97 lines
3.0 KiB
Go
97 lines
3.0 KiB
Go
package x25519
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import (
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fp "github.com/cloudflare/circl/math/fp25519"
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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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fp.SetOne(&w[1]) // x1 = 1
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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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0xbd, 0xaa, 0x2f, 0xc8, 0xfe, 0xe1, 0x94, 0x7e,
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0xf8, 0xed, 0xb2, 0x14, 0xae, 0x95, 0xf0, 0xbb,
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0xe2, 0x48, 0x5d, 0x23, 0xb9, 0xa0, 0xc7, 0xad,
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0x34, 0xab, 0x7c, 0xe2, 0xee, 0xcd, 0xae, 0x1e,
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}
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fp.SetOne(&w[4]) // z2 = 1
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const n = 255
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const h = 3
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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 := 255 - 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 = [5]fp.Elt{
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{ /* (0,_,1) point of order 2 on Curve25519 */
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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 Curve25519 */
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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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},
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{ /* (x,_,1) first point of order 8 on Curve25519 */
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0xe0, 0xeb, 0x7a, 0x7c, 0x3b, 0x41, 0xb8, 0xae,
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0x16, 0x56, 0xe3, 0xfa, 0xf1, 0x9f, 0xc4, 0x6a,
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0xda, 0x09, 0x8d, 0xeb, 0x9c, 0x32, 0xb1, 0xfd,
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0x86, 0x62, 0x05, 0x16, 0x5f, 0x49, 0xb8, 0x00,
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},
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{ /* (x,_,1) second point of order 8 on Curve25519 */
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0x5f, 0x9c, 0x95, 0xbc, 0xa3, 0x50, 0x8c, 0x24,
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0xb1, 0xd0, 0xb1, 0x55, 0x9c, 0x83, 0xef, 0x5b,
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0x04, 0x44, 0x5c, 0xc4, 0x58, 0x1c, 0x8e, 0x86,
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0xd8, 0x22, 0x4e, 0xdd, 0xd0, 0x9f, 0x11, 0x57,
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},
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{ /* (-1,_,1) a point of order 4 on the twist of Curve25519 */
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0xec, 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, 0xff, 0xff, 0xff, 0x7f,
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},
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}
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