLQ $0x3f, Y2, Y11 + VPSRLQ $0x3f, Y3, Y12 + VPSRLQ $0x3f, Y4, Y13 + VPSRLQ $0x3f, Y0, Y14 + VPOR Y5, Y10, Y10 + VPOR Y6, Y11, Y11 + VPOR Y7, Y12, Y12 + VPOR Y8, Y13, Y13 + VPOR Y9, Y14, Y14 + VPXOR Y10, Y4, Y10 + VPXOR Y11, Y0, Y11 + VPXOR Y12, Y1, Y12 + VPXOR Y13, Y2, Y13 + VPXOR Y14, Y3, Y14 + VPXOR (AX), Y10, Y0 + VPXOR 192(AX), Y11, Y1 + VPXOR 384(AX), Y12, Y2 + VPXOR 576(AX), Y13, Y3 + VPXOR 768(AX), Y14, Y4 + VPSLLQ $0x2c, Y1, Y6 + VPSLLQ $0x2b, Y2, Y7 + VPSLLQ $0x15, Y3, Y8 + VPSLLQ $0x0e, Y4, Y9 + VPSRLQ $0x14, Y1, Y1 + VPSRLQ $0x15, Y2, Y2 + VPSRLQ $0x2b, Y3, Y3 + VPSRLQ $0x32, Y4, Y4 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VPBROADCASTQ (CX), Y0 + VPXOR Y0, Y5, Y5 + VMOVDQA Y5, (AX) + VMOVDQA Y6, 192(AX) + VMOVDQA Y7, 384(AX) + VMOVDQA Y8, 576(AX) + VMOVDQA Y9, 768(AX) + VPXOR 96(AX), Y13, Y0 + VPXOR 288(AX), Y14, Y1 + VPXOR 320(AX), Y10, Y2 + VPXOR 512(AX), Y11, Y3 + VPXOR 704(AX), Y12, Y4 + VPSLLQ $0x1c, Y0, Y5 + VPSLLQ $0x14, Y1, Y6 + VPSLLQ $0x03, Y2, Y7 + VPSLLQ $0x2d, Y3, Y8 + VPSLLQ $0x3d, Y4, Y9 + VPSRLQ $0x24, Y0, Y0 + VPSRLQ $0x2c, Y1, Y1 + VPSRLQ $0x3d, Y2, Y2 + VPSRLQ $0x13, Y3, Y3 + VPSRLQ $0x03, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 320(AX) + VMOVDQA Y6, 512(AX) + VMOVDQA Y7, 704(AX) + VMOVDQA Y8, 96(AX) + VMOVDQA Y9, 288(AX) + VPXOR 32(AX), Y11, Y0 + VPXOR 224(AX), Y12, Y1 + VPXOR 416(AX), Y13, Y2 + VPXOR 608(AX), Y14, Y3 + VPXOR 640(AX), Y10, Y4 + VPSLLQ $0x01, Y0, Y5 + VPSLLQ $0x06, Y1, Y6 + VPSLLQ $0x19, Y2, Y7 + VPSLLQ $0x08, Y3, Y8 + VPSLLQ $0x12, Y4, Y9 + VPSRLQ $0x3f, Y0, Y0 + VPSRLQ $0x3a, Y1, Y1 + VPSRLQ $0x27, Y2, Y2 + VPSRLQ $0x38, Y3, Y3 + VPSRLQ $0x2e, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 640(AX) + VMOVDQA Y6, 32(AX) + VMOVDQA Y7, 224(AX) + VMOVDQA Y8, 416(AX) + VMOVDQA Y9, 608(AX) + VPXOR 128(AX), Y14, Y0 + VPXOR 160(AX), Y10, Y1 + VPXOR 352(AX), Y11, Y2 + VPXOR 544(AX), Y12, Y3 + VPXOR 736(AX), Y13, Y4 + VPSLLQ $0x1b, Y0, Y5 + VPSLLQ $0x24, Y1, Y6 + VPSLLQ $0x0a, Y2, Y7 + VPSLLQ $0x0f, Y3, Y8 + VPSLLQ $0x38, Y4, Y9 + VPSRLQ $0x25, Y0, Y0 + VPSRLQ $0x1c, Y1, Y1 + VPSRLQ $0x36, Y2, Y2 + VPSRLQ $0x31, Y3, Y3 + VPSRLQ $0x08, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 160(AX) + VMOVDQA Y6, 352(AX) + VMOVDQA Y7, 544(AX) + VMOVDQA Y8, 736(AX) + VMOVDQA Y9, 128(AX) + VPXOR 64(AX), Y12, Y0 + VPXOR 256(AX), Y13, Y1 + VPXOR 448(AX), Y14, Y2 + VPXOR 480(AX), Y10, Y3 + VPXOR 672(AX), Y11, Y4 + VPSLLQ $0x3e, Y0, Y5 + VPSLLQ $0x37, Y1, Y6 + VPSLLQ $0x27, Y2, Y7 + VPSLLQ $0x29, Y3, Y8 + VPSLLQ $0x02, Y4, Y9 + VPSRLQ $0x02, Y0, Y0 + VPSRLQ $0x09, Y1, Y1 + VPSRLQ $0x19, Y2, Y2 + VPSRLQ $0x17, Y3, Y3 + VPSRLQ $0x3e, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 480(AX) + VMOVDQA Y6, 672(AX) + VMOVDQA Y7, 64(AX) + VMOVDQA Y8, 256(AX) + VMOVDQA Y9, 448(AX) + VMOVDQA (AX), Y0 + VMOVDQA 32(AX), Y1 + VMOVDQA 64(AX), Y2 + VMOVDQA 96(AX), Y3 + VMOVDQA 128(AX), Y4 + VPXOR 160(AX), Y0, Y0 + VPXOR 192(AX), Y1, Y1 + VPXOR 224(AX), Y2, Y2 + VPXOR 256(AX), Y3, Y3 + VPXOR 288(AX), Y4, Y4 + VPXOR 320(AX), Y0, Y0 + VPXOR 352(AX), Y1, Y1 + VPXOR 384(AX), Y2, Y2 + VPXOR 416(AX), Y3, Y3 + VPXOR 448(AX), Y4, Y4 + VPXOR 480(AX), Y0, Y0 + VPXOR 512(AX), Y1, Y1 + VPXOR 544(AX), Y2, Y2 + VPXOR 576(AX), Y3, Y3 + VPXOR 608(AX), Y4, Y4 + VPXOR 640(AX), Y0, Y0 + VPXOR 672(AX), Y1, Y1 + VPXOR 704(AX), Y2, Y2 + VPXOR 736(AX), Y3, Y3 + VPXOR 768(AX), Y4, Y4 + VPSLLQ $0x01, Y1, Y5 + VPSLLQ $0x01, Y2, Y6 + VPSLLQ $0x01, Y3, Y7 + VPSLLQ $0x01, Y4, Y8 + VPSLLQ $0x01, Y0, Y9 + VPSRLQ $0x3f, Y1, Y10 + VPSRLQ $0x3f, Y2, Y11 + VPSRLQ $0x3f, Y3, Y12 + VPSRLQ $0x3f, Y4, Y13 + VPSRLQ $0x3f, Y0, Y14 + VPOR Y5, Y10, Y10 + VPOR Y6, Y11, Y11 + VPOR Y7, Y12, Y12 + VPOR Y8, Y13, Y13 + VPOR Y9, Y14, Y14 + VPXOR Y10, Y4, Y10 + VPXOR Y11, Y0, Y11 + VPXOR Y12, Y1, Y12 + VPXOR Y13, Y2, Y13 + VPXOR Y14, Y3, Y14 + VPXOR (AX), Y10, Y0 + VPXOR 512(AX), Y11, Y1 + VPXOR 224(AX), Y12, Y2 + VPXOR 736(AX), Y13, Y3 + VPXOR 448(AX), Y14, Y4 + VPSLLQ $0x2c, Y1, Y6 + VPSLLQ $0x2b, Y2, Y7 + VPSLLQ $0x15, Y3, Y8 + VPSLLQ $0x0e, Y4, Y9 + VPSRLQ $0x14, Y1, Y1 + VPSRLQ $0x15, Y2, Y2 + VPSRLQ $0x2b, Y3, Y3 + VPSRLQ $0x32, Y4, Y4 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VPBROADCASTQ 8(CX), Y0 + VPXOR Y0, Y5, Y5 + VMOVDQA Y5, (AX) + VMOVDQA Y6, 512(AX) + VMOVDQA Y7, 224(AX) + VMOVDQA Y8, 736(AX) + VMOVDQA Y9, 448(AX) + VPXOR 576(AX), Y13, Y0 + VPXOR 288(AX), Y14, Y1 + VPXOR 640(AX), Y10, Y2 + VPXOR 352(AX), Y11, Y3 + VPXOR 64(AX), Y12, Y4 + VPSLLQ $0x1c, Y0, Y5 + VPSLLQ $0x14, Y1, Y6 + VPSLLQ $0x03, Y2, Y7 + VPSLLQ $0x2d, Y3, Y8 + VPSLLQ $0x3d, Y4, Y9 + VPSRLQ $0x24, Y0, Y0 + VPSRLQ $0x2c, Y1, Y1 + VPSRLQ $0x3d, Y2, Y2 + VPSRLQ $0x13, Y3, Y3 + VPSRLQ $0x03, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 640(AX) + VMOVDQA Y6, 352(AX) + VMOVDQA Y7, 64(AX) + VMOVDQA Y8, 576(AX) + VMOVDQA Y9, 288(AX) + VPXOR 192(AX), Y11, Y0 + VPXOR 704(AX), Y12, Y1 + VPXOR 416(AX), Y13, Y2 + VPXOR 128(AX), Y14, Y3 + VPXOR 480(AX), Y10, Y4 + VPSLLQ $0x01, Y0, Y5 + VPSLLQ $0x06, Y1, Y6 + VPSLLQ $0x19, Y2, Y7 + VPSLLQ $0x08, Y3, Y8 + VPSLLQ $0x12, Y4, Y9 + VPSRLQ $0x3f, Y0, Y0 + VPSRLQ $0x3a, Y1, Y1 + VPSRLQ $0x27, Y2, Y2 + VPSRLQ $0x38, Y3, Y3 + VPSRLQ $0x2e, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 480(AX) + VMOVDQA Y6, 192(AX) + VMOVDQA Y7, 704(AX) + VMOVDQA Y8, 416(AX) + VMOVDQA Y9, 128(AX) + VPXOR 768(AX), Y14, Y0 + VPXOR 320(AX), Y10, Y1 + VPXOR 32(AX), Y11, Y2 + VPXOR 544(AX), Y12, Y3 + VPXOR 256(AX), Y13, Y4 + VPSLLQ $0x1b, Y0, Y5 + VPSLLQ $0x24, Y1, Y6 + VPSLLQ $0x0a, Y2, Y7 + VPSLLQ $0x0f, Y3, Y8 + VPSLLQ $0x38, Y4, Y9 + VPSRLQ $0x25, Y0, Y0 + VPSRLQ $0x1c, Y1, Y1 + VPSRLQ $0x36, Y2, Y2 + VPSRLQ $0x31, Y3, Y3 + VPSRLQ $0x08, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 320(AX) + VMOVDQA Y6, 32(AX) + VMOVDQA Y7, 544(AX) + VMOVDQA Y8, 256(AX) + VMOVDQA Y9, 768(AX) + VPXOR 384(AX), Y12, Y0 + VPXOR 96(AX), Y13, Y1 + VPXOR 608(AX), Y14, Y2 + VPXOR 160(AX), Y10, Y3 + VPXOR 672(AX), Y11, Y4 + VPSLLQ $0x3e, Y0, Y5 + VPSLLQ $0x37, Y1, Y6 + VPSLLQ $0x27, Y2, Y7 + VPSLLQ $0x29, Y3, Y8 + VPSLLQ $0x02, Y4, Y9 + VPSRLQ $0x02, Y0, Y0 + VPSRLQ $0x09, Y1, Y1 + VPSRLQ $0x19, Y2, Y2 + VPSRLQ $0x17, Y3, Y3 + VPSRLQ $0x3e, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 160(AX) + VMOVDQA Y6, 672(AX) + VMOVDQA Y7, 384(AX) + VMOVDQA Y8, 96(AX) + VMOVDQA Y9, 608(AX) + VMOVDQA (AX), Y0 + VMOVDQA 32(AX), Y1 + VMOVDQA 64(AX), Y2 + VMOVDQA 96(AX), Y3 + VMOVDQA 128(AX), Y4 + VPXOR 160(AX), Y0, Y0 + VPXOR 192(AX), Y1, Y1 + VPXOR 224(AX), Y2, Y2 + VPXOR 256(AX), Y3, Y3 + VPXOR 288(AX), Y4, Y4 + VPXOR 320(AX), Y0, Y0 + VPXOR 352(AX), Y1, Y1 + VPXOR 384(AX), Y2, Y2 + VPXOR 416(AX), Y3, Y3 + VPXOR 448(AX), Y4, Y4 + VPXOR 480(AX), Y0, Y0 + VPXOR 512(AX), Y1, Y1 + VPXOR 544(AX), Y2, Y2 + VPXOR 576(AX), Y3, Y3 + VPXOR 608(AX), Y4, Y4 + VPXOR 640(AX), Y0, Y0 + VPXOR 672(AX), Y1, Y1 + VPXOR 704(AX), Y2, Y2 + VPXOR 736(AX), Y3, Y3 + VPXOR 768(AX), Y4, Y4 + VPSLLQ $0x01, Y1, Y5 + VPSLLQ $0x01, Y2, Y6 + VPSLLQ $0x01, Y3, Y7 + VPSLLQ $0x01, Y4, Y8 + VPSLLQ $0x01, Y0, Y9 + VPSRLQ $0x3f, Y1, Y10 + VPSRLQ $0x3f, Y2, Y11 + VPSRLQ $0x3f, Y3, Y12 + VPSRLQ $0x3f, Y4, Y13 + VPSRLQ $0x3f, Y0, Y14 + VPOR Y5, Y10, Y10 + VPOR Y6, Y11, Y11 + VPOR Y7, Y12, Y12 + VPOR Y8, Y13, Y13 + VPOR Y9, Y14, Y14 + VPXOR Y10, Y4, Y10 + VPXOR Y11, Y0, Y11 + VPXOR Y12, Y1, Y12 + VPXOR Y13, Y2, Y13 + VPXOR Y14, Y3, Y14 + VPXOR (AX), Y10, Y0 + VPXOR 352(AX), Y11, Y1 + VPXOR 704(AX), Y12, Y2 + VPXOR 256(AX), Y13, Y3 + VPXOR 608(AX), Y14, Y4 + VPSLLQ $0x2c, Y1, Y6 + VPSLLQ $0x2b, Y2, Y7 + VPSLLQ $0x15, Y3, Y8 + VPSLLQ $0x0e, Y4, Y9 + VPSRLQ $0x14, Y1, Y1 + VPSRLQ $0x15, Y2, Y2 + VPSRLQ $0x2b, Y3, Y3 + VPSRLQ $0x32, Y4, Y4 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VPBROADCASTQ 16(CX), Y0 + VPXOR Y0, Y5, Y5 + VMOVDQA Y5, (AX) + VMOVDQA Y6, 352(AX) + VMOVDQA Y7, 704(AX) + VMOVDQA Y8, 256(AX) + VMOVDQA Y9, 608(AX) + VPXOR 736(AX), Y13, Y0 + VPXOR 288(AX), Y14, Y1 + VPXOR 480(AX), Y10, Y2 + VPXOR 32(AX), Y11, Y3 + VPXOR 384(AX), Y12, Y4 + VPSLLQ $0x1c, Y0, Y5 + VPSLLQ $0x14, Y1, Y6 + VPSLLQ $0x03, Y2, Y7 + VPSLLQ $0x2d, Y3, Y8 + VPSLLQ $0x3d, Y4, Y9 + VPSRLQ $0x24, Y0, Y0 + VPSRLQ $0x2c, Y1, Y1 + VPSRLQ $0x3d, Y2, Y2 + VPSRLQ $0x13, Y3, Y3 + VPSRLQ $0x03, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 480(AX) + VMOVDQA Y6, 32(AX) + VMOVDQA Y7, 384(AX) + VMOVDQA Y8, 736(AX) + VMOVDQA Y9, 288(AX) + VPXOR 512(AX), Y11, Y0 + VPXOR 64(AX), Y12, Y1 + VPXOR 416(AX), Y13, Y2 + VPXOR 768(AX), Y14, Y3 + VPXOR 160(AX), Y10, Y4 + VPSLLQ $0x01, Y0, Y5 + VPSLLQ $0x06, Y1, Y6 + VPSLLQ $0x19, Y2, Y7 + VPSLLQ $0x08, Y3, Y8 + VPSLLQ $0x12, Y4, Y9 + VPSRLQ $0x3f, Y0, Y0 + VPSRLQ $0x3a, Y1, Y1 + VPSRLQ $0x27, Y2, Y2 + VPSRLQ $0x38, Y3, Y3 + VPSRLQ $0x2e, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 160(AX) + VMOVDQA Y6, 512(AX) + VMOVDQA Y7, 64(AX) + VMOVDQA Y8, 416(AX) + VMOVDQA Y9, 768(AX) + VPXOR 448(AX), Y14, Y0 + VPXOR 640(AX), Y10, Y1 + VPXOR 192(AX), Y11, Y2 + VPXOR 544(AX), Y12, Y3 + VPXOR 96(AX), Y13, Y4 + VPSLLQ $0x1b, Y0, Y5 + VPSLLQ $0x24, Y1, Y6 + VPSLLQ $0x0a, Y2, Y7 + VPSLLQ $0x0f, Y3, Y8 + VPSLLQ $0x38, Y4, Y9 + VPSRLQ $0x25, Y0, Y0 + VPSRLQ $0x1c, Y1, Y1 + VPSRLQ $0x36, Y2, Y2 + VPSRLQ $0x31, Y3, Y3 + VPSRLQ $0x08, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 640(AX) + VMOVDQA Y6, 192(AX) + VMOVDQA Y7, 544(AX) + VMOVDQA Y8, 96(AX) + VMOVDQA Y9, 448(AX) + VPXOR 224(AX), Y12, Y0 + VPXOR 576(AX), Y13, Y1 + VPXOR 128(AX), Y14, Y2 + VPXOR 320(AX), Y10, Y3 + VPXOR 672(AX), Y11, Y4 + VPSLLQ $0x3e, Y0, Y5 + VPSLLQ $0x37, Y1, Y6 + VPSLLQ $0x27, Y2, Y7 + VPSLLQ $0x29, Y3, Y8 + VPSLLQ $0x02, Y4, Y9 + VPSRLQ $0x02, Y0, Y0 + VPSRLQ $0x09, Y1, Y1 + VPSRLQ $0x19, Y2, Y2 + VPSRLQ $0x17, Y3, Y3 + VPSRLQ $0x3e, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 320(AX) + VMOVDQA Y6, 672(AX) + VMOVDQA Y7, 224(AX) + VMOVDQA Y8, 576(AX) + VMOVDQA Y9, 128(AX) + VMOVDQA (AX), Y0 + VMOVDQA 32(AX), Y1 + VMOVDQA 64(AX), Y2 + VMOVDQA 96(AX), Y3 + VMOVDQA 128(AX), Y4 + VPXOR 160(AX), Y0, Y0 + VPXOR 192(AX), Y1, Y1 + VPXOR 224(AX), Y2, Y2 + VPXOR 256(AX), Y3, Y3 + VPXOR 288(AX), Y4, Y4 + VPXOR 320(AX), Y0, Y0 + VPXOR 352(AX), Y1, Y1 + VPXOR 384(AX), Y2, Y2 + VPXOR 416(AX), Y3, Y3 + VPXOR 448(AX), Y4, Y4 + VPXOR 480(AX), Y0, Y0 + VPXOR 512(AX), Y1, Y1 + VPXOR 544(AX), Y2, Y2 + VPXOR 576(AX), Y3, Y3 + VPXOR 608(AX), Y4, Y4 + VPXOR 640(AX), Y0, Y0 + VPXOR 672(AX), Y1, Y1 + VPXOR 704(AX), Y2, Y2 + VPXOR 736(AX), Y3, Y3 + VPXOR 768(AX), Y4, Y4 + VPSLLQ $0x01, Y1, Y5 + VPSLLQ $0x01, Y2, Y6 + VPSLLQ $0x01, Y3, Y7 + VPSLLQ $0x01, Y4, Y8 + VPSLLQ $0x01, Y0, Y9 + VPSRLQ $0x3f, Y1, Y10 + VPSRLQ $0x3f, Y2, Y11 + VPSRLQ $0x3f, Y3, Y12 + VPSRLQ $0x3f, Y4, Y13 + VPSRLQ $0x3f, Y0, Y14 + VPOR Y5, Y10, Y10 + VPOR Y6, Y11, Y11 + VPOR Y7, Y12, Y12 + VPOR Y8, Y13, Y13 + VPOR Y9, Y14, Y14 + VPXOR Y10, Y4, Y10 + VPXOR Y11, Y0, Y11 + VPXOR Y12, Y1, Y12 + VPXOR Y13, Y2, Y13 + VPXOR Y14, Y3, Y14 + VPXOR (AX), Y10, Y0 + VPXOR 32(AX), Y11, Y1 + VPXOR 64(AX), Y12, Y2 + VPXOR 96(AX), Y13, Y3 + VPXOR 128(AX), Y14, Y4 + VPSLLQ $0x2c, Y1, Y6 + VPSLLQ $0x2b, Y2, Y7 + VPSLLQ $0x15, Y3, Y8 + VPSLLQ $0x0e, Y4, Y9 + VPSRLQ $0x14, Y1, Y1 + VPSRLQ $0x15, Y2, Y2 + VPSRLQ $0x2b, Y3, Y3 + VPSRLQ $0x32, Y4, Y4 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VPBROADCASTQ 24(CX), Y0 + VPXOR Y0, Y5, Y5 + VMOVDQA Y5, (AX) + VMOVDQA Y6, 32(AX) + VMOVDQA Y7, 64(AX) + VMOVDQA Y8, 96(AX) + VMOVDQA Y9, 128(AX) + VPXOR 256(AX), Y13, Y0 + VPXOR 288(AX), Y14, Y1 + VPXOR 160(AX), Y10, Y2 + VPXOR 192(AX), Y11, Y3 + VPXOR 224(AX), Y12, Y4 + VPSLLQ $0x1c, Y0, Y5 + VPSLLQ $0x14, Y1, Y6 + VPSLLQ $0x03, Y2, Y7 + VPSLLQ $0x2d, Y3, Y8 + VPSLLQ $0x3d, Y4, Y9 + VPSRLQ $0x24, Y0, Y0 + VPSRLQ $0x2c, Y1, Y1 + VPSRLQ $0x3d, Y2, Y2 + VPSRLQ $0x13, Y3, Y3 + VPSRLQ $0x03, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 160(AX) + VMOVDQA Y6, 192(AX) + VMOVDQA Y7, 224(AX) + VMOVDQA Y8, 256(AX) + VMOVDQA Y9, 288(AX) + VPXOR 352(AX), Y11, Y0 + VPXOR 384(AX), Y12, Y1 + VPXOR 416(AX), Y13, Y2 + VPXOR 448(AX), Y14, Y3 + VPXOR 320(AX), Y10, Y4 + VPSLLQ $0x01, Y0, Y5 + VPSLLQ $0x06, Y1, Y6 + VPSLLQ $0x19, Y2, Y7 + VPSLLQ $0x08, Y3, Y8 + VPSLLQ $0x12, Y4, Y9 + VPSRLQ $0x3f, Y0, Y0 + VPSRLQ $0x3a, Y1, Y1 + VPSRLQ $0x27, Y2, Y2 + VPSRLQ $0x38, Y3, Y3 + VPSRLQ $0x2e, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 320(AX) + VMOVDQA Y6, 352(AX) + VMOVDQA Y7, 384(AX) + VMOVDQA Y8, 416(AX) + VMOVDQA Y9, 448(AX) + VPXOR 608(AX), Y14, Y0 + VPXOR 480(AX), Y10, Y1 + VPXOR 512(AX), Y11, Y2 + VPXOR 544(AX), Y12, Y3 + VPXOR 576(AX), Y13, Y4 + VPSLLQ $0x1b, Y0, Y5 + VPSLLQ $0x24, Y1, Y6 + VPSLLQ $0x0a, Y2, Y7 + VPSLLQ $0x0f, Y3, Y8 + VPSLLQ $0x38, Y4, Y9 + VPSRLQ $0x25, Y0, Y0 + VPSRLQ $0x1c, Y1, Y1 + VPSRLQ $0x36, Y2, Y2 + VPSRLQ $0x31, Y3, Y3 + VPSRLQ $0x08, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 480(AX) + VMOVDQA Y6, 512(AX) + VMOVDQA Y7, 544(AX) + VMOVDQA Y8, 576(AX) + VMOVDQA Y9, 608(AX) + VPXOR 704(AX), Y12, Y0 + VPXOR 736(AX), Y13, Y1 + VPXOR 768(AX), Y14, Y2 + VPXOR 640(AX), Y10, Y3 + VPXOR 672(AX), Y11, Y4 + VPSLLQ $0x3e, Y0, Y5 + VPSLLQ $0x37, Y1, Y6 + VPSLLQ $0x27, Y2, Y7 + VPSLLQ $0x29, Y3, Y8 + VPSLLQ $0x02, Y4, Y9 + VPSRLQ $0x02, Y0, Y0 + VPSRLQ $0x09, Y1, Y1 + VPSRLQ $0x19, Y2, Y2 + VPSRLQ $0x17, Y3, Y3 + VPSRLQ $0x3e, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 640(AX) + VMOVDQA Y6, 672(AX) + VMOVDQA Y7, 704(AX) + VMOVDQA Y8, 736(AX) + VMOVDQA Y9, 768(AX) + ADDQ $0x20, CX + SUBQ $0x00000001, DX + JNZ loop + RET diff --git a/vendor/github.com/cloudflare/circl/simd/keccakf1600/f1600x4stubs_amd64.go b/vendor/github.com/cloudflare/circl/simd/keccakf1600/f1600x4stubs_amd64.go new file mode 100644 index 00000000..76c6cf99 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/simd/keccakf1600/f1600x4stubs_amd64.go @@ -0,0 +1,9 @@ +// Code generated by command: go run src.go -out ../../f1600x4_amd64.s -stubs ../../f1600x4stubs_amd64.go -pkg keccakf1600. DO NOT EDIT. + +//go:build amd64 +// +build amd64 + +package keccakf1600 + +//go:noescape +func f1600x4AVX2(state *uint64, rc *[24]uint64) diff --git a/vendor/github.com/cloudflare/circl/simd/keccakf1600/fallback.go b/vendor/github.com/cloudflare/circl/simd/keccakf1600/fallback.go new file mode 100644 index 00000000..5d56c09b --- /dev/null +++ b/vendor/github.com/cloudflare/circl/simd/keccakf1600/fallback.go @@ -0,0 +1,8 @@ +//go:build (!amd64 && !arm64) || (arm64 && !go1.16) +// +build !amd64,!arm64 arm64,!go1.16 + +package keccakf1600 + +func permuteSIMDx2(state []uint64) { permuteScalarX2(state) } + +func permuteSIMDx4(state []uint64) { permuteScalarX4(state) } diff --git a/vendor/github.com/marten-seemann/qtls-go1-18/cfkem.go b/vendor/github.com/marten-seemann/qtls-go1-18/cfkem.go new file mode 100644 index 00000000..dc2f2302 --- /dev/null +++ b/vendor/github.com/marten-seemann/qtls-go1-18/cfkem.go @@ -0,0 +1,170 @@ +// Copyright 2022 Cloudflare, Inc. All rights reserved. Use of this source code +// is governed by a BSD-style license that can be found in the LICENSE file. +// +// Glue to add Circl's (post-quantum) hybrid KEMs. +// +// To enable set CurvePreferences with the desired scheme as the first element: +// +// import ( +// "github.com/cloudflare/circl/kem/tls" +// "github.com/cloudflare/circl/kem/hybrid" +// +// [...] +// +// config.CurvePreferences = []tls.CurveID{ +// qtls.X25519Kyber512Draft00, +// qtls.X25519, +// qtls.P256, +// } + +package qtls + +import ( + "github.com/cloudflare/circl/kem" + "github.com/cloudflare/circl/kem/hybrid" + + "crypto/tls" + "fmt" + "io" + "sync" + "time" +) + +// Either ecdheParameters or kem.PrivateKey +type clientKeySharePrivate interface{} + +var ( + X25519Kyber512Draft00 = CurveID(0xfe30) + X25519Kyber768Draft00 = CurveID(0xfe31) + invalidCurveID = CurveID(0) +) + +func kemSchemeKeyToCurveID(s kem.Scheme) CurveID { + switch s.Name() { + case "Kyber512-X25519": + return X25519Kyber512Draft00 + case "Kyber768-X25519": + return X25519Kyber768Draft00 + default: + return invalidCurveID + } +} + +// Extract CurveID from clientKeySharePrivate +func clientKeySharePrivateCurveID(ks clientKeySharePrivate) CurveID { + switch v := ks.(type) { + case kem.PrivateKey: + ret := kemSchemeKeyToCurveID(v.Scheme()) + if ret == invalidCurveID { + panic("cfkem: internal error: don't know CurveID for this KEM") + } + return ret + case ecdheParameters: + return v.CurveID() + default: + panic("cfkem: internal error: unknown clientKeySharePrivate") + } +} + +// Returns scheme by CurveID if supported by Circl +func curveIdToCirclScheme(id CurveID) kem.Scheme { + switch id { + case X25519Kyber512Draft00: + return hybrid.Kyber512X25519() + case X25519Kyber768Draft00: + return hybrid.Kyber768X25519() + } + return nil +} + +// Generate a new shared secret and encapsulates it for the packed +// public key in ppk using randomness from rnd. +func encapsulateForKem(scheme kem.Scheme, rnd io.Reader, ppk []byte) ( + ct, ss []byte, alert alert, err error) { + pk, err := scheme.UnmarshalBinaryPublicKey(ppk) + if err != nil { + return nil, nil, alertIllegalParameter, fmt.Errorf("unpack pk: %w", err) + } + seed := make([]byte, scheme.EncapsulationSeedSize()) + if _, err := io.ReadFull(rnd, seed); err != nil { + return nil, nil, alertInternalError, fmt.Errorf("random: %w", err) + } + ct, ss, err = scheme.EncapsulateDeterministically(pk, seed) + return ct, ss, alertIllegalParameter, err +} + +// Generate a new keypair using randomness from rnd. +func generateKemKeyPair(scheme kem.Scheme, rnd io.Reader) ( + kem.PublicKey, kem.PrivateKey, error) { + seed := make([]byte, scheme.SeedSize()) + if _, err := io.ReadFull(rnd, seed); err != nil { + return nil, nil, err + } + pk, sk := scheme.DeriveKeyPair(seed) + return pk, sk, nil +} + +// Events. We cannot use the same approach as used in our plain Go fork +// as we cannot change tls.Config, tls.ConnectionState, etc. Also we do +// not want to maintain a fork of quic-go itself as well. This seems +// the simplest option. + +// CFEvent. There are two events: one emitted on HRR and one emitted +type CFEvent interface { + // Common to all events + ServerSide() bool // true if server-side; false if on client-side + + // HRR event. Emitted when an HRR happened. + IsHRR() bool // true if this is an HRR event + + // Handshake event. + IsHandshake() bool // true if this is a handshake event. + Duration() time.Duration // how long did the handshake take? + KEX() tls.CurveID // which kex was established? +} + +type CFEventHandler func(CFEvent) + +// Registers a handler to be called when a CFEvent is emitted; returns +// the previous handler. +func SetCFEventHandler(handler CFEventHandler) CFEventHandler { + cfEventMux.Lock() + ret := cfEventHandler + cfEventHandler = handler + cfEventMux.Unlock() + return ret +} + +func raiseCFEvent(ev CFEvent) { + cfEventMux.Lock() + handler := cfEventHandler + cfEventMux.Unlock() + if handler != nil { + handler(ev) + } +} + +var ( + cfEventMux sync.Mutex + cfEventHandler CFEventHandler +) + +type cfEventHRR struct{ serverSide bool } + +func (*cfEventHRR) IsHRR() bool { return true } +func (ev *cfEventHRR) ServerSide() bool { return ev.serverSide } +func (*cfEventHRR) IsHandshake() bool { return false } +func (ev *cfEventHRR) Duration() time.Duration { panic("wrong event") } +func (ev *cfEventHRR) KEX() tls.CurveID { panic("wrong event") } + +type cfEventHandshake struct { + serverSide bool + duration time.Duration + kex tls.CurveID +} + +func (*cfEventHandshake) IsHRR() bool { return false } +func (ev *cfEventHandshake) ServerSide() bool { return ev.serverSide } +func (*cfEventHandshake) IsHandshake() bool { return true } +func (ev *cfEventHandshake) Duration() time.Duration { return ev.duration } +func (ev *cfEventHandshake) KEX() tls.CurveID { return ev.kex } diff --git a/vendor/github.com/marten-seemann/qtls-go1-18/common.go b/vendor/github.com/marten-seemann/qtls-go1-18/common.go index 4c9aeeb4..d4334f9a 100644 --- a/vendor/github.com/marten-seemann/qtls-go1-18/common.go +++ b/vendor/github.com/marten-seemann/qtls-go1-18/common.go @@ -345,6 +345,7 @@ type clientSessionState struct { // goroutines. Up to TLS 1.2, only ticket-based resumption is supported, not // SessionID-based resumption. In TLS 1.3 they were merged into PSK modes, which // are supported via this interface. +// //go:generate sh -c "mockgen -package qtls -destination mock_client_session_cache_test.go github.com/marten-seemann/qtls-go1-17 ClientSessionCache" type ClientSessionCache = tls.ClientSessionCache diff --git a/vendor/github.com/marten-seemann/qtls-go1-18/handshake_client.go b/vendor/github.com/marten-seemann/qtls-go1-18/handshake_client.go index ab691d56..4d026c66 100644 --- a/vendor/github.com/marten-seemann/qtls-go1-18/handshake_client.go +++ b/vendor/github.com/marten-seemann/qtls-go1-18/handshake_client.go @@ -38,7 +38,7 @@ type clientHandshakeState struct { session *clientSessionState } -func (c *Conn) makeClientHello() (*clientHelloMsg, ecdheParameters, error) { +func (c *Conn) makeClientHello() (*clientHelloMsg, clientKeySharePrivate, error) { config := c.config if len(config.ServerName) == 0 && !config.InsecureSkipVerify { return nil, nil, errors.New("tls: either ServerName or InsecureSkipVerify must be specified in the tls.Config") @@ -137,7 +137,7 @@ func (c *Conn) makeClientHello() (*clientHelloMsg, ecdheParameters, error) { hello.supportedSignatureAlgorithms = supportedSignatureAlgorithms } - var params ecdheParameters + var secret clientKeySharePrivate if hello.supportedVersions[0] == VersionTLS13 { var suites []uint16 for _, suiteID := range configCipherSuites { @@ -158,21 +158,37 @@ func (c *Conn) makeClientHello() (*clientHelloMsg, ecdheParameters, error) { } curveID := config.curvePreferences()[0] - if _, ok := curveForCurveID(curveID); curveID != X25519 && !ok { - return nil, nil, errors.New("tls: CurvePreferences includes unsupported curve") + if scheme := curveIdToCirclScheme(curveID); scheme != nil { + pk, sk, err := generateKemKeyPair(scheme, config.rand()) + if err != nil { + return nil, nil, fmt.Errorf("generateKemKeyPair %s: %w", + scheme.Name(), err) + } + packedPk, err := pk.MarshalBinary() + if err != nil { + return nil, nil, fmt.Errorf("pack circl public key %s: %w", + scheme.Name(), err) + } + hello.keyShares = []keyShare{{group: curveID, data: packedPk}} + secret = sk + } else { + if _, ok := curveForCurveID(curveID); curveID != X25519 && !ok { + return nil, nil, errors.New("tls: CurvePreferences includes unsupported curve") + } + params, err := generateECDHEParameters(config.rand(), curveID) + if err != nil { + return nil, nil, err + } + hello.keyShares = []keyShare{{group: curveID, data: params.PublicKey()}} + secret = params } - params, err = generateECDHEParameters(config.rand(), curveID) - if err != nil { - return nil, nil, err - } - hello.keyShares = []keyShare{{group: curveID, data: params.PublicKey()}} } if hello.supportedVersions[0] == VersionTLS13 && c.extraConfig != nil && c.extraConfig.GetExtensions != nil { hello.additionalExtensions = c.extraConfig.GetExtensions(typeClientHello) } - return hello, params, nil + return hello, secret, nil } func (c *Conn) clientHandshake(ctx context.Context) (err error) { @@ -258,14 +274,14 @@ func (c *Conn) clientHandshake(ctx context.Context) (err error) { if c.vers == VersionTLS13 { hs := &clientHandshakeStateTLS13{ - c: c, - ctx: ctx, - serverHello: serverHello, - hello: hello, - ecdheParams: ecdheParams, - session: session, - earlySecret: earlySecret, - binderKey: binderKey, + c: c, + ctx: ctx, + serverHello: serverHello, + hello: hello, + keySharePrivate: ecdheParams, + session: session, + earlySecret: earlySecret, + binderKey: binderKey, } // In TLS 1.3, session tickets are delivered after the handshake. diff --git a/vendor/github.com/marten-seemann/qtls-go1-18/handshake_client_tls13.go b/vendor/github.com/marten-seemann/qtls-go1-18/handshake_client_tls13.go index 0de59fc1..349d3f20 100644 --- a/vendor/github.com/marten-seemann/qtls-go1-18/handshake_client_tls13.go +++ b/vendor/github.com/marten-seemann/qtls-go1-18/handshake_client_tls13.go @@ -12,10 +12,12 @@ import ( "crypto/rsa" "encoding/binary" "errors" + "fmt" "hash" "sync/atomic" "time" + circlKem "github.com/cloudflare/circl/kem" "golang.org/x/crypto/cryptobyte" ) @@ -24,7 +26,8 @@ type clientHandshakeStateTLS13 struct { ctx context.Context serverHello *serverHelloMsg hello *clientHelloMsg - ecdheParams ecdheParameters + + keySharePrivate clientKeySharePrivate session *clientSessionState earlySecret []byte @@ -44,6 +47,8 @@ type clientHandshakeStateTLS13 struct { func (hs *clientHandshakeStateTLS13) handshake() error { c := hs.c + startTime := time.Now() + // The server must not select TLS 1.3 in a renegotiation. See RFC 8446, // sections 4.1.2 and 4.1.3. if c.handshakes > 0 { @@ -52,7 +57,7 @@ func (hs *clientHandshakeStateTLS13) handshake() error { } // Consistency check on the presence of a keyShare and its parameters. - if hs.ecdheParams == nil || len(hs.hello.keyShares) != 1 { + if hs.keySharePrivate == nil || len(hs.hello.keyShares) != 1 { return c.sendAlert(alertInternalError) } @@ -103,6 +108,12 @@ func (hs *clientHandshakeStateTLS13) handshake() error { return err } + raiseCFEvent(&cfEventHandshake{ + serverSide: false, + duration: time.Since(startTime), + kex: hs.serverHello.serverShare.group, + }) + atomic.StoreUint32(&c.handshakeStatus, 1) return nil @@ -180,6 +191,8 @@ func (hs *clientHandshakeStateTLS13) sendDummyChangeCipherSpec() error { func (hs *clientHandshakeStateTLS13) processHelloRetryRequest() error { c := hs.c + raiseCFEvent(&cfEventHRR{serverSide: false}) + // The first ClientHello gets double-hashed into the transcript upon a // HelloRetryRequest. (The idea is that the server might offload transcript // storage to the client in the cookie.) See RFC 8446, Section 4.4.1. @@ -221,21 +234,38 @@ func (hs *clientHandshakeStateTLS13) processHelloRetryRequest() error { c.sendAlert(alertIllegalParameter) return errors.New("tls: server selected unsupported group") } - if hs.ecdheParams.CurveID() == curveID { + if clientKeySharePrivateCurveID(hs.keySharePrivate) == curveID { c.sendAlert(alertIllegalParameter) return errors.New("tls: server sent an unnecessary HelloRetryRequest key_share") } - if _, ok := curveForCurveID(curveID); curveID != X25519 && !ok { - c.sendAlert(alertInternalError) - return errors.New("tls: CurvePreferences includes unsupported curve") + if scheme := curveIdToCirclScheme(curveID); scheme != nil { + pk, sk, err := generateKemKeyPair(scheme, c.config.rand()) + if err != nil { + c.sendAlert(alertInternalError) + return fmt.Errorf("HRR generateKeyPair %s: %w", + scheme.Name(), err) + } + packedPk, err := pk.MarshalBinary() + if err != nil { + c.sendAlert(alertInternalError) + return fmt.Errorf("HRR pack circl public key %s: %w", + scheme.Name(), err) + } + hs.keySharePrivate = sk + hs.hello.keyShares = []keyShare{{group: curveID, data: packedPk}} + } else { + if _, ok := curveForCurveID(curveID); curveID != X25519 && !ok { + c.sendAlert(alertInternalError) + return errors.New("tls: CurvePreferences includes unsupported curve") + } + params, err := generateECDHEParameters(c.config.rand(), curveID) + if err != nil { + c.sendAlert(alertInternalError) + return err + } + hs.keySharePrivate = params + hs.hello.keyShares = []keyShare{{group: curveID, data: params.PublicKey()}} } - params, err := generateECDHEParameters(c.config.rand(), curveID) - if err != nil { - c.sendAlert(alertInternalError) - return err - } - hs.ecdheParams = params - hs.hello.keyShares = []keyShare{{group: curveID, data: params.PublicKey()}} } hs.hello.raw = nil @@ -314,7 +344,7 @@ func (hs *clientHandshakeStateTLS13) processServerHello() error { c.sendAlert(alertIllegalParameter) return errors.New("tls: server did not send a key share") } - if hs.serverHello.serverShare.group != hs.ecdheParams.CurveID() { + if hs.serverHello.serverShare.group != clientKeySharePrivateCurveID(hs.keySharePrivate) { c.sendAlert(alertIllegalParameter) return errors.New("tls: server selected unsupported group") } @@ -352,7 +382,18 @@ func (hs *clientHandshakeStateTLS13) processServerHello() error { func (hs *clientHandshakeStateTLS13) establishHandshakeKeys() error { c := hs.c - sharedKey := hs.ecdheParams.SharedKey(hs.serverHello.serverShare.data) + var sharedKey []byte + if params, ok := hs.keySharePrivate.(ecdheParameters); ok { + sharedKey = params.SharedKey(hs.serverHello.serverShare.data) + } else if sk, ok := hs.keySharePrivate.(circlKem.PrivateKey); ok { + var err error + sharedKey, err = sk.Scheme().Decapsulate(sk, hs.serverHello.serverShare.data) + if err != nil { + c.sendAlert(alertIllegalParameter) + return fmt.Errorf("%s decaps: %w", sk.Scheme().Name(), err) + } + } + if sharedKey == nil { c.sendAlert(alertIllegalParameter) return errors.New("tls: invalid server key share") diff --git a/vendor/github.com/marten-seemann/qtls-go1-18/handshake_server_tls13.go b/vendor/github.com/marten-seemann/qtls-go1-18/handshake_server_tls13.go index dd8d801e..58fbb8d0 100644 --- a/vendor/github.com/marten-seemann/qtls-go1-18/handshake_server_tls13.go +++ b/vendor/github.com/marten-seemann/qtls-go1-18/handshake_server_tls13.go @@ -11,6 +11,7 @@ import ( "crypto/hmac" "crypto/rsa" "errors" + "fmt" "hash" "io" "sync/atomic" @@ -46,6 +47,8 @@ type serverHandshakeStateTLS13 struct { func (hs *serverHandshakeStateTLS13) handshake() error { c := hs.c + startTime := time.Now() + // For an overview of the TLS 1.3 handshake, see RFC 8446, Section 2. if err := hs.processClientHello(); err != nil { return err @@ -79,6 +82,12 @@ func (hs *serverHandshakeStateTLS13) handshake() error { return err } + raiseCFEvent(&cfEventHandshake{ + serverSide: true, + duration: time.Since(startTime), + kex: hs.hello.serverShare.group, + }) + atomic.StoreUint32(&c.handshakeStatus, 1) return nil @@ -206,17 +215,27 @@ GroupSelection: clientKeyShare = &hs.clientHello.keyShares[0] } - if _, ok := curveForCurveID(selectedGroup); selectedGroup != X25519 && !ok { + if _, ok := curveForCurveID(selectedGroup); selectedGroup != X25519 && curveIdToCirclScheme(selectedGroup) == nil && !ok { c.sendAlert(alertInternalError) return errors.New("tls: CurvePreferences includes unsupported curve") } - params, err := generateECDHEParameters(c.config.rand(), selectedGroup) - if err != nil { - c.sendAlert(alertInternalError) - return err + if kem := curveIdToCirclScheme(selectedGroup); kem != nil { + ct, ss, alert, err := encapsulateForKem(kem, c.config.rand(), clientKeyShare.data) + if err != nil { + c.sendAlert(alert) + return fmt.Errorf("%s encap: %w", kem.Name(), err) + } + hs.hello.serverShare = keyShare{group: selectedGroup, data: ct} + hs.sharedKey = ss + } else { + params, err := generateECDHEParameters(c.config.rand(), selectedGroup) + if err != nil { + c.sendAlert(alertInternalError) + return err + } + hs.hello.serverShare = keyShare{group: selectedGroup, data: params.PublicKey()} + hs.sharedKey = params.SharedKey(clientKeyShare.data) } - hs.hello.serverShare = keyShare{group: selectedGroup, data: params.PublicKey()} - hs.sharedKey = params.SharedKey(clientKeyShare.data) if hs.sharedKey == nil { c.sendAlert(alertIllegalParameter) return errors.New("tls: invalid client key share") @@ -437,6 +456,8 @@ func (hs *serverHandshakeStateTLS13) sendDummyChangeCipherSpec() error { func (hs *serverHandshakeStateTLS13) doHelloRetryRequest(selectedGroup CurveID) error { c := hs.c + raiseCFEvent(&cfEventHRR{serverSide: true}) + // The first ClientHello gets double-hashed into the transcript upon a // HelloRetryRequest. See RFC 8446, Section 4.4.1. hs.transcript.Write(hs.clientHello.marshal()) diff --git a/vendor/github.com/marten-seemann/qtls-go1-18/key_agreement.go b/vendor/github.com/marten-seemann/qtls-go1-18/key_agreement.go index 453a8dcf..8a6fd692 100644 --- a/vendor/github.com/marten-seemann/qtls-go1-18/key_agreement.go +++ b/vendor/github.com/marten-seemann/qtls-go1-18/key_agreement.go @@ -168,7 +168,7 @@ type ecdheKeyAgreement struct { func (ka *ecdheKeyAgreement) generateServerKeyExchange(config *config, cert *Certificate, clientHello *clientHelloMsg, hello *serverHelloMsg) (*serverKeyExchangeMsg, error) { var curveID CurveID for _, c := range clientHello.supportedCurves { - if config.supportsCurve(c) { + if config.supportsCurve(c) && curveIdToCirclScheme(c) == nil { curveID = c break } diff --git a/vendor/github.com/marten-seemann/qtls-go1-19/cfkem.go b/vendor/github.com/marten-seemann/qtls-go1-19/cfkem.go new file mode 100644 index 00000000..dc2f2302 --- /dev/null +++ b/vendor/github.com/marten-seemann/qtls-go1-19/cfkem.go @@ -0,0 +1,170 @@ +// Copyright 2022 Cloudflare, Inc. All rights reserved. Use of this source code +// is governed by a BSD-style license that can be found in the LICENSE file. +// +// Glue to add Circl's (post-quantum) hybrid KEMs. +// +// To enable set CurvePreferences with the desired scheme as the first element: +// +// import ( +// "github.com/cloudflare/circl/kem/tls" +// "github.com/cloudflare/circl/kem/hybrid" +// +// [...] +// +// config.CurvePreferences = []tls.CurveID{ +// qtls.X25519Kyber512Draft00, +// qtls.X25519, +// qtls.P256, +// } + +package qtls + +import ( + "github.com/cloudflare/circl/kem" + "github.com/cloudflare/circl/kem/hybrid" + + "crypto/tls" + "fmt" + "io" + "sync" + "time" +) + +// Either ecdheParameters or kem.PrivateKey +type clientKeySharePrivate interface{} + +var ( + X25519Kyber512Draft00 = CurveID(0xfe30) + X25519Kyber768Draft00 = CurveID(0xfe31) + invalidCurveID = CurveID(0) +) + +func kemSchemeKeyToCurveID(s kem.Scheme) CurveID { + switch s.Name() { + case "Kyber512-X25519": + return X25519Kyber512Draft00 + case "Kyber768-X25519": + return X25519Kyber768Draft00 + default: + return invalidCurveID + } +} + +// Extract CurveID from clientKeySharePrivate +func clientKeySharePrivateCurveID(ks clientKeySharePrivate) CurveID { + switch v := ks.(type) { + case kem.PrivateKey: + ret := kemSchemeKeyToCurveID(v.Scheme()) + if ret == invalidCurveID { + panic("cfkem: internal error: don't know CurveID for this KEM") + } + return ret + case ecdheParameters: + return v.CurveID() + default: + panic("cfkem: internal error: unknown clientKeySharePrivate") + } +} + +// Returns scheme by CurveID if supported by Circl +func curveIdToCirclScheme(id CurveID) kem.Scheme { + switch id { + case X25519Kyber512Draft00: + return hybrid.Kyber512X25519() + case X25519Kyber768Draft00: + return hybrid.Kyber768X25519() + } + return nil +} + +// Generate a new shared secret and encapsulates it for the packed +// public key in ppk using randomness from rnd. +func encapsulateForKem(scheme kem.Scheme, rnd io.Reader, ppk []byte) ( + ct, ss []byte, alert alert, err error) { + pk, err := scheme.UnmarshalBinaryPublicKey(ppk) + if err != nil { + return nil, nil, alertIllegalParameter, fmt.Errorf("unpack pk: %w", err) + } + seed := make([]byte, scheme.EncapsulationSeedSize()) + if _, err := io.ReadFull(rnd, seed); err != nil { + return nil, nil, alertInternalError, fmt.Errorf("random: %w", err) + } + ct, ss, err = scheme.EncapsulateDeterministically(pk, seed) + return ct, ss, alertIllegalParameter, err +} + +// Generate a new keypair using randomness from rnd. +func generateKemKeyPair(scheme kem.Scheme, rnd io.Reader) ( + kem.PublicKey, kem.PrivateKey, error) { + seed := make([]byte, scheme.SeedSize()) + if _, err := io.ReadFull(rnd, seed); err != nil { + return nil, nil, err + } + pk, sk := scheme.DeriveKeyPair(seed) + return pk, sk, nil +} + +// Events. We cannot use the same approach as used in our plain Go fork +// as we cannot change tls.Config, tls.ConnectionState, etc. Also we do +// not want to maintain a fork of quic-go itself as well. This seems +// the simplest option. + +// CFEvent. There are two events: one emitted on HRR and one emitted +type CFEvent interface { + // Common to all events + ServerSide() bool // true if server-side; false if on client-side + + // HRR event. Emitted when an HRR happened. + IsHRR() bool // true if this is an HRR event + + // Handshake event. + IsHandshake() bool // true if this is a handshake event. + Duration() time.Duration // how long did the handshake take? + KEX() tls.CurveID // which kex was established? +} + +type CFEventHandler func(CFEvent) + +// Registers a handler to be called when a CFEvent is emitted; returns +// the previous handler. +func SetCFEventHandler(handler CFEventHandler) CFEventHandler { + cfEventMux.Lock() + ret := cfEventHandler + cfEventHandler = handler + cfEventMux.Unlock() + return ret +} + +func raiseCFEvent(ev CFEvent) { + cfEventMux.Lock() + handler := cfEventHandler + cfEventMux.Unlock() + if handler != nil { + handler(ev) + } +} + +var ( + cfEventMux sync.Mutex + cfEventHandler CFEventHandler +) + +type cfEventHRR struct{ serverSide bool } + +func (*cfEventHRR) IsHRR() bool { return true } +func (ev *cfEventHRR) ServerSide() bool { return ev.serverSide } +func (*cfEventHRR) IsHandshake() bool { return false } +func (ev *cfEventHRR) Duration() time.Duration { panic("wrong event") } +func (ev *cfEventHRR) KEX() tls.CurveID { panic("wrong event") } + +type cfEventHandshake struct { + serverSide bool + duration time.Duration + kex tls.CurveID +} + +func (*cfEventHandshake) IsHRR() bool { return false } +func (ev *cfEventHandshake) ServerSide() bool { return ev.serverSide } +func (*cfEventHandshake) IsHandshake() bool { return true } +func (ev *cfEventHandshake) Duration() time.Duration { return ev.duration } +func (ev *cfEventHandshake) KEX() tls.CurveID { return ev.kex } diff --git a/vendor/github.com/marten-seemann/qtls-go1-19/common.go b/vendor/github.com/marten-seemann/qtls-go1-19/common.go index 6670ce2f..3b8de4c5 100644 --- a/vendor/github.com/marten-seemann/qtls-go1-19/common.go +++ b/vendor/github.com/marten-seemann/qtls-go1-19/common.go @@ -345,6 +345,7 @@ type clientSessionState struct { // goroutines. Up to TLS 1.2, only ticket-based resumption is supported, not // SessionID-based resumption. In TLS 1.3 they were merged into PSK modes, which // are supported via this interface. +// //go:generate sh -c "mockgen -package qtls -destination mock_client_session_cache_test.go github.com/marten-seemann/qtls-go1-17 ClientSessionCache" type ClientSessionCache = tls.ClientSessionCache diff --git a/vendor/github.com/marten-seemann/qtls-go1-19/handshake_client.go b/vendor/github.com/marten-seemann/qtls-go1-19/handshake_client.go index 4407683a..65aae636 100644 --- a/vendor/github.com/marten-seemann/qtls-go1-19/handshake_client.go +++ b/vendor/github.com/marten-seemann/qtls-go1-19/handshake_client.go @@ -40,7 +40,7 @@ type clientHandshakeState struct { var testingOnlyForceClientHelloSignatureAlgorithms []SignatureScheme -func (c *Conn) makeClientHello() (*clientHelloMsg, ecdheParameters, error) { +func (c *Conn) makeClientHello() (*clientHelloMsg, clientKeySharePrivate, error) { config := c.config if len(config.ServerName) == 0 && !config.InsecureSkipVerify { return nil, nil, errors.New("tls: either ServerName or InsecureSkipVerify must be specified in the tls.Config") @@ -142,7 +142,7 @@ func (c *Conn) makeClientHello() (*clientHelloMsg, ecdheParameters, error) { hello.supportedSignatureAlgorithms = testingOnlyForceClientHelloSignatureAlgorithms } - var params ecdheParameters + var secret clientKeySharePrivate if hello.supportedVersions[0] == VersionTLS13 { var suites []uint16 for _, suiteID := range configCipherSuites { @@ -163,21 +163,37 @@ func (c *Conn) makeClientHello() (*clientHelloMsg, ecdheParameters, error) { } curveID := config.curvePreferences()[0] - if _, ok := curveForCurveID(curveID); curveID != X25519 && !ok { - return nil, nil, errors.New("tls: CurvePreferences includes unsupported curve") + if scheme := curveIdToCirclScheme(curveID); scheme != nil { + pk, sk, err := generateKemKeyPair(scheme, config.rand()) + if err != nil { + return nil, nil, fmt.Errorf("generateKemKeyPair %s: %w", + scheme.Name(), err) + } + packedPk, err := pk.MarshalBinary() + if err != nil { + return nil, nil, fmt.Errorf("pack circl public key %s: %w", + scheme.Name(), err) + } + hello.keyShares = []keyShare{{group: curveID, data: packedPk}} + secret = sk + } else { + if _, ok := curveForCurveID(curveID); curveID != X25519 && !ok { + return nil, nil, errors.New("tls: CurvePreferences includes unsupported curve") + } + params, err := generateECDHEParameters(config.rand(), curveID) + if err != nil { + return nil, nil, err + } + hello.keyShares = []keyShare{{group: curveID, data: params.PublicKey()}} + secret = params } - params, err = generateECDHEParameters(config.rand(), curveID) - if err != nil { - return nil, nil, err - } - hello.keyShares = []keyShare{{group: curveID, data: params.PublicKey()}} } if hello.supportedVersions[0] == VersionTLS13 && c.extraConfig != nil && c.extraConfig.GetExtensions != nil { hello.additionalExtensions = c.extraConfig.GetExtensions(typeClientHello) } - return hello, params, nil + return hello, secret, nil } func (c *Conn) clientHandshake(ctx context.Context) (err error) { @@ -263,14 +279,14 @@ func (c *Conn) clientHandshake(ctx context.Context) (err error) { if c.vers == VersionTLS13 { hs := &clientHandshakeStateTLS13{ - c: c, - ctx: ctx, - serverHello: serverHello, - hello: hello, - ecdheParams: ecdheParams, - session: session, - earlySecret: earlySecret, - binderKey: binderKey, + c: c, + ctx: ctx, + serverHello: serverHello, + hello: hello, + keySharePrivate: ecdheParams, + session: session, + earlySecret: earlySecret, + binderKey: binderKey, } // In TLS 1.3, session tickets are delivered after the handshake. diff --git a/vendor/github.com/marten-seemann/qtls-go1-19/handshake_client_tls13.go b/vendor/github.com/marten-seemann/qtls-go1-19/handshake_client_tls13.go index 7f05f2c6..7d470c42 100644 --- a/vendor/github.com/marten-seemann/qtls-go1-19/handshake_client_tls13.go +++ b/vendor/github.com/marten-seemann/qtls-go1-19/handshake_client_tls13.go @@ -12,10 +12,12 @@ import ( "crypto/rsa" "encoding/binary" "errors" + "fmt" "hash" "sync/atomic" "time" + circlKem "github.com/cloudflare/circl/kem" "golang.org/x/crypto/cryptobyte" ) @@ -24,7 +26,8 @@ type clientHandshakeStateTLS13 struct { ctx context.Context serverHello *serverHelloMsg hello *clientHelloMsg - ecdheParams ecdheParameters + + keySharePrivate clientKeySharePrivate session *clientSessionState earlySecret []byte @@ -44,6 +47,8 @@ type clientHandshakeStateTLS13 struct { func (hs *clientHandshakeStateTLS13) handshake() error { c := hs.c + startTime := time.Now() + if needFIPS() { return errors.New("tls: internal error: TLS 1.3 reached in FIPS mode") } @@ -56,7 +61,7 @@ func (hs *clientHandshakeStateTLS13) handshake() error { } // Consistency check on the presence of a keyShare and its parameters. - if hs.ecdheParams == nil || len(hs.hello.keyShares) != 1 { + if hs.keySharePrivate == nil || len(hs.hello.keyShares) != 1 { return c.sendAlert(alertInternalError) } @@ -107,6 +112,12 @@ func (hs *clientHandshakeStateTLS13) handshake() error { return err } + raiseCFEvent(&cfEventHandshake{ + serverSide: false, + duration: time.Since(startTime), + kex: hs.serverHello.serverShare.group, + }) + atomic.StoreUint32(&c.handshakeStatus, 1) return nil @@ -184,6 +195,8 @@ func (hs *clientHandshakeStateTLS13) sendDummyChangeCipherSpec() error { func (hs *clientHandshakeStateTLS13) processHelloRetryRequest() error { c := hs.c + raiseCFEvent(&cfEventHRR{serverSide: false}) + // The first ClientHello gets double-hashed into the transcript upon a // HelloRetryRequest. (The idea is that the server might offload transcript // storage to the client in the cookie.) See RFC 8446, Section 4.4.1. @@ -225,21 +238,38 @@ func (hs *clientHandshakeStateTLS13) processHelloRetryRequest() error { c.sendAlert(alertIllegalParameter) return errors.New("tls: server selected unsupported group") } - if hs.ecdheParams.CurveID() == curveID { + if clientKeySharePrivateCurveID(hs.keySharePrivate) == curveID { c.sendAlert(alertIllegalParameter) return errors.New("tls: server sent an unnecessary HelloRetryRequest key_share") } - if _, ok := curveForCurveID(curveID); curveID != X25519 && !ok { - c.sendAlert(alertInternalError) - return errors.New("tls: CurvePreferences includes unsupported curve") + if scheme := curveIdToCirclScheme(curveID); scheme != nil { + pk, sk, err := generateKemKeyPair(scheme, c.config.rand()) + if err != nil { + c.sendAlert(alertInternalError) + return fmt.Errorf("HRR generateKeyPair %s: %w", + scheme.Name(), err) + } + packedPk, err := pk.MarshalBinary() + if err != nil { + c.sendAlert(alertInternalError) + return fmt.Errorf("HRR pack circl public key %s: %w", + scheme.Name(), err) + } + hs.keySharePrivate = sk + hs.hello.keyShares = []keyShare{{group: curveID, data: packedPk}} + } else { + if _, ok := curveForCurveID(curveID); curveID != X25519 && !ok { + c.sendAlert(alertInternalError) + return errors.New("tls: CurvePreferences includes unsupported curve") + } + params, err := generateECDHEParameters(c.config.rand(), curveID) + if err != nil { + c.sendAlert(alertInternalError) + return err + } + hs.keySharePrivate = params + hs.hello.keyShares = []keyShare{{group: curveID, data: params.PublicKey()}} } - params, err := generateECDHEParameters(c.config.rand(), curveID) - if err != nil { - c.sendAlert(alertInternalError) - return err - } - hs.ecdheParams = params - hs.hello.keyShares = []keyShare{{group: curveID, data: params.PublicKey()}} } hs.hello.raw = nil @@ -318,7 +348,7 @@ func (hs *clientHandshakeStateTLS13) processServerHello() error { c.sendAlert(alertIllegalParameter) return errors.New("tls: server did not send a key share") } - if hs.serverHello.serverShare.group != hs.ecdheParams.CurveID() { + if hs.serverHello.serverShare.group != clientKeySharePrivateCurveID(hs.keySharePrivate) { c.sendAlert(alertIllegalParameter) return errors.New("tls: server selected unsupported group") } @@ -356,7 +386,18 @@ func (hs *clientHandshakeStateTLS13) processServerHello() error { func (hs *clientHandshakeStateTLS13) establishHandshakeKeys() error { c := hs.c - sharedKey := hs.ecdheParams.SharedKey(hs.serverHello.serverShare.data) + var sharedKey []byte + if params, ok := hs.keySharePrivate.(ecdheParameters); ok { + sharedKey = params.SharedKey(hs.serverHello.serverShare.data) + } else if sk, ok := hs.keySharePrivate.(circlKem.PrivateKey); ok { + var err error + sharedKey, err = sk.Scheme().Decapsulate(sk, hs.serverHello.serverShare.data) + if err != nil { + c.sendAlert(alertIllegalParameter) + return fmt.Errorf("%s decaps: %w", sk.Scheme().Name(), err) + } + } + if sharedKey == nil { c.sendAlert(alertIllegalParameter) return errors.New("tls: invalid server key share") diff --git a/vendor/github.com/marten-seemann/qtls-go1-19/handshake_server_tls13.go b/vendor/github.com/marten-seemann/qtls-go1-19/handshake_server_tls13.go index e3db8063..9fb32c35 100644 --- a/vendor/github.com/marten-seemann/qtls-go1-19/handshake_server_tls13.go +++ b/vendor/github.com/marten-seemann/qtls-go1-19/handshake_server_tls13.go @@ -11,6 +11,7 @@ import ( "crypto/hmac" "crypto/rsa" "errors" + "fmt" "hash" "io" "sync/atomic" @@ -46,6 +47,8 @@ type serverHandshakeStateTLS13 struct { func (hs *serverHandshakeStateTLS13) handshake() error { c := hs.c + startTime := time.Now() + if needFIPS() { return errors.New("tls: internal error: TLS 1.3 reached in FIPS mode") } @@ -83,6 +86,12 @@ func (hs *serverHandshakeStateTLS13) handshake() error { return err } + raiseCFEvent(&cfEventHandshake{ + serverSide: true, + duration: time.Since(startTime), + kex: hs.hello.serverShare.group, + }) + atomic.StoreUint32(&c.handshakeStatus, 1) return nil @@ -210,17 +219,27 @@ GroupSelection: clientKeyShare = &hs.clientHello.keyShares[0] } - if _, ok := curveForCurveID(selectedGroup); selectedGroup != X25519 && !ok { + if _, ok := curveForCurveID(selectedGroup); selectedGroup != X25519 && curveIdToCirclScheme(selectedGroup) == nil && !ok { c.sendAlert(alertInternalError) return errors.New("tls: CurvePreferences includes unsupported curve") } - params, err := generateECDHEParameters(c.config.rand(), selectedGroup) - if err != nil { - c.sendAlert(alertInternalError) - return err + if kem := curveIdToCirclScheme(selectedGroup); kem != nil { + ct, ss, alert, err := encapsulateForKem(kem, c.config.rand(), clientKeyShare.data) + if err != nil { + c.sendAlert(alert) + return fmt.Errorf("%s encap: %w", kem.Name(), err) + } + hs.hello.serverShare = keyShare{group: selectedGroup, data: ct} + hs.sharedKey = ss + } else { + params, err := generateECDHEParameters(c.config.rand(), selectedGroup) + if err != nil { + c.sendAlert(alertInternalError) + return err + } + hs.hello.serverShare = keyShare{group: selectedGroup, data: params.PublicKey()} + hs.sharedKey = params.SharedKey(clientKeyShare.data) } - hs.hello.serverShare = keyShare{group: selectedGroup, data: params.PublicKey()} - hs.sharedKey = params.SharedKey(clientKeyShare.data) if hs.sharedKey == nil { c.sendAlert(alertIllegalParameter) return errors.New("tls: invalid client key share") @@ -441,6 +460,8 @@ func (hs *serverHandshakeStateTLS13) sendDummyChangeCipherSpec() error { func (hs *serverHandshakeStateTLS13) doHelloRetryRequest(selectedGroup CurveID) error { c := hs.c + raiseCFEvent(&cfEventHRR{serverSide: true}) + // The first ClientHello gets double-hashed into the transcript upon a // HelloRetryRequest. See RFC 8446, Section 4.4.1. hs.transcript.Write(hs.clientHello.marshal()) diff --git a/vendor/github.com/marten-seemann/qtls-go1-19/key_agreement.go b/vendor/github.com/marten-seemann/qtls-go1-19/key_agreement.go index 453a8dcf..8a6fd692 100644 --- a/vendor/github.com/marten-seemann/qtls-go1-19/key_agreement.go +++ b/vendor/github.com/marten-seemann/qtls-go1-19/key_agreement.go @@ -168,7 +168,7 @@ type ecdheKeyAgreement struct { func (ka *ecdheKeyAgreement) generateServerKeyExchange(config *config, cert *Certificate, clientHello *clientHelloMsg, hello *serverHelloMsg) (*serverKeyExchangeMsg, error) { var curveID CurveID for _, c := range clientHello.supportedCurves { - if config.supportsCurve(c) { + if config.supportsCurve(c) && curveIdToCirclScheme(c) == nil { curveID = c break } diff --git a/vendor/golang.org/x/crypto/AUTHORS b/vendor/golang.org/x/crypto/AUTHORS deleted file mode 100644 index 2b00ddba..00000000 --- a/vendor/golang.org/x/crypto/AUTHORS +++ /dev/null @@ -1,3 +0,0 @@ -# This source code refers to The Go Authors for copyright purposes. -# The master list of authors is in the main Go distribution, -# visible at https://tip.golang.org/AUTHORS. diff --git a/vendor/golang.org/x/crypto/CONTRIBUTORS b/vendor/golang.org/x/crypto/CONTRIBUTORS deleted file mode 100644 index 1fbd3e97..00000000 --- a/vendor/golang.org/x/crypto/CONTRIBUTORS +++ /dev/null @@ -1,3 +0,0 @@ -# This source code was written by the Go contributors. -# The master list of contributors is in the main Go distribution, -# visible at https://tip.golang.org/CONTRIBUTORS. diff --git a/vendor/golang.org/x/crypto/curve25519/curve25519.go b/vendor/golang.org/x/crypto/curve25519/curve25519.go index cda3fdd3..bc62161d 100644 --- a/vendor/golang.org/x/crypto/curve25519/curve25519.go +++ b/vendor/golang.org/x/crypto/curve25519/curve25519.go @@ -9,7 +9,8 @@ package curve25519 // import "golang.org/x/crypto/curve25519" import ( "crypto/subtle" - "fmt" + "errors" + "strconv" "golang.org/x/crypto/curve25519/internal/field" ) @@ -124,10 +125,10 @@ func X25519(scalar, point []byte) ([]byte, error) { func x25519(dst *[32]byte, scalar, point []byte) ([]byte, error) { var in [32]byte if l := len(scalar); l != 32 { - return nil, fmt.Errorf("bad scalar length: %d, expected %d", l, 32) + return nil, errors.New("bad scalar length: " + strconv.Itoa(l) + ", expected 32") } if l := len(point); l != 32 { - return nil, fmt.Errorf("bad point length: %d, expected %d", l, 32) + return nil, errors.New("bad point length: " + strconv.Itoa(l) + ", expected 32") } copy(in[:], scalar) if &point[0] == &Basepoint[0] { @@ -138,7 +139,7 @@ func x25519(dst *[32]byte, scalar, point []byte) ([]byte, error) { copy(base[:], point) ScalarMult(dst, &in, &base) if subtle.ConstantTimeCompare(dst[:], zero[:]) == 1 { - return nil, fmt.Errorf("bad input point: low order point") + return nil, errors.New("bad input point: low order point") } } return dst[:], nil diff --git a/vendor/golang.org/x/crypto/ssh/certs.go b/vendor/golang.org/x/crypto/ssh/certs.go index a69e2249..4600c207 100644 --- a/vendor/golang.org/x/crypto/ssh/certs.go +++ b/vendor/golang.org/x/crypto/ssh/certs.go @@ -460,6 +460,8 @@ func (c *Certificate) SignCert(rand io.Reader, authority Signer) error { // certKeyAlgoNames is a mapping from known certificate algorithm names to the // corresponding public key signature algorithm. +// +// This map must be kept in sync with the one in agent/client.go. var certKeyAlgoNames = map[string]string{ CertAlgoRSAv01: KeyAlgoRSA, CertAlgoRSASHA256v01: KeyAlgoRSASHA256, diff --git a/vendor/golang.org/x/sys/cpu/cpu_arm64.go b/vendor/golang.org/x/sys/cpu/cpu_arm64.go index 87dd5e30..bbaba18b 100644 --- a/vendor/golang.org/x/sys/cpu/cpu_arm64.go +++ b/vendor/golang.org/x/sys/cpu/cpu_arm64.go @@ -41,13 +41,10 @@ func archInit() { switch runtime.GOOS { case "freebsd": readARM64Registers() - case "linux", "netbsd": + case "linux", "netbsd", "openbsd": doinit() default: - // Most platforms don't seem to allow reading these registers. - // - // OpenBSD: - // See https://golang.org/issue/31746 + // Many platforms don't seem to allow reading these registers. setMinimalFeatures() } } diff --git a/vendor/golang.org/x/sys/cpu/cpu_openbsd_arm64.go b/vendor/golang.org/x/sys/cpu/cpu_openbsd_arm64.go new file mode 100644 index 00000000..85b64d5c --- /dev/null +++ b/vendor/golang.org/x/sys/cpu/cpu_openbsd_arm64.go @@ -0,0 +1,65 @@ +// Copyright 2022 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package cpu + +import ( + "syscall" + "unsafe" +) + +// Minimal copy of functionality from x/sys/unix so the cpu package can call +// sysctl without depending on x/sys/unix. + +const ( + // From OpenBSD's sys/sysctl.h. + _CTL_MACHDEP = 7 + + // From OpenBSD's machine/cpu.h. + _CPU_ID_AA64ISAR0 = 2 + _CPU_ID_AA64ISAR1 = 3 +) + +// Implemented in the runtime package (runtime/sys_openbsd3.go) +func syscall_syscall6(fn, a1, a2, a3, a4, a5, a6 uintptr) (r1, r2 uintptr, err syscall.Errno) + +//go:linkname syscall_syscall6 syscall.syscall6 + +func sysctl(mib []uint32, old *byte, oldlen *uintptr, new *byte, newlen uintptr) (err error) { + _, _, errno := syscall_syscall6(libc_sysctl_trampoline_addr, uintptr(unsafe.Pointer(&mib[0])), uintptr(len(mib)), uintptr(unsafe.Pointer(old)), uintptr(unsafe.Pointer(oldlen)), uintptr(unsafe.Pointer(new)), uintptr(newlen)) + if errno != 0 { + return errno + } + return nil +} + +var libc_sysctl_trampoline_addr uintptr + +//go:cgo_import_dynamic libc_sysctl sysctl "libc.so" + +func sysctlUint64(mib []uint32) (uint64, bool) { + var out uint64 + nout := unsafe.Sizeof(out) + if err := sysctl(mib, (*byte)(unsafe.Pointer(&out)), &nout, nil, 0); err != nil { + return 0, false + } + return out, true +} + +func doinit() { + setMinimalFeatures() + + // Get ID_AA64ISAR0 and ID_AA64ISAR1 from sysctl. + isar0, ok := sysctlUint64([]uint32{_CTL_MACHDEP, _CPU_ID_AA64ISAR0}) + if !ok { + return + } + isar1, ok := sysctlUint64([]uint32{_CTL_MACHDEP, _CPU_ID_AA64ISAR1}) + if !ok { + return + } + parseARM64SystemRegisters(isar0, isar1, 0) + + Initialized = true +} diff --git a/vendor/golang.org/x/sys/cpu/cpu_openbsd_arm64.s b/vendor/golang.org/x/sys/cpu/cpu_openbsd_arm64.s new file mode 100644 index 00000000..054ba05d --- /dev/null +++ b/vendor/golang.org/x/sys/cpu/cpu_openbsd_arm64.s @@ -0,0 +1,11 @@ +// Copyright 2022 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +#include "textflag.h" + +TEXT libc_sysctl_trampoline<>(SB),NOSPLIT,$0-0 + JMP libc_sysctl(SB) + +GLOBL ·libc_sysctl_trampoline_addr(SB), RODATA, $8 +DATA ·libc_sysctl_trampoline_addr(SB)/8, $libc_sysctl_trampoline<>(SB) diff --git a/vendor/golang.org/x/sys/cpu/cpu_other_arm64.go b/vendor/golang.org/x/sys/cpu/cpu_other_arm64.go index f8c484f5..f3cde129 100644 --- a/vendor/golang.org/x/sys/cpu/cpu_other_arm64.go +++ b/vendor/golang.org/x/sys/cpu/cpu_other_arm64.go @@ -2,8 +2,8 @@ // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. -//go:build !linux && !netbsd && arm64 -// +build !linux,!netbsd,arm64 +//go:build !linux && !netbsd && !openbsd && arm64 +// +build !linux,!netbsd,!openbsd,arm64 package cpu diff --git a/vendor/golang.org/x/sys/unix/mkall.sh b/vendor/golang.org/x/sys/unix/mkall.sh index dcef4de6..2cd0e916 100644 --- a/vendor/golang.org/x/sys/unix/mkall.sh +++ b/vendor/golang.org/x/sys/unix/mkall.sh @@ -73,12 +73,12 @@ aix_ppc64) darwin_amd64) mkerrors="$mkerrors -m64" mktypes="GOARCH=$GOARCH go tool cgo -godefs" - mkasm="go run mkasm_darwin.go" + mkasm="go run mkasm.go" ;; darwin_arm64) mkerrors="$mkerrors -m64" mktypes="GOARCH=$GOARCH go tool cgo -godefs" - mkasm="go run mkasm_darwin.go" + mkasm="go run mkasm.go" ;; dragonfly_amd64) mkerrors="$mkerrors -m64" @@ -232,5 +232,5 @@ esac if [ -n "$mksysctl" ]; then echo "$mksysctl |gofmt >$zsysctl"; fi if [ -n "$mksysnum" ]; then echo "$mksysnum |gofmt >zsysnum_$GOOSARCH.go"; fi if [ -n "$mktypes" ]; then echo "$mktypes types_$GOOS.go | go run mkpost.go > ztypes_$GOOSARCH.go"; fi - if [ -n "$mkasm" ]; then echo "$mkasm $GOARCH"; fi + if [ -n "$mkasm" ]; then echo "$mkasm $GOOS $GOARCH"; fi ) | $run diff --git a/vendor/golang.org/x/sys/unix/syscall_aix.go b/vendor/golang.org/x/sys/unix/syscall_aix.go index e2a30e88..2db1b51e 100644 --- a/vendor/golang.org/x/sys/unix/syscall_aix.go +++ b/vendor/golang.org/x/sys/unix/syscall_aix.go @@ -253,7 +253,7 @@ func sendmsgN(fd int, iov []Iovec, oob []byte, ptr unsafe.Pointer, salen _Sockle var empty bool if len(oob) > 0 { // send at least one normal byte - empty := emptyIovecs(iov) + empty = emptyIovecs(iov) if empty { var iova [1]Iovec iova[0].Base = &dummy diff --git a/vendor/golang.org/x/sys/unix/syscall_bsd.go b/vendor/golang.org/x/sys/unix/syscall_bsd.go index c437fc5d..eda42671 100644 --- a/vendor/golang.org/x/sys/unix/syscall_bsd.go +++ b/vendor/golang.org/x/sys/unix/syscall_bsd.go @@ -363,7 +363,7 @@ func sendmsgN(fd int, iov []Iovec, oob []byte, ptr unsafe.Pointer, salen _Sockle var empty bool if len(oob) > 0 { // send at least one normal byte - empty := emptyIovecs(iov) + empty = emptyIovecs(iov) if empty { var iova [1]Iovec iova[0].Base = &dummy diff --git a/vendor/golang.org/x/sys/unix/syscall_linux.go b/vendor/golang.org/x/sys/unix/syscall_linux.go index 5e4a94f7..ecb0f27f 100644 --- a/vendor/golang.org/x/sys/unix/syscall_linux.go +++ b/vendor/golang.org/x/sys/unix/syscall_linux.go @@ -1541,7 +1541,7 @@ func sendmsgN(fd int, iov []Iovec, oob []byte, ptr unsafe.Pointer, salen _Sockle var dummy byte var empty bool if len(oob) > 0 { - empty := emptyIovecs(iov) + empty = emptyIovecs(iov) if empty { var sockType int sockType, err = GetsockoptInt(fd, SOL_SOCKET, SO_TYPE) diff --git a/vendor/golang.org/x/sys/unix/zerrors_linux_386.go b/vendor/golang.org/x/sys/unix/zerrors_linux_386.go index 274e2dab..36c0dfc7 100644 --- a/vendor/golang.org/x/sys/unix/zerrors_linux_386.go +++ b/vendor/golang.org/x/sys/unix/zerrors_linux_386.go @@ -1,11 +1,11 @@ -// mkerrors.sh -Wall -Werror -static -I/tmp/include -m32 +// mkerrors.sh -Wall -Werror -static -I/tmp/386/include -m32 // Code generated by the command above; see README.md. DO NOT EDIT. //go:build 386 && linux // +build 386,linux // Code generated by cmd/cgo -godefs; DO NOT EDIT. -// cgo -godefs -- -Wall -Werror -static -I/tmp/include -m32 _const.go +// cgo -godefs -- -Wall -Werror -static -I/tmp/386/include -m32 _const.go package unix diff --git a/vendor/golang.org/x/sys/unix/zerrors_linux_amd64.go b/vendor/golang.org/x/sys/unix/zerrors_linux_amd64.go index 95b6eeed..4ff94270 100644 --- a/vendor/golang.org/x/sys/unix/zerrors_linux_amd64.go +++ b/vendor/golang.org/x/sys/unix/zerrors_linux_amd64.go @@ -1,11 +1,11 @@ -// mkerrors.sh -Wall -Werror -static -I/tmp/include -m64 +// mkerrors.sh -Wall -Werror -static -I/tmp/amd64/include -m64 // Code generated by the command above; see README.md. DO NOT EDIT. //go:build amd64 && linux // +build amd64,linux // Code generated by cmd/cgo -godefs; DO NOT EDIT. -// cgo -godefs -- -Wall -Werror -static -I/tmp/include -m64 _const.go +// cgo -godefs -- -Wall -Werror -static -I/tmp/amd64/include -m64 _const.go package unix diff --git a/vendor/golang.org/x/sys/unix/zerrors_linux_arm.go b/vendor/golang.org/x/sys/unix/zerrors_linux_arm.go index 918cd130..3eaa0fb7 100644 --- a/vendor/golang.org/x/sys/unix/zerrors_linux_arm.go +++ b/vendor/golang.org/x/sys/unix/zerrors_linux_arm.go @@ -1,11 +1,11 @@ -// mkerrors.sh -Wall -Werror -static -I/tmp/include +// mkerrors.sh -Wall -Werror -static -I/tmp/arm/include // Code generated by the command above; see README.md. DO NOT EDIT. //go:build arm && linux // +build arm,linux // Code generated by cmd/cgo -godefs; DO NOT EDIT. -// cgo -godefs -- -Wall -Werror -static -I/tmp/include _const.go +// cgo -godefs -- -Wall -Werror -static -I/tmp/arm/include _const.go package unix diff --git a/vendor/golang.org/x/sys/unix/zerrors_linux_arm64.go b/vendor/golang.org/x/sys/unix/zerrors_linux_arm64.go index 3907dc5a..d7995bdc 100644 --- a/vendor/golang.org/x/sys/unix/zerrors_linux_arm64.go +++ b/vendor/golang.org/x/sys/unix/zerrors_linux_arm64.go @@ -1,11 +1,11 @@ -// mkerrors.sh -Wall -Werror -static -I/tmp/include -fsigned-char +// mkerrors.sh -Wall -Werror -static -I/tmp/arm64/include -fsigned-char // Code generated by the command above; see README.md. DO NOT EDIT. //go:build arm64 && linux // +build arm64,linux // Code generated by cmd/cgo -godefs; DO NOT EDIT. -// cgo -godefs -- -Wall -Werror -static -I/tmp/include -fsigned-char _const.go +// cgo -godefs -- -Wall -Werror -static -I/tmp/arm64/include -fsigned-char _const.go package unix diff --git a/vendor/golang.org/x/sys/unix/zerrors_linux_loong64.go b/vendor/golang.org/x/sys/unix/zerrors_linux_loong64.go index 03d5c105..928e24c2 100644 --- a/vendor/golang.org/x/sys/unix/zerrors_linux_loong64.go +++ b/vendor/golang.org/x/sys/unix/zerrors_linux_loong64.go @@ -1,11 +1,11 @@ -// mkerrors.sh -Wall -Werror -static -I/tmp/include +// mkerrors.sh -Wall -Werror -static -I/tmp/loong64/include // Code generated by the command above; see README.md. DO NOT EDIT. //go:build loong64 && linux // +build loong64,linux // Code generated by cmd/cgo -godefs; DO NOT EDIT. -// cgo -godefs -- -Wall -Werror -static -I/tmp/include _const.go +// cgo -godefs -- -Wall -Werror -static -I/tmp/loong64/include _const.go package unix diff --git a/vendor/golang.org/x/sys/unix/zerrors_linux_mips.go b/vendor/golang.org/x/sys/unix/zerrors_linux_mips.go index bd794e01..179bffb4 100644 --- a/vendor/golang.org/x/sys/unix/zerrors_linux_mips.go +++ b/vendor/golang.org/x/sys/unix/zerrors_linux_mips.go @@ -1,11 +1,11 @@ -// mkerrors.sh -Wall -Werror -static -I/tmp/include +// mkerrors.sh -Wall -Werror -static -I/tmp/mips/include // Code generated by the command above; see README.md. DO NOT EDIT. //go:build mips && linux // +build mips,linux // Code generated by cmd/cgo -godefs; DO NOT EDIT. -// cgo -godefs -- -Wall -Werror -static -I/tmp/include _const.go +// cgo -godefs -- -Wall -Werror -static -I/tmp/mips/include _const.go package unix diff --git a/vendor/golang.org/x/sys/unix/zerrors_linux_mips64.go b/vendor/golang.org/x/sys/unix/zerrors_linux_mips64.go index 6c741b05..1fba17bd 100644 --- a/vendor/golang.org/x/sys/unix/zerrors_linux_mips64.go +++ b/vendor/golang.org/x/sys/unix/zerrors_linux_mips64.go @@ -1,11 +1,11 @@ -// mkerrors.sh -Wall -Werror -static -I/tmp/include +// mkerrors.sh -Wall -Werror -static -I/tmp/mips64/include // Code generated by the command above; see README.md. DO NOT EDIT. //go:build mips64 && linux // +build mips64,linux // Code generated by cmd/cgo -godefs; DO NOT EDIT. -// cgo -godefs -- -Wall -Werror -static -I/tmp/include _const.go +// cgo -godefs -- -Wall -Werror -static -I/tmp/mips64/include _const.go package unix diff --git a/vendor/golang.org/x/sys/unix/zerrors_linux_mips64le.go b/vendor/golang.org/x/sys/unix/zerrors_linux_mips64le.go index 807b8cd2..b77dde31 100644 --- a/vendor/golang.org/x/sys/unix/zerrors_linux_mips64le.go +++ b/vendor/golang.org/x/sys/unix/zerrors_linux_mips64le.go @@ -1,11 +1,11 @@ -// mkerrors.sh -Wall -Werror -static -I/tmp/include +// mkerrors.sh -Wall -Werror -static -I/tmp/mips64le/include // Code generated by the command above; see README.md. DO NOT EDIT. //go:build mips64le && linux // +build mips64le,linux // Code generated by cmd/cgo -godefs; DO NOT EDIT. -// cgo -godefs -- -Wall -Werror -static -I/tmp/include _const.go +// cgo -godefs -- -Wall -Werror -static -I/tmp/mips64le/include _const.go package unix diff --git a/vendor/golang.org/x/sys/unix/zerrors_linux_mipsle.go b/vendor/golang.org/x/sys/unix/zerrors_linux_mipsle.go index a39e4f5c..78c6c751 100644 --- a/vendor/golang.org/x/sys/unix/zerrors_linux_mipsle.go +++ b/vendor/golang.org/x/sys/unix/zerrors_linux_mipsle.go @@ -1,11 +1,11 @@ -// mkerrors.sh -Wall -Werror -static -I/tmp/include +// mkerrors.sh -Wall -Werror -static -I/tmp/mipsle/include // Code generated by the command above; see README.md. DO NOT EDIT. //go:build mipsle && linux // +build mipsle,linux // Code generated by cmd/cgo -godefs; DO NOT EDIT. -// cgo -godefs -- -Wall -Werror -static -I/tmp/include _const.go +// cgo -godefs -- -Wall -Werror -static -I/tmp/mipsle/include _const.go package unix diff --git a/vendor/golang.org/x/sys/unix/zerrors_linux_ppc.go b/vendor/golang.org/x/sys/unix/zerrors_linux_ppc.go index c0fcda86..1c0d31f0 100644 --- a/vendor/golang.org/x/sys/unix/zerrors_linux_ppc.go +++ b/vendor/golang.org/x/sys/unix/zerrors_linux_ppc.go @@ -1,11 +1,11 @@ -// mkerrors.sh -Wall -Werror -static -I/tmp/include +// mkerrors.sh -Wall -Werror -static -I/tmp/ppc/include // Code generated by the command above; see README.md. DO NOT EDIT. //go:build ppc && linux // +build ppc,linux // Code generated by cmd/cgo -godefs; DO NOT EDIT. -// cgo -godefs -- -Wall -Werror -static -I/tmp/include _const.go +// cgo -godefs -- -Wall -Werror -static -I/tmp/ppc/include _const.go package unix diff --git a/vendor/golang.org/x/sys/unix/zerrors_linux_ppc64.go b/vendor/golang.org/x/sys/unix/zerrors_linux_ppc64.go index f3b72407..959dd9bb 100644 --- a/vendor/golang.org/x/sys/unix/zerrors_linux_ppc64.go +++ b/vendor/golang.org/x/sys/unix/zerrors_linux_ppc64.go @@ -1,11 +1,11 @@ -// mkerrors.sh -Wall -Werror -static -I/tmp/include +// mkerrors.sh -Wall -Werror -static -I/tmp/ppc64/include // Code generated by the command above; see README.md. DO NOT EDIT. //go:build ppc64 && linux // +build ppc64,linux // Code generated by cmd/cgo -godefs; DO NOT EDIT. -// cgo -godefs -- -Wall -Werror -static -I/tmp/include _const.go +// cgo -godefs -- -Wall -Werror -static -I/tmp/ppc64/include _const.go package unix diff --git a/vendor/golang.org/x/sys/unix/zerrors_linux_ppc64le.go b/vendor/golang.org/x/sys/unix/zerrors_linux_ppc64le.go index 72f2a45d..5a873cdb 100644 --- a/vendor/golang.org/x/sys/unix/zerrors_linux_ppc64le.go +++ b/vendor/golang.org/x/sys/unix/zerrors_linux_ppc64le.go @@ -1,11 +1,11 @@ -// mkerrors.sh -Wall -Werror -static -I/tmp/include +// mkerrors.sh -Wall -Werror -static -I/tmp/ppc64le/include // Code generated by the command above; see README.md. DO NOT EDIT. //go:build ppc64le && linux // +build ppc64le,linux // Code generated by cmd/cgo -godefs; DO NOT EDIT. -// cgo -godefs -- -Wall -Werror -static -I/tmp/include _const.go +// cgo -godefs -- -Wall -Werror -static -I/tmp/ppc64le/include _const.go package unix diff --git a/vendor/golang.org/x/sys/unix/zerrors_linux_riscv64.go b/vendor/golang.org/x/sys/unix/zerrors_linux_riscv64.go index 45b214b4..e336d141 100644 --- a/vendor/golang.org/x/sys/unix/zerrors_linux_riscv64.go +++ b/vendor/golang.org/x/sys/unix/zerrors_linux_riscv64.go @@ -1,11 +1,11 @@ -// mkerrors.sh -Wall -Werror -static -I/tmp/include +// mkerrors.sh -Wall -Werror -static -I/tmp/riscv64/include // Code generated by the command above; see README.md. DO NOT EDIT. //go:build riscv64 && linux // +build riscv64,linux // Code generated by cmd/cgo -godefs; DO NOT EDIT. -// cgo -godefs -- -Wall -Werror -static -I/tmp/include _const.go +// cgo -godefs -- -Wall -Werror -static -I/tmp/riscv64/include _const.go package unix diff --git a/vendor/golang.org/x/sys/unix/zerrors_linux_s390x.go b/vendor/golang.org/x/sys/unix/zerrors_linux_s390x.go index 1897f207..390c01d9 100644 --- a/vendor/golang.org/x/sys/unix/zerrors_linux_s390x.go +++ b/vendor/golang.org/x/sys/unix/zerrors_linux_s390x.go @@ -1,11 +1,11 @@ -// mkerrors.sh -Wall -Werror -static -I/tmp/include -fsigned-char +// mkerrors.sh -Wall -Werror -static -I/tmp/s390x/include -fsigned-char // Code generated by the command above; see README.md. DO NOT EDIT. //go:build s390x && linux // +build s390x,linux // Code generated by cmd/cgo -godefs; DO NOT EDIT. -// cgo -godefs -- -Wall -Werror -static -I/tmp/include -fsigned-char _const.go +// cgo -godefs -- -Wall -Werror -static -I/tmp/s390x/include -fsigned-char _const.go package unix diff --git a/vendor/golang.org/x/sys/unix/zerrors_linux_sparc64.go b/vendor/golang.org/x/sys/unix/zerrors_linux_sparc64.go index 1fb7a395..98a6e5f1 100644 --- a/vendor/golang.org/x/sys/unix/zerrors_linux_sparc64.go +++ b/vendor/golang.org/x/sys/unix/zerrors_linux_sparc64.go @@ -1,11 +1,11 @@ -// mkerrors.sh -Wall -Werror -static -I/tmp/include +// mkerrors.sh -Wall -Werror -static -I/tmp/sparc64/include // Code generated by the command above; see README.md. DO NOT EDIT. //go:build sparc64 && linux // +build sparc64,linux // Code generated by cmd/cgo -godefs; DO NOT EDIT. -// cgo -godefs -- -Wall -Werror -static -I/tmp/include _const.go +// cgo -godefs -- -Wall -Werror -static -I/tmp/sparc64/include _const.go package unix diff --git a/vendor/golang.org/x/sys/unix/zsyscall_darwin_amd64.1_13.s b/vendor/golang.org/x/sys/unix/zsyscall_darwin_amd64.1_13.s index d6c3e25c..f5bb40ed 100644 --- a/vendor/golang.org/x/sys/unix/zsyscall_darwin_amd64.1_13.s +++ b/vendor/golang.org/x/sys/unix/zsyscall_darwin_amd64.1_13.s @@ -1,4 +1,4 @@ -// go run mkasm_darwin.go amd64 +// go run mkasm.go darwin amd64 // Code generated by the command above; DO NOT EDIT. //go:build go1.13 diff --git a/vendor/golang.org/x/sys/unix/zsyscall_darwin_amd64.s b/vendor/golang.org/x/sys/unix/zsyscall_darwin_amd64.s index 7e308a47..b41467a0 100644 --- a/vendor/golang.org/x/sys/unix/zsyscall_darwin_amd64.s +++ b/vendor/golang.org/x/sys/unix/zsyscall_darwin_amd64.s @@ -1,4 +1,4 @@ -// go run mkasm_darwin.go amd64 +// go run mkasm.go darwin amd64 // Code generated by the command above; DO NOT EDIT. //go:build go1.12 diff --git a/vendor/golang.org/x/sys/unix/zsyscall_darwin_arm64.1_13.s b/vendor/golang.org/x/sys/unix/zsyscall_darwin_arm64.1_13.s index 35798972..0c3f76bc 100644 --- a/vendor/golang.org/x/sys/unix/zsyscall_darwin_arm64.1_13.s +++ b/vendor/golang.org/x/sys/unix/zsyscall_darwin_arm64.1_13.s @@ -1,4 +1,4 @@ -// go run mkasm_darwin.go arm64 +// go run mkasm.go darwin arm64 // Code generated by the command above; DO NOT EDIT. //go:build go1.13 diff --git a/vendor/golang.org/x/sys/unix/zsyscall_darwin_arm64.s b/vendor/golang.org/x/sys/unix/zsyscall_darwin_arm64.s index b09e5bb0..e1f9204a 100644 --- a/vendor/golang.org/x/sys/unix/zsyscall_darwin_arm64.s +++ b/vendor/golang.org/x/sys/unix/zsyscall_darwin_arm64.s @@ -1,4 +1,4 @@ -// go run mkasm_darwin.go arm64 +// go run mkasm.go darwin arm64 // Code generated by the command above; DO NOT EDIT. //go:build go1.12 diff --git a/vendor/golang.org/x/sys/unix/zsysnum_linux_386.go b/vendor/golang.org/x/sys/unix/zsysnum_linux_386.go index 62192e1d..c9c4ad03 100644 --- a/vendor/golang.org/x/sys/unix/zsysnum_linux_386.go +++ b/vendor/golang.org/x/sys/unix/zsysnum_linux_386.go @@ -1,4 +1,4 @@ -// go run linux/mksysnum.go -Wall -Werror -static -I/tmp/include -m32 /tmp/include/asm/unistd.h +// go run linux/mksysnum.go -Wall -Werror -static -I/tmp/386/include -m32 /tmp/386/include/asm/unistd.h // Code generated by the command above; see README.md. DO NOT EDIT. //go:build 386 && linux diff --git a/vendor/golang.org/x/sys/unix/zsysnum_linux_amd64.go b/vendor/golang.org/x/sys/unix/zsysnum_linux_amd64.go index 490aab5d..12ff3417 100644 --- a/vendor/golang.org/x/sys/unix/zsysnum_linux_amd64.go +++ b/vendor/golang.org/x/sys/unix/zsysnum_linux_amd64.go @@ -1,4 +1,4 @@ -// go run linux/mksysnum.go -Wall -Werror -static -I/tmp/include -m64 /tmp/include/asm/unistd.h +// go run linux/mksysnum.go -Wall -Werror -static -I/tmp/amd64/include -m64 /tmp/amd64/include/asm/unistd.h // Code generated by the command above; see README.md. DO NOT EDIT. //go:build amd64 && linux diff --git a/vendor/golang.org/x/sys/unix/zsysnum_linux_arm.go b/vendor/golang.org/x/sys/unix/zsysnum_linux_arm.go index aca17b6f..c3fb5e77 100644 --- a/vendor/golang.org/x/sys/unix/zsysnum_linux_arm.go +++ b/vendor/golang.org/x/sys/unix/zsysnum_linux_arm.go @@ -1,4 +1,4 @@ -// go run linux/mksysnum.go -Wall -Werror -static -I/tmp/include /tmp/include/asm/unistd.h +// go run linux/mksysnum.go -Wall -Werror -static -I/tmp/arm/include /tmp/arm/include/asm/unistd.h // Code generated by the command above; see README.md. DO NOT EDIT. //go:build arm && linux diff --git a/vendor/golang.org/x/sys/unix/zsysnum_linux_arm64.go b/vendor/golang.org/x/sys/unix/zsysnum_linux_arm64.go index 54b4dfa5..358c847a 100644 --- a/vendor/golang.org/x/sys/unix/zsysnum_linux_arm64.go +++ b/vendor/golang.org/x/sys/unix/zsysnum_linux_arm64.go @@ -1,4 +1,4 @@ -// go run linux/mksysnum.go -Wall -Werror -static -I/tmp/include -fsigned-char /tmp/include/asm/unistd.h +// go run linux/mksysnum.go -Wall -Werror -static -I/tmp/arm64/include -fsigned-char /tmp/arm64/include/asm/unistd.h // Code generated by the command above; see README.md. DO NOT EDIT. //go:build arm64 && linux diff --git a/vendor/golang.org/x/sys/unix/zsysnum_linux_loong64.go b/vendor/golang.org/x/sys/unix/zsysnum_linux_loong64.go index 44a764c9..81c4849b 100644 --- a/vendor/golang.org/x/sys/unix/zsysnum_linux_loong64.go +++ b/vendor/golang.org/x/sys/unix/zsysnum_linux_loong64.go @@ -1,4 +1,4 @@ -// go run linux/mksysnum.go -Wall -Werror -static -I/tmp/include /tmp/include/asm/unistd.h +// go run linux/mksysnum.go -Wall -Werror -static -I/tmp/loong64/include /tmp/loong64/include/asm/unistd.h // Code generated by the command above; see README.md. DO NOT EDIT. //go:build loong64 && linux diff --git a/vendor/golang.org/x/sys/unix/zsysnum_linux_mips.go b/vendor/golang.org/x/sys/unix/zsysnum_linux_mips.go index 65a99efc..202a57e9 100644 --- a/vendor/golang.org/x/sys/unix/zsysnum_linux_mips.go +++ b/vendor/golang.org/x/sys/unix/zsysnum_linux_mips.go @@ -1,4 +1,4 @@ -// go run linux/mksysnum.go -Wall -Werror -static -I/tmp/include /tmp/include/asm/unistd.h +// go run linux/mksysnum.go -Wall -Werror -static -I/tmp/mips/include /tmp/mips/include/asm/unistd.h // Code generated by the command above; see README.md. DO NOT EDIT. //go:build mips && linux diff --git a/vendor/golang.org/x/sys/unix/zsysnum_linux_mips64.go b/vendor/golang.org/x/sys/unix/zsysnum_linux_mips64.go index 841c8a66..1fbceb52 100644 --- a/vendor/golang.org/x/sys/unix/zsysnum_linux_mips64.go +++ b/vendor/golang.org/x/sys/unix/zsysnum_linux_mips64.go @@ -1,4 +1,4 @@ -// go run linux/mksysnum.go -Wall -Werror -static -I/tmp/include /tmp/include/asm/unistd.h +// go run linux/mksysnum.go -Wall -Werror -static -I/tmp/mips64/include /tmp/mips64/include/asm/unistd.h // Code generated by the command above; see README.md. DO NOT EDIT. //go:build mips64 && linux diff --git a/vendor/golang.org/x/sys/unix/zsysnum_linux_mips64le.go b/vendor/golang.org/x/sys/unix/zsysnum_linux_mips64le.go index e26a7c76..b4ffb7a2 100644 --- a/vendor/golang.org/x/sys/unix/zsysnum_linux_mips64le.go +++ b/vendor/golang.org/x/sys/unix/zsysnum_linux_mips64le.go @@ -1,4 +1,4 @@ -// go run linux/mksysnum.go -Wall -Werror -static -I/tmp/include /tmp/include/asm/unistd.h +// go run linux/mksysnum.go -Wall -Werror -static -I/tmp/mips64le/include /tmp/mips64le/include/asm/unistd.h // Code generated by the command above; see README.md. DO NOT EDIT. //go:build mips64le && linux diff --git a/vendor/golang.org/x/sys/unix/zsysnum_linux_mipsle.go b/vendor/golang.org/x/sys/unix/zsysnum_linux_mipsle.go index 26447260..867985f9 100644 --- a/vendor/golang.org/x/sys/unix/zsysnum_linux_mipsle.go +++ b/vendor/golang.org/x/sys/unix/zsysnum_linux_mipsle.go @@ -1,4 +1,4 @@ -// go run linux/mksysnum.go -Wall -Werror -static -I/tmp/include /tmp/include/asm/unistd.h +// go run linux/mksysnum.go -Wall -Werror -static -I/tmp/mipsle/include /tmp/mipsle/include/asm/unistd.h // Code generated by the command above; see README.md. DO NOT EDIT. //go:build mipsle && linux diff --git a/vendor/golang.org/x/sys/unix/zsysnum_linux_ppc.go b/vendor/golang.org/x/sys/unix/zsysnum_linux_ppc.go index 26aefc18..a8cce69e 100644 --- a/vendor/golang.org/x/sys/unix/zsysnum_linux_ppc.go +++ b/vendor/golang.org/x/sys/unix/zsysnum_linux_ppc.go @@ -1,4 +1,4 @@ -// go run linux/mksysnum.go -Wall -Werror -static -I/tmp/include /tmp/include/asm/unistd.h +// go run linux/mksysnum.go -Wall -Werror -static -I/tmp/ppc/include /tmp/ppc/include/asm/unistd.h // Code generated by the command above; see README.md. DO NOT EDIT. //go:build ppc && linux diff --git a/vendor/golang.org/x/sys/unix/zsysnum_linux_ppc64.go b/vendor/golang.org/x/sys/unix/zsysnum_linux_ppc64.go index 8d4cd9d9..d44c5b39 100644 --- a/vendor/golang.org/x/sys/unix/zsysnum_linux_ppc64.go +++ b/vendor/golang.org/x/sys/unix/zsysnum_linux_ppc64.go @@ -1,4 +1,4 @@ -// go run linux/mksysnum.go -Wall -Werror -static -I/tmp/include /tmp/include/asm/unistd.h +// go run linux/mksysnum.go -Wall -Werror -static -I/tmp/ppc64/include /tmp/ppc64/include/asm/unistd.h // Code generated by the command above; see README.md. DO NOT EDIT. //go:build ppc64 && linux diff --git a/vendor/golang.org/x/sys/unix/zsysnum_linux_ppc64le.go b/vendor/golang.org/x/sys/unix/zsysnum_linux_ppc64le.go index 3b405d1f..4214dd9c 100644 --- a/vendor/golang.org/x/sys/unix/zsysnum_linux_ppc64le.go +++ b/vendor/golang.org/x/sys/unix/zsysnum_linux_ppc64le.go @@ -1,4 +1,4 @@ -// go run linux/mksysnum.go -Wall -Werror -static -I/tmp/include /tmp/include/asm/unistd.h +// go run linux/mksysnum.go -Wall -Werror -static -I/tmp/ppc64le/include /tmp/ppc64le/include/asm/unistd.h // Code generated by the command above; see README.md. DO NOT EDIT. //go:build ppc64le && linux diff --git a/vendor/golang.org/x/sys/unix/zsysnum_linux_riscv64.go b/vendor/golang.org/x/sys/unix/zsysnum_linux_riscv64.go index 3a9c96b2..3e594a8c 100644 --- a/vendor/golang.org/x/sys/unix/zsysnum_linux_riscv64.go +++ b/vendor/golang.org/x/sys/unix/zsysnum_linux_riscv64.go @@ -1,4 +1,4 @@ -// go run linux/mksysnum.go -Wall -Werror -static -I/tmp/include /tmp/include/asm/unistd.h +// go run linux/mksysnum.go -Wall -Werror -static -I/tmp/riscv64/include /tmp/riscv64/include/asm/unistd.h // Code generated by the command above; see README.md. DO NOT EDIT. //go:build riscv64 && linux diff --git a/vendor/golang.org/x/sys/unix/zsysnum_linux_s390x.go b/vendor/golang.org/x/sys/unix/zsysnum_linux_s390x.go index 8ffa6646..7ea46520 100644 --- a/vendor/golang.org/x/sys/unix/zsysnum_linux_s390x.go +++ b/vendor/golang.org/x/sys/unix/zsysnum_linux_s390x.go @@ -1,4 +1,4 @@ -// go run linux/mksysnum.go -Wall -Werror -static -I/tmp/include -fsigned-char /tmp/include/asm/unistd.h +// go run linux/mksysnum.go -Wall -Werror -static -I/tmp/s390x/include -fsigned-char /tmp/s390x/include/asm/unistd.h // Code generated by the command above; see README.md. DO NOT EDIT. //go:build s390x && linux diff --git a/vendor/golang.org/x/sys/unix/zsysnum_linux_sparc64.go b/vendor/golang.org/x/sys/unix/zsysnum_linux_sparc64.go index 6a39640e..92f628ef 100644 --- a/vendor/golang.org/x/sys/unix/zsysnum_linux_sparc64.go +++ b/vendor/golang.org/x/sys/unix/zsysnum_linux_sparc64.go @@ -1,4 +1,4 @@ -// go run linux/mksysnum.go -Wall -Werror -static -I/tmp/include /tmp/include/asm/unistd.h +// go run linux/mksysnum.go -Wall -Werror -static -I/tmp/sparc64/include /tmp/sparc64/include/asm/unistd.h // Code generated by the command above; see README.md. DO NOT EDIT. //go:build sparc64 && linux diff --git a/vendor/golang.org/x/sys/unix/ztypes_linux.go b/vendor/golang.org/x/sys/unix/ztypes_linux.go index 86984798..ff688116 100644 --- a/vendor/golang.org/x/sys/unix/ztypes_linux.go +++ b/vendor/golang.org/x/sys/unix/ztypes_linux.go @@ -945,6 +945,9 @@ type PerfEventAttr struct { Aux_watermark uint32 Sample_max_stack uint16 _ uint16 + Aux_sample_size uint32 + _ uint32 + Sig_data uint64 } type PerfEventMmapPage struct { @@ -1463,6 +1466,11 @@ const ( IFLA_ALT_IFNAME = 0x35 IFLA_PERM_ADDRESS = 0x36 IFLA_PROTO_DOWN_REASON = 0x37 + IFLA_PARENT_DEV_NAME = 0x38 + IFLA_PARENT_DEV_BUS_NAME = 0x39 + IFLA_GRO_MAX_SIZE = 0x3a + IFLA_TSO_MAX_SIZE = 0x3b + IFLA_TSO_MAX_SEGS = 0x3c IFLA_PROTO_DOWN_REASON_UNSPEC = 0x0 IFLA_PROTO_DOWN_REASON_MASK = 0x1 IFLA_PROTO_DOWN_REASON_VALUE = 0x2 diff --git a/vendor/golang.org/x/sys/unix/ztypes_linux_386.go b/vendor/golang.org/x/sys/unix/ztypes_linux_386.go index 7551af48..26360440 100644 --- a/vendor/golang.org/x/sys/unix/ztypes_linux_386.go +++ b/vendor/golang.org/x/sys/unix/ztypes_linux_386.go @@ -1,4 +1,4 @@ -// cgo -godefs -- -Wall -Werror -static -I/tmp/include -m32 linux/types.go | go run mkpost.go +// cgo -godefs -objdir=/tmp/386/cgo -- -Wall -Werror -static -I/tmp/386/include -m32 linux/types.go | go run mkpost.go // Code generated by the command above; see README.md. DO NOT EDIT. //go:build 386 && linux diff --git a/vendor/golang.org/x/sys/unix/ztypes_linux_amd64.go b/vendor/golang.org/x/sys/unix/ztypes_linux_amd64.go index 3e738ac0..8187489d 100644 --- a/vendor/golang.org/x/sys/unix/ztypes_linux_amd64.go +++ b/vendor/golang.org/x/sys/unix/ztypes_linux_amd64.go @@ -1,4 +1,4 @@ -// cgo -godefs -- -Wall -Werror -static -I/tmp/include -m64 linux/types.go | go run mkpost.go +// cgo -godefs -objdir=/tmp/amd64/cgo -- -Wall -Werror -static -I/tmp/amd64/include -m64 linux/types.go | go run mkpost.go // Code generated by the command above; see README.md. DO NOT EDIT. //go:build amd64 && linux diff --git a/vendor/golang.org/x/sys/unix/ztypes_linux_arm.go b/vendor/golang.org/x/sys/unix/ztypes_linux_arm.go index 6183eef4..d1612335 100644 --- a/vendor/golang.org/x/sys/unix/ztypes_linux_arm.go +++ b/vendor/golang.org/x/sys/unix/ztypes_linux_arm.go @@ -1,4 +1,4 @@ -// cgo -godefs -- -Wall -Werror -static -I/tmp/include linux/types.go | go run mkpost.go +// cgo -godefs -objdir=/tmp/arm/cgo -- -Wall -Werror -static -I/tmp/arm/include linux/types.go | go run mkpost.go // Code generated by the command above; see README.md. DO NOT EDIT. //go:build arm && linux diff --git a/vendor/golang.org/x/sys/unix/ztypes_linux_arm64.go b/vendor/golang.org/x/sys/unix/ztypes_linux_arm64.go index 968cecb1..c28e5556 100644 --- a/vendor/golang.org/x/sys/unix/ztypes_linux_arm64.go +++ b/vendor/golang.org/x/sys/unix/ztypes_linux_arm64.go @@ -1,4 +1,4 @@ -// cgo -godefs -- -Wall -Werror -static -I/tmp/include -fsigned-char linux/types.go | go run mkpost.go +// cgo -godefs -objdir=/tmp/arm64/cgo -- -Wall -Werror -static -I/tmp/arm64/include -fsigned-char linux/types.go | go run mkpost.go // Code generated by the command above; see README.md. DO NOT EDIT. //go:build arm64 && linux diff --git a/vendor/golang.org/x/sys/unix/ztypes_linux_loong64.go b/vendor/golang.org/x/sys/unix/ztypes_linux_loong64.go index 8fe4c522..187061f9 100644 --- a/vendor/golang.org/x/sys/unix/ztypes_linux_loong64.go +++ b/vendor/golang.org/x/sys/unix/ztypes_linux_loong64.go @@ -1,4 +1,4 @@ -// cgo -godefs -- -Wall -Werror -static -I/tmp/include linux/types.go | go run mkpost.go +// cgo -godefs -objdir=/tmp/loong64/cgo -- -Wall -Werror -static -I/tmp/loong64/include linux/types.go | go run mkpost.go // Code generated by the command above; see README.md. DO NOT EDIT. //go:build loong64 && linux diff --git a/vendor/golang.org/x/sys/unix/ztypes_linux_mips.go b/vendor/golang.org/x/sys/unix/ztypes_linux_mips.go index 11426a30..36912991 100644 --- a/vendor/golang.org/x/sys/unix/ztypes_linux_mips.go +++ b/vendor/golang.org/x/sys/unix/ztypes_linux_mips.go @@ -1,4 +1,4 @@ -// cgo -godefs -- -Wall -Werror -static -I/tmp/include linux/types.go | go run mkpost.go +// cgo -godefs -objdir=/tmp/mips/cgo -- -Wall -Werror -static -I/tmp/mips/include linux/types.go | go run mkpost.go // Code generated by the command above; see README.md. DO NOT EDIT. //go:build mips && linux diff --git a/vendor/golang.org/x/sys/unix/ztypes_linux_mips64.go b/vendor/golang.org/x/sys/unix/ztypes_linux_mips64.go index ad1c3b3d..7473468d 100644 --- a/vendor/golang.org/x/sys/unix/ztypes_linux_mips64.go +++ b/vendor/golang.org/x/sys/unix/ztypes_linux_mips64.go @@ -1,4 +1,4 @@ -// cgo -godefs -- -Wall -Werror -static -I/tmp/include linux/types.go | go run mkpost.go +// cgo -godefs -objdir=/tmp/mips64/cgo -- -Wall -Werror -static -I/tmp/mips64/include linux/types.go | go run mkpost.go // Code generated by the command above; see README.md. DO NOT EDIT. //go:build mips64 && linux diff --git a/vendor/golang.org/x/sys/unix/ztypes_linux_mips64le.go b/vendor/golang.org/x/sys/unix/ztypes_linux_mips64le.go index 15fd84e4..ed944852 100644 --- a/vendor/golang.org/x/sys/unix/ztypes_linux_mips64le.go +++ b/vendor/golang.org/x/sys/unix/ztypes_linux_mips64le.go @@ -1,4 +1,4 @@ -// cgo -godefs -- -Wall -Werror -static -I/tmp/include linux/types.go | go run mkpost.go +// cgo -godefs -objdir=/tmp/mips64le/cgo -- -Wall -Werror -static -I/tmp/mips64le/include linux/types.go | go run mkpost.go // Code generated by the command above; see README.md. DO NOT EDIT. //go:build mips64le && linux diff --git a/vendor/golang.org/x/sys/unix/ztypes_linux_mipsle.go b/vendor/golang.org/x/sys/unix/ztypes_linux_mipsle.go index 49c49825..0892a73a 100644 --- a/vendor/golang.org/x/sys/unix/ztypes_linux_mipsle.go +++ b/vendor/golang.org/x/sys/unix/ztypes_linux_mipsle.go @@ -1,4 +1,4 @@ -// cgo -godefs -- -Wall -Werror -static -I/tmp/include linux/types.go | go run mkpost.go +// cgo -godefs -objdir=/tmp/mipsle/cgo -- -Wall -Werror -static -I/tmp/mipsle/include linux/types.go | go run mkpost.go // Code generated by the command above; see README.md. DO NOT EDIT. //go:build mipsle && linux diff --git a/vendor/golang.org/x/sys/unix/ztypes_linux_ppc.go b/vendor/golang.org/x/sys/unix/ztypes_linux_ppc.go index cd36d0da..e1dd4833 100644 --- a/vendor/golang.org/x/sys/unix/ztypes_linux_ppc.go +++ b/vendor/golang.org/x/sys/unix/ztypes_linux_ppc.go @@ -1,4 +1,4 @@ -// cgo -godefs -- -Wall -Werror -static -I/tmp/include linux/types.go | go run mkpost.go +// cgo -godefs -objdir=/tmp/ppc/cgo -- -Wall -Werror -static -I/tmp/ppc/include linux/types.go | go run mkpost.go // Code generated by the command above; see README.md. DO NOT EDIT. //go:build ppc && linux diff --git a/vendor/golang.org/x/sys/unix/ztypes_linux_ppc64.go b/vendor/golang.org/x/sys/unix/ztypes_linux_ppc64.go index 8c6fce03..d9f654c7 100644 --- a/vendor/golang.org/x/sys/unix/ztypes_linux_ppc64.go +++ b/vendor/golang.org/x/sys/unix/ztypes_linux_ppc64.go @@ -1,4 +1,4 @@ -// cgo -godefs -- -Wall -Werror -static -I/tmp/include linux/types.go | go run mkpost.go +// cgo -godefs -objdir=/tmp/ppc64/cgo -- -Wall -Werror -static -I/tmp/ppc64/include linux/types.go | go run mkpost.go // Code generated by the command above; see README.md. DO NOT EDIT. //go:build ppc64 && linux diff --git a/vendor/golang.org/x/sys/unix/ztypes_linux_ppc64le.go b/vendor/golang.org/x/sys/unix/ztypes_linux_ppc64le.go index 20910f2a..74acda9f 100644 --- a/vendor/golang.org/x/sys/unix/ztypes_linux_ppc64le.go +++ b/vendor/golang.org/x/sys/unix/ztypes_linux_ppc64le.go @@ -1,4 +1,4 @@ -// cgo -godefs -- -Wall -Werror -static -I/tmp/include linux/types.go | go run mkpost.go +// cgo -godefs -objdir=/tmp/ppc64le/cgo -- -Wall -Werror -static -I/tmp/ppc64le/include linux/types.go | go run mkpost.go // Code generated by the command above; see README.md. DO NOT EDIT. //go:build ppc64le && linux diff --git a/vendor/golang.org/x/sys/unix/ztypes_linux_riscv64.go b/vendor/golang.org/x/sys/unix/ztypes_linux_riscv64.go index 71b7b333..50ebe69e 100644 --- a/vendor/golang.org/x/sys/unix/ztypes_linux_riscv64.go +++ b/vendor/golang.org/x/sys/unix/ztypes_linux_riscv64.go @@ -1,4 +1,4 @@ -// cgo -godefs -- -Wall -Werror -static -I/tmp/include linux/types.go | go run mkpost.go +// cgo -godefs -objdir=/tmp/riscv64/cgo -- -Wall -Werror -static -I/tmp/riscv64/include linux/types.go | go run mkpost.go // Code generated by the command above; see README.md. DO NOT EDIT. //go:build riscv64 && linux diff --git a/vendor/golang.org/x/sys/unix/ztypes_linux_s390x.go b/vendor/golang.org/x/sys/unix/ztypes_linux_s390x.go index 71184cc2..75b34c25 100644 --- a/vendor/golang.org/x/sys/unix/ztypes_linux_s390x.go +++ b/vendor/golang.org/x/sys/unix/ztypes_linux_s390x.go @@ -1,4 +1,4 @@ -// cgo -godefs -- -Wall -Werror -static -I/tmp/include -fsigned-char linux/types.go | go run mkpost.go +// cgo -godefs -objdir=/tmp/s390x/cgo -- -Wall -Werror -static -I/tmp/s390x/include -fsigned-char linux/types.go | go run mkpost.go // Code generated by the command above; see README.md. DO NOT EDIT. //go:build s390x && linux diff --git a/vendor/golang.org/x/sys/unix/ztypes_linux_sparc64.go b/vendor/golang.org/x/sys/unix/ztypes_linux_sparc64.go index 06156285..429c3bf7 100644 --- a/vendor/golang.org/x/sys/unix/ztypes_linux_sparc64.go +++ b/vendor/golang.org/x/sys/unix/ztypes_linux_sparc64.go @@ -1,4 +1,4 @@ -// cgo -godefs -- -Wall -Werror -static -I/tmp/include linux/types.go | go run mkpost.go +// cgo -godefs -objdir=/tmp/sparc64/cgo -- -Wall -Werror -static -I/tmp/sparc64/include linux/types.go | go run mkpost.go // Code generated by the command above; see README.md. DO NOT EDIT. //go:build sparc64 && linux diff --git a/vendor/golang.org/x/sys/windows/syscall_windows.go b/vendor/golang.org/x/sys/windows/syscall_windows.go index be3ec2bd..e2791381 100644 --- a/vendor/golang.org/x/sys/windows/syscall_windows.go +++ b/vendor/golang.org/x/sys/windows/syscall_windows.go @@ -417,6 +417,7 @@ func NewCallbackCDecl(fn interface{}) uintptr { //sys GetModuleInformation(process Handle, module Handle, modinfo *ModuleInfo, cb uint32) (err error) = psapi.GetModuleInformation //sys GetModuleFileNameEx(process Handle, module Handle, filename *uint16, size uint32) (err error) = psapi.GetModuleFileNameExW //sys GetModuleBaseName(process Handle, module Handle, baseName *uint16, size uint32) (err error) = psapi.GetModuleBaseNameW +//sys QueryWorkingSetEx(process Handle, pv uintptr, cb uint32) (err error) = psapi.QueryWorkingSetEx // NT Native APIs //sys rtlNtStatusToDosErrorNoTeb(ntstatus NTStatus) (ret syscall.Errno) = ntdll.RtlNtStatusToDosErrorNoTeb @@ -971,6 +972,32 @@ func (sa *SockaddrUnix) sockaddr() (unsafe.Pointer, int32, error) { return unsafe.Pointer(&sa.raw), sl, nil } +type RawSockaddrBth struct { + AddressFamily [2]byte + BtAddr [8]byte + ServiceClassId [16]byte + Port [4]byte +} + +type SockaddrBth struct { + BtAddr uint64 + ServiceClassId GUID + Port uint32 + + raw RawSockaddrBth +} + +func (sa *SockaddrBth) sockaddr() (unsafe.Pointer, int32, error) { + family := AF_BTH + sa.raw = RawSockaddrBth{ + AddressFamily: *(*[2]byte)(unsafe.Pointer(&family)), + BtAddr: *(*[8]byte)(unsafe.Pointer(&sa.BtAddr)), + Port: *(*[4]byte)(unsafe.Pointer(&sa.Port)), + ServiceClassId: *(*[16]byte)(unsafe.Pointer(&sa.ServiceClassId)), + } + return unsafe.Pointer(&sa.raw), int32(unsafe.Sizeof(sa.raw)), nil +} + func (rsa *RawSockaddrAny) Sockaddr() (Sockaddr, error) { switch rsa.Addr.Family { case AF_UNIX: @@ -1707,3 +1734,71 @@ func LoadResourceData(module, resInfo Handle) (data []byte, err error) { h.Cap = int(size) return } + +// PSAPI_WORKING_SET_EX_BLOCK contains extended working set information for a page. +type PSAPI_WORKING_SET_EX_BLOCK uint64 + +// Valid returns the validity of this page. +// If this bit is 1, the subsequent members are valid; otherwise they should be ignored. +func (b PSAPI_WORKING_SET_EX_BLOCK) Valid() bool { + return (b & 1) == 1 +} + +// ShareCount is the number of processes that share this page. The maximum value of this member is 7. +func (b PSAPI_WORKING_SET_EX_BLOCK) ShareCount() uint64 { + return b.intField(1, 3) +} + +// Win32Protection is the memory protection attributes of the page. For a list of values, see +// https://docs.microsoft.com/en-us/windows/win32/memory/memory-protection-constants +func (b PSAPI_WORKING_SET_EX_BLOCK) Win32Protection() uint64 { + return b.intField(4, 11) +} + +// Shared returns the shared status of this page. +// If this bit is 1, the page can be shared. +func (b PSAPI_WORKING_SET_EX_BLOCK) Shared() bool { + return (b & (1 << 15)) == 1 +} + +// Node is the NUMA node. The maximum value of this member is 63. +func (b PSAPI_WORKING_SET_EX_BLOCK) Node() uint64 { + return b.intField(16, 6) +} + +// Locked returns the locked status of this page. +// If this bit is 1, the virtual page is locked in physical memory. +func (b PSAPI_WORKING_SET_EX_BLOCK) Locked() bool { + return (b & (1 << 22)) == 1 +} + +// LargePage returns the large page status of this page. +// If this bit is 1, the page is a large page. +func (b PSAPI_WORKING_SET_EX_BLOCK) LargePage() bool { + return (b & (1 << 23)) == 1 +} + +// Bad returns the bad status of this page. +// If this bit is 1, the page is has been reported as bad. +func (b PSAPI_WORKING_SET_EX_BLOCK) Bad() bool { + return (b & (1 << 31)) == 1 +} + +// intField extracts an integer field in the PSAPI_WORKING_SET_EX_BLOCK union. +func (b PSAPI_WORKING_SET_EX_BLOCK) intField(start, length int) uint64 { + var mask PSAPI_WORKING_SET_EX_BLOCK + for pos := start; pos < start+length; pos++ { + mask |= (1 << pos) + } + + masked := b & mask + return uint64(masked >> start) +} + +// PSAPI_WORKING_SET_EX_INFORMATION contains extended working set information for a process. +type PSAPI_WORKING_SET_EX_INFORMATION struct { + // The virtual address. + VirtualAddress Pointer + // A PSAPI_WORKING_SET_EX_BLOCK union that indicates the attributes of the page at VirtualAddress. + VirtualAttributes PSAPI_WORKING_SET_EX_BLOCK +} diff --git a/vendor/golang.org/x/sys/windows/zsyscall_windows.go b/vendor/golang.org/x/sys/windows/zsyscall_windows.go index 678262cd..52d4742c 100644 --- a/vendor/golang.org/x/sys/windows/zsyscall_windows.go +++ b/vendor/golang.org/x/sys/windows/zsyscall_windows.go @@ -408,6 +408,7 @@ var ( procGetModuleBaseNameW = modpsapi.NewProc("GetModuleBaseNameW") procGetModuleFileNameExW = modpsapi.NewProc("GetModuleFileNameExW") procGetModuleInformation = modpsapi.NewProc("GetModuleInformation") + procQueryWorkingSetEx = modpsapi.NewProc("QueryWorkingSetEx") procSubscribeServiceChangeNotifications = modsechost.NewProc("SubscribeServiceChangeNotifications") procUnsubscribeServiceChangeNotifications = modsechost.NewProc("UnsubscribeServiceChangeNotifications") procGetUserNameExW = modsecur32.NewProc("GetUserNameExW") @@ -3504,6 +3505,14 @@ func GetModuleInformation(process Handle, module Handle, modinfo *ModuleInfo, cb return } +func QueryWorkingSetEx(process Handle, pv uintptr, cb uint32) (err error) { + r1, _, e1 := syscall.Syscall(procQueryWorkingSetEx.Addr(), 3, uintptr(process), uintptr(pv), uintptr(cb)) + if r1 == 0 { + err = errnoErr(e1) + } + return +} + func SubscribeServiceChangeNotifications(service Handle, eventType uint32, callback uintptr, callbackCtx uintptr, subscription *uintptr) (ret error) { ret = procSubscribeServiceChangeNotifications.Find() if ret != nil { diff --git a/vendor/modules.txt b/vendor/modules.txt index 5c3ca424..0ae2b93a 100644 --- a/vendor/modules.txt +++ b/vendor/modules.txt @@ -26,6 +26,28 @@ github.com/cloudflare/brotli-go/brotli github.com/cloudflare/brotli-go/common github.com/cloudflare/brotli-go/dec github.com/cloudflare/brotli-go/enc +# github.com/cloudflare/circl v1.2.1-0.20220809205628-0a9554f37a47 +## explicit; go 1.16 +github.com/cloudflare/circl/dh/x25519 +github.com/cloudflare/circl/dh/x448 +github.com/cloudflare/circl/internal/conv +github.com/cloudflare/circl/internal/sha3 +github.com/cloudflare/circl/kem +github.com/cloudflare/circl/kem/hybrid +github.com/cloudflare/circl/kem/kyber/kyber1024 +github.com/cloudflare/circl/kem/kyber/kyber512 +github.com/cloudflare/circl/kem/kyber/kyber768 +github.com/cloudflare/circl/math/fp25519 +github.com/cloudflare/circl/math/fp448 +github.com/cloudflare/circl/pke/kyber/internal/common +github.com/cloudflare/circl/pke/kyber/internal/common/params +github.com/cloudflare/circl/pke/kyber/kyber1024 +github.com/cloudflare/circl/pke/kyber/kyber1024/internal +github.com/cloudflare/circl/pke/kyber/kyber512 +github.com/cloudflare/circl/pke/kyber/kyber512/internal +github.com/cloudflare/circl/pke/kyber/kyber768 +github.com/cloudflare/circl/pke/kyber/kyber768/internal +github.com/cloudflare/circl/simd/keccakf1600 # github.com/cloudflare/golibs v0.0.0-20170913112048-333127dbecfc ## explicit github.com/cloudflare/golibs/lrucache @@ -171,10 +193,10 @@ github.com/marten-seemann/qtls-go1-16 # github.com/marten-seemann/qtls-go1-17 v0.1.2 ## explicit; go 1.17 github.com/marten-seemann/qtls-go1-17 -# github.com/marten-seemann/qtls-go1-18 v0.1.2 +# github.com/marten-seemann/qtls-go1-18 v0.1.2 => github.com/cloudflare/qtls-pq v0.0.0-20220824105406-fb955667e0af ## explicit; go 1.18 github.com/marten-seemann/qtls-go1-18 -# github.com/marten-seemann/qtls-go1-19 v0.1.0-beta.1 +# github.com/marten-seemann/qtls-go1-19 v0.1.0-beta.1 => github.com/cloudflare/qtls-pq v0.0.0-20220824104809-96561a41e0af ## explicit; go 1.19 github.com/marten-seemann/qtls-go1-19 # github.com/mattn/go-colorable v0.1.8 @@ -320,7 +342,7 @@ go.opentelemetry.io/proto/otlp/trace/v1 go.uber.org/automaxprocs/internal/cgroups go.uber.org/automaxprocs/internal/runtime go.uber.org/automaxprocs/maxprocs -# golang.org/x/crypto v0.0.0-20220427172511-eb4f295cb31f +# golang.org/x/crypto v0.0.0-20220722155217-630584e8d5aa ## explicit; go 1.17 golang.org/x/crypto/blake2b golang.org/x/crypto/blowfish @@ -371,7 +393,7 @@ golang.org/x/oauth2/internal # golang.org/x/sync v0.0.0-20210220032951-036812b2e83c ## explicit golang.org/x/sync/errgroup -# golang.org/x/sys v0.0.0-20220728004956-3c1f35247d10 +# golang.org/x/sys v0.0.0-20220808155132-1c4a2a72c664 ## explicit; go 1.17 golang.org/x/sys/cpu golang.org/x/sys/execabs @@ -554,3 +576,5 @@ zombiezen.com/go/capnproto2/std/capnp/rpc # github.com/lucas-clemente/quic-go => github.com/chungthuang/quic-go v0.27.1-0.20220809135021-ca330f1dec9f # github.com/prometheus/golang_client => github.com/prometheus/golang_client v1.12.1 # gopkg.in/yaml.v3 => gopkg.in/yaml.v3 v3.0.1 +# github.com/marten-seemann/qtls-go1-18 => github.com/cloudflare/qtls-pq v0.0.0-20220824105406-fb955667e0af +# github.com/marten-seemann/qtls-go1-19 => github.com/cloudflare/qtls-pq v0.0.0-20220824104809-96561a41e0af