// 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)
}
// Verify checks whether the message has a valid signature.
func Verify(publicKey [32]byte, message []byte, signature *[64]byte) bool {
publicKey[31] &= 0x7F
/* Convert the Curve25519 public key into an Ed25519 public key. In
particular, convert Curve25519's "montgomery" x-coordinate into an
Ed25519 "edwards" y-coordinate:
ed_y = (mont_x - 1) / (mont_x + 1)
NOTE: mont_x=-1 is converted to ed_y=0 since fe_invert is mod-exp
Then move the sign bit into the pubkey from the signature.
*/
var edY, one, montX, montXMinusOne, montXPlusOne edwards25519.FieldElement
edwards25519.FeFromBytes(&montX, &publicKey)
edwards25519.FeOne(&one)
edwards25519.FeSub(&montXMinusOne, &montX, &one)
edwards25519.FeAdd(&montXPlusOne, &montX, &one)
edwards25519.FeInvert(&montXPlusOne, &montXPlusOne)
edwards25519.FeMul(&edY, &montXMinusOne, &montXPlusOne)
var A_ed [32]byte
edwards25519.FeToBytes(&A_ed, &edY)
A_ed[31] |= signature[63] & 0x80
signature[63] &= 0x7F
return ed25519.Verify(&A_ed, message, signature)
}