status-go/vendor/github.com/agl/ed25519/extra25519/extra25519.go

341 lines
11 KiB
Go

// Copyright 2013 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 extra25519
import (
"crypto/sha512"
"github.com/agl/ed25519/edwards25519"
)
// PrivateKeyToCurve25519 converts an ed25519 private key into a corresponding
// curve25519 private key such that the resulting curve25519 public key will
// equal the result from PublicKeyToCurve25519.
func PrivateKeyToCurve25519(curve25519Private *[32]byte, privateKey *[64]byte) {
h := sha512.New()
h.Write(privateKey[:32])
digest := h.Sum(nil)
digest[0] &= 248
digest[31] &= 127
digest[31] |= 64
copy(curve25519Private[:], digest)
}
func edwardsToMontgomeryX(outX, y *edwards25519.FieldElement) {
// We only need the x-coordinate of the curve25519 point, which I'll
// call u. The isomorphism is u=(y+1)/(1-y), since y=Y/Z, this gives
// u=(Y+Z)/(Z-Y). We know that Z=1, thus u=(Y+1)/(1-Y).
var oneMinusY edwards25519.FieldElement
edwards25519.FeOne(&oneMinusY)
edwards25519.FeSub(&oneMinusY, &oneMinusY, y)
edwards25519.FeInvert(&oneMinusY, &oneMinusY)
edwards25519.FeOne(outX)
edwards25519.FeAdd(outX, outX, y)
edwards25519.FeMul(outX, outX, &oneMinusY)
}
// PublicKeyToCurve25519 converts an Ed25519 public key into the curve25519
// public key that would be generated from the same private key.
func PublicKeyToCurve25519(curve25519Public *[32]byte, publicKey *[32]byte) bool {
var A edwards25519.ExtendedGroupElement
if !A.FromBytes(publicKey) {
return false
}
// A.Z = 1 as a postcondition of FromBytes.
var x edwards25519.FieldElement
edwardsToMontgomeryX(&x, &A.Y)
edwards25519.FeToBytes(curve25519Public, &x)
return true
}
// sqrtMinusAPlus2 is sqrt(-(486662+2))
var sqrtMinusAPlus2 = edwards25519.FieldElement{
-12222970, -8312128, -11511410, 9067497, -15300785, -241793, 25456130, 14121551, -12187136, 3972024,
}
// sqrtMinusHalf is sqrt(-1/2)
var sqrtMinusHalf = edwards25519.FieldElement{
-17256545, 3971863, 28865457, -1750208, 27359696, -16640980, 12573105, 1002827, -163343, 11073975,
}
// halfQMinus1Bytes is (2^255-20)/2 expressed in little endian form.
var halfQMinus1Bytes = [32]byte{
0xf6, 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, 0x3f,
}
// feBytesLess returns one if a <= b and zero otherwise.
func feBytesLE(a, b *[32]byte) int32 {
equalSoFar := int32(-1)
greater := int32(0)
for i := uint(31); i < 32; i-- {
x := int32(a[i])
y := int32(b[i])
greater = (^equalSoFar & greater) | (equalSoFar & ((x - y) >> 31))
equalSoFar = equalSoFar & (((x ^ y) - 1) >> 31)
}
return int32(^equalSoFar & 1 & greater)
}
// ScalarBaseMult computes a curve25519 public key from a private key and also
// a uniform representative for that public key. Note that this function will
// fail and return false for about half of private keys.
// See http://elligator.cr.yp.to/elligator-20130828.pdf.
func ScalarBaseMult(publicKey, representative, privateKey *[32]byte) bool {
var maskedPrivateKey [32]byte
copy(maskedPrivateKey[:], privateKey[:])
maskedPrivateKey[0] &= 248
maskedPrivateKey[31] &= 127
maskedPrivateKey[31] |= 64
var A edwards25519.ExtendedGroupElement
edwards25519.GeScalarMultBase(&A, &maskedPrivateKey)
var inv1 edwards25519.FieldElement
edwards25519.FeSub(&inv1, &A.Z, &A.Y)
edwards25519.FeMul(&inv1, &inv1, &A.X)
edwards25519.FeInvert(&inv1, &inv1)
var t0, u edwards25519.FieldElement
edwards25519.FeMul(&u, &inv1, &A.X)
edwards25519.FeAdd(&t0, &A.Y, &A.Z)
edwards25519.FeMul(&u, &u, &t0)
var v edwards25519.FieldElement
edwards25519.FeMul(&v, &t0, &inv1)
edwards25519.FeMul(&v, &v, &A.Z)
edwards25519.FeMul(&v, &v, &sqrtMinusAPlus2)
var b edwards25519.FieldElement
edwards25519.FeAdd(&b, &u, &edwards25519.A)
var c, b3, b7, b8 edwards25519.FieldElement
edwards25519.FeSquare(&b3, &b) // 2
edwards25519.FeMul(&b3, &b3, &b) // 3
edwards25519.FeSquare(&c, &b3) // 6
edwards25519.FeMul(&b7, &c, &b) // 7
edwards25519.FeMul(&b8, &b7, &b) // 8
edwards25519.FeMul(&c, &b7, &u)
q58(&c, &c)
var chi edwards25519.FieldElement
edwards25519.FeSquare(&chi, &c)
edwards25519.FeSquare(&chi, &chi)
edwards25519.FeSquare(&t0, &u)
edwards25519.FeMul(&chi, &chi, &t0)
edwards25519.FeSquare(&t0, &b7) // 14
edwards25519.FeMul(&chi, &chi, &t0)
edwards25519.FeNeg(&chi, &chi)
var chiBytes [32]byte
edwards25519.FeToBytes(&chiBytes, &chi)
// chi[1] is either 0 or 0xff
if chiBytes[1] == 0xff {
return false
}
// Calculate r1 = sqrt(-u/(2*(u+A)))
var r1 edwards25519.FieldElement
edwards25519.FeMul(&r1, &c, &u)
edwards25519.FeMul(&r1, &r1, &b3)
edwards25519.FeMul(&r1, &r1, &sqrtMinusHalf)
var maybeSqrtM1 edwards25519.FieldElement
edwards25519.FeSquare(&t0, &r1)
edwards25519.FeMul(&t0, &t0, &b)
edwards25519.FeAdd(&t0, &t0, &t0)
edwards25519.FeAdd(&t0, &t0, &u)
edwards25519.FeOne(&maybeSqrtM1)
edwards25519.FeCMove(&maybeSqrtM1, &edwards25519.SqrtM1, edwards25519.FeIsNonZero(&t0))
edwards25519.FeMul(&r1, &r1, &maybeSqrtM1)
// Calculate r = sqrt(-(u+A)/(2u))
var r edwards25519.FieldElement
edwards25519.FeSquare(&t0, &c) // 2
edwards25519.FeMul(&t0, &t0, &c) // 3
edwards25519.FeSquare(&t0, &t0) // 6
edwards25519.FeMul(&r, &t0, &c) // 7
edwards25519.FeSquare(&t0, &u) // 2
edwards25519.FeMul(&t0, &t0, &u) // 3
edwards25519.FeMul(&r, &r, &t0)
edwards25519.FeSquare(&t0, &b8) // 16
edwards25519.FeMul(&t0, &t0, &b8) // 24
edwards25519.FeMul(&t0, &t0, &b) // 25
edwards25519.FeMul(&r, &r, &t0)
edwards25519.FeMul(&r, &r, &sqrtMinusHalf)
edwards25519.FeSquare(&t0, &r)
edwards25519.FeMul(&t0, &t0, &u)
edwards25519.FeAdd(&t0, &t0, &t0)
edwards25519.FeAdd(&t0, &t0, &b)
edwards25519.FeOne(&maybeSqrtM1)
edwards25519.FeCMove(&maybeSqrtM1, &edwards25519.SqrtM1, edwards25519.FeIsNonZero(&t0))
edwards25519.FeMul(&r, &r, &maybeSqrtM1)
var vBytes [32]byte
edwards25519.FeToBytes(&vBytes, &v)
vInSquareRootImage := feBytesLE(&vBytes, &halfQMinus1Bytes)
edwards25519.FeCMove(&r, &r1, vInSquareRootImage)
edwards25519.FeToBytes(publicKey, &u)
edwards25519.FeToBytes(representative, &r)
return true
}
// q58 calculates out = z^((p-5)/8).
func q58(out, z *edwards25519.FieldElement) {
var t1, t2, t3 edwards25519.FieldElement
var i int
edwards25519.FeSquare(&t1, z) // 2^1
edwards25519.FeMul(&t1, &t1, z) // 2^1 + 2^0
edwards25519.FeSquare(&t1, &t1) // 2^2 + 2^1
edwards25519.FeSquare(&t2, &t1) // 2^3 + 2^2
edwards25519.FeSquare(&t2, &t2) // 2^4 + 2^3
edwards25519.FeMul(&t2, &t2, &t1) // 4,3,2,1
edwards25519.FeMul(&t1, &t2, z) // 4..0
edwards25519.FeSquare(&t2, &t1) // 5..1
for i = 1; i < 5; i++ { // 9,8,7,6,5
edwards25519.FeSquare(&t2, &t2)
}
edwards25519.FeMul(&t1, &t2, &t1) // 9,8,7,6,5,4,3,2,1,0
edwards25519.FeSquare(&t2, &t1) // 10..1
for i = 1; i < 10; i++ { // 19..10
edwards25519.FeSquare(&t2, &t2)
}
edwards25519.FeMul(&t2, &t2, &t1) // 19..0
edwards25519.FeSquare(&t3, &t2) // 20..1
for i = 1; i < 20; i++ { // 39..20
edwards25519.FeSquare(&t3, &t3)
}
edwards25519.FeMul(&t2, &t3, &t2) // 39..0
edwards25519.FeSquare(&t2, &t2) // 40..1
for i = 1; i < 10; i++ { // 49..10
edwards25519.FeSquare(&t2, &t2)
}
edwards25519.FeMul(&t1, &t2, &t1) // 49..0
edwards25519.FeSquare(&t2, &t1) // 50..1
for i = 1; i < 50; i++ { // 99..50
edwards25519.FeSquare(&t2, &t2)
}
edwards25519.FeMul(&t2, &t2, &t1) // 99..0
edwards25519.FeSquare(&t3, &t2) // 100..1
for i = 1; i < 100; i++ { // 199..100
edwards25519.FeSquare(&t3, &t3)
}
edwards25519.FeMul(&t2, &t3, &t2) // 199..0
edwards25519.FeSquare(&t2, &t2) // 200..1
for i = 1; i < 50; i++ { // 249..50
edwards25519.FeSquare(&t2, &t2)
}
edwards25519.FeMul(&t1, &t2, &t1) // 249..0
edwards25519.FeSquare(&t1, &t1) // 250..1
edwards25519.FeSquare(&t1, &t1) // 251..2
edwards25519.FeMul(out, &t1, z) // 251..2,0
}
// chi calculates out = z^((p-1)/2). The result is either 1, 0, or -1 depending
// on whether z is a non-zero square, zero, or a non-square.
func chi(out, z *edwards25519.FieldElement) {
var t0, t1, t2, t3 edwards25519.FieldElement
var i int
edwards25519.FeSquare(&t0, z) // 2^1
edwards25519.FeMul(&t1, &t0, z) // 2^1 + 2^0
edwards25519.FeSquare(&t0, &t1) // 2^2 + 2^1
edwards25519.FeSquare(&t2, &t0) // 2^3 + 2^2
edwards25519.FeSquare(&t2, &t2) // 4,3
edwards25519.FeMul(&t2, &t2, &t0) // 4,3,2,1
edwards25519.FeMul(&t1, &t2, z) // 4..0
edwards25519.FeSquare(&t2, &t1) // 5..1
for i = 1; i < 5; i++ { // 9,8,7,6,5
edwards25519.FeSquare(&t2, &t2)
}
edwards25519.FeMul(&t1, &t2, &t1) // 9,8,7,6,5,4,3,2,1,0
edwards25519.FeSquare(&t2, &t1) // 10..1
for i = 1; i < 10; i++ { // 19..10
edwards25519.FeSquare(&t2, &t2)
}
edwards25519.FeMul(&t2, &t2, &t1) // 19..0
edwards25519.FeSquare(&t3, &t2) // 20..1
for i = 1; i < 20; i++ { // 39..20
edwards25519.FeSquare(&t3, &t3)
}
edwards25519.FeMul(&t2, &t3, &t2) // 39..0
edwards25519.FeSquare(&t2, &t2) // 40..1
for i = 1; i < 10; i++ { // 49..10
edwards25519.FeSquare(&t2, &t2)
}
edwards25519.FeMul(&t1, &t2, &t1) // 49..0
edwards25519.FeSquare(&t2, &t1) // 50..1
for i = 1; i < 50; i++ { // 99..50
edwards25519.FeSquare(&t2, &t2)
}
edwards25519.FeMul(&t2, &t2, &t1) // 99..0
edwards25519.FeSquare(&t3, &t2) // 100..1
for i = 1; i < 100; i++ { // 199..100
edwards25519.FeSquare(&t3, &t3)
}
edwards25519.FeMul(&t2, &t3, &t2) // 199..0
edwards25519.FeSquare(&t2, &t2) // 200..1
for i = 1; i < 50; i++ { // 249..50
edwards25519.FeSquare(&t2, &t2)
}
edwards25519.FeMul(&t1, &t2, &t1) // 249..0
edwards25519.FeSquare(&t1, &t1) // 250..1
for i = 1; i < 4; i++ { // 253..4
edwards25519.FeSquare(&t1, &t1)
}
edwards25519.FeMul(out, &t1, &t0) // 253..4,2,1
}
// RepresentativeToPublicKey converts a uniform representative value for a
// curve25519 public key, as produced by ScalarBaseMult, to a curve25519 public
// key.
func RepresentativeToPublicKey(publicKey, representative *[32]byte) {
var rr2, v, e edwards25519.FieldElement
edwards25519.FeFromBytes(&rr2, representative)
edwards25519.FeSquare2(&rr2, &rr2)
rr2[0]++
edwards25519.FeInvert(&rr2, &rr2)
edwards25519.FeMul(&v, &edwards25519.A, &rr2)
edwards25519.FeNeg(&v, &v)
var v2, v3 edwards25519.FieldElement
edwards25519.FeSquare(&v2, &v)
edwards25519.FeMul(&v3, &v, &v2)
edwards25519.FeAdd(&e, &v3, &v)
edwards25519.FeMul(&v2, &v2, &edwards25519.A)
edwards25519.FeAdd(&e, &v2, &e)
chi(&e, &e)
var eBytes [32]byte
edwards25519.FeToBytes(&eBytes, &e)
// eBytes[1] is either 0 (for e = 1) or 0xff (for e = -1)
eIsMinus1 := int32(eBytes[1]) & 1
var negV edwards25519.FieldElement
edwards25519.FeNeg(&negV, &v)
edwards25519.FeCMove(&v, &negV, eIsMinus1)
edwards25519.FeZero(&v2)
edwards25519.FeCMove(&v2, &edwards25519.A, eIsMinus1)
edwards25519.FeSub(&v, &v, &v2)
edwards25519.FeToBytes(publicKey, &v)
}