105 lines
3.4 KiB
Go
105 lines
3.4 KiB
Go
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package x448
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import (
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fp "github.com/cloudflare/circl/math/fp448"
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)
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// ladderJoye calculates a fixed-point multiplication with the generator point.
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// The algorithm is the right-to-left Joye's ladder as described
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// in "How to precompute a ladder" in SAC'2017.
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func ladderJoye(k *Key) {
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w := [5]fp.Elt{} // [mu,x1,z1,x2,z2] order must be preserved.
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w[1] = fp.Elt{ // x1 = S
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0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
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0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
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0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
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0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff,
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0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
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0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
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0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
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}
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fp.SetOne(&w[2]) // z1 = 1
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w[3] = fp.Elt{ // x2 = G-S
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0x20, 0x27, 0x9d, 0xc9, 0x7d, 0x19, 0xb1, 0xac,
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0xf8, 0xba, 0x69, 0x1c, 0xff, 0x33, 0xac, 0x23,
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0x51, 0x1b, 0xce, 0x3a, 0x64, 0x65, 0xbd, 0xf1,
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0x23, 0xf8, 0xc1, 0x84, 0x9d, 0x45, 0x54, 0x29,
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0x67, 0xb9, 0x81, 0x1c, 0x03, 0xd1, 0xcd, 0xda,
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0x7b, 0xeb, 0xff, 0x1a, 0x88, 0x03, 0xcf, 0x3a,
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0x42, 0x44, 0x32, 0x01, 0x25, 0xb7, 0xfa, 0xf0,
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}
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fp.SetOne(&w[4]) // z2 = 1
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const n = 448
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const h = 2
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swap := uint(1)
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for s := 0; s < n-h; s++ {
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i := (s + h) / 8
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j := (s + h) % 8
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bit := uint((k[i] >> uint(j)) & 1)
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copy(w[0][:], tableGenerator[s*Size:(s+1)*Size])
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diffAdd(&w, swap^bit)
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swap = bit
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}
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for s := 0; s < h; s++ {
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double(&w[1], &w[2])
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}
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toAffine((*[fp.Size]byte)(k), &w[1], &w[2])
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}
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// ladderMontgomery calculates a generic scalar point multiplication
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// The algorithm implemented is the left-to-right Montgomery's ladder.
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func ladderMontgomery(k, xP *Key) {
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w := [5]fp.Elt{} // [x1, x2, z2, x3, z3] order must be preserved.
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w[0] = *(*fp.Elt)(xP) // x1 = xP
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fp.SetOne(&w[1]) // x2 = 1
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w[3] = *(*fp.Elt)(xP) // x3 = xP
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fp.SetOne(&w[4]) // z3 = 1
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move := uint(0)
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for s := 448 - 1; s >= 0; s-- {
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i := s / 8
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j := s % 8
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bit := uint((k[i] >> uint(j)) & 1)
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ladderStep(&w, move^bit)
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move = bit
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}
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toAffine((*[fp.Size]byte)(k), &w[1], &w[2])
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}
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func toAffine(k *[fp.Size]byte, x, z *fp.Elt) {
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fp.Inv(z, z)
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fp.Mul(x, x, z)
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_ = fp.ToBytes(k[:], x)
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}
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var lowOrderPoints = [3]fp.Elt{
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{ /* (0,_,1) point of order 2 on Curve448 */
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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},
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{ /* (1,_,1) a point of order 4 on the twist of Curve448 */
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0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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},
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{ /* (-1,_,1) point of order 4 on Curve448 */
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0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
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0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
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0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
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0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff,
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0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
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0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
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0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
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},
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}
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