// schnorrRecover recovers a public key using a signature, hash function,
// and message. It also attempts to verify the signature against the
// regenerated public key.
func schnorrRecover(curve *secp256k1.KoblitzCurve, sig, msg []byte,
hashFunc func([]byte) []byte) (*secp256k1.PublicKey, bool, error) {
if len(msg) != scalarSize {
str := fmt.Sprintf("wrong size for message (got %v, want %v)",
len(msg), scalarSize)
return nil, false, schnorrError(ErrBadInputSize, str)
}
if len(sig) != SignatureSize {
str := fmt.Sprintf("wrong size for signature (got %v, want %v)",
len(sig), SignatureSize)
return nil, false, schnorrError(ErrBadInputSize, str)
}
sigR := sig[:32]
sigS := sig[32:]
sigRCopy := make([]byte, scalarSize, scalarSize)
copy(sigRCopy, sigR)
toHash := append(sigRCopy, msg...)
h := hashFunc(toHash)
hBig := new(big.Int).SetBytes(h)
// If the hash ends up larger than the order of the curve, abort.
// Same thing for hash == 0 (as unlikely as that is...).
if hBig.Cmp(curve.N) >= 0 {
str := fmt.Sprintf("hash of (R || m) too big")
return nil, false, schnorrError(ErrSchnorrHashValue, str)
}
if hBig.Cmp(bigZero) == 0 {
str := fmt.Sprintf("hash of (R || m) is zero value")
return nil, false, schnorrError(ErrSchnorrHashValue, str)
}
// Convert s to big int.
sBig := EncodedBytesToBigInt(copyBytes(sigS))
// We also can't have s greater than the order of the curve.
if sBig.Cmp(curve.N) >= 0 {
str := fmt.Sprintf("s value is too big")
return nil, false, schnorrError(ErrInputValue, str)
}
// r can't be larger than the curve prime.
rBig := EncodedBytesToBigInt(copyBytes(sigR))
if rBig.Cmp(curve.P) == 1 {
str := fmt.Sprintf("given R was greater than curve prime")
return nil, false, schnorrError(ErrBadSigRNotOnCurve, str)
}
// Decompress the Y value. We know that the first bit must
// be even. Use the PublicKey struct to make it easier.
compressedPoint := make([]byte, PubKeyBytesLen, PubKeyBytesLen)
compressedPoint[0] = pubkeyCompressed
copy(compressedPoint[1:], sigR)
rPoint, err := secp256k1.ParsePubKey(compressedPoint, curve)
if err != nil {
str := fmt.Sprintf("bad r point")
return nil, false, schnorrError(ErrRegenerateRPoint, str)
}
// Get the inverse of the hash.
hInv := new(big.Int).ModInverse(hBig, curve.N)
hInv.Mod(hInv, curve.N)
// Negate s.
sBig.Sub(curve.N, sBig)
sBig.Mod(sBig, curve.N)
// s' = -s * inverse(h).
sBig.Mul(sBig, hInv)
sBig.Mod(sBig, curve.N)
// Q = h^(-1)R + s'G
lx, ly := curve.ScalarMult(rPoint.GetX(), rPoint.GetY(), hInv.Bytes())
rx, ry := curve.ScalarBaseMult(sBig.Bytes())
pkx, pky := curve.Add(lx, ly, rx, ry)
// Check if the public key is on the curve.
if !curve.IsOnCurve(pkx, pky) {
str := fmt.Sprintf("pubkey not on curve")
return nil, false, schnorrError(ErrPubKeyOffCurve, str)
}
pubkey := secp256k1.NewPublicKey(curve, pkx, pky)
// Verify this signature. Slow, lots of double checks, could be more
// cheaply implemented as
// hQ + sG - R == 0
// which this function checks.
// This will sometimes pass even for corrupted signatures, but
// this shouldn't be a concern because whoever is using the
// results should be checking the returned public key against
// some known one anyway. In the case of these Schnorr signatures,
// relatively high numbers of corrupted signatures (50-70%)
// seem to produce valid pubkeys and valid signatures.
_, err = schnorrVerify(curve, sig, pubkey, msg, hashFunc)
if err != nil {
str := fmt.Sprintf("pubkey/sig pair could not be validated")
return nil, false, schnorrError(ErrRegenSig, str)
}
return pubkey, true, nil
}
// schnorrVerify is the internal function for verification of a secp256k1
// Schnorr signature. A secure hash function may be passed for the calculation
// of r.
// This is identical to the Schnorr verification function found in libsecp256k1:
// https://github.com/bitcoin/secp256k1/tree/master/src/modules/schnorr
func schnorrVerify(curve *secp256k1.KoblitzCurve, sig []byte,
pubkey *secp256k1.PublicKey, msg []byte, hashFunc func([]byte) []byte) (bool,
error) {
if len(msg) != scalarSize {
str := fmt.Sprintf("wrong size for message (got %v, want %v)",
len(msg), scalarSize)
return false, schnorrError(ErrBadInputSize, str)
}
if len(sig) != SignatureSize {
str := fmt.Sprintf("wrong size for signature (got %v, want %v)",
len(sig), SignatureSize)
return false, schnorrError(ErrBadInputSize, str)
}
if pubkey == nil {
str := fmt.Sprintf("nil pubkey")
return false, schnorrError(ErrInputValue, str)
}
if !curve.IsOnCurve(pubkey.GetX(), pubkey.GetY()) {
str := fmt.Sprintf("pubkey point is not on curve")
return false, schnorrError(ErrPointNotOnCurve, str)
}
sigR := sig[:32]
sigS := sig[32:]
sigRCopy := make([]byte, scalarSize, scalarSize)
copy(sigRCopy, sigR)
toHash := append(sigRCopy, msg...)
h := hashFunc(toHash)
hBig := new(big.Int).SetBytes(h)
// If the hash ends up larger than the order of the curve, abort.
// Same thing for hash == 0 (as unlikely as that is...).
if hBig.Cmp(curve.N) >= 0 {
str := fmt.Sprintf("hash of (R || m) too big")
return false, schnorrError(ErrSchnorrHashValue, str)
}
if hBig.Cmp(bigZero) == 0 {
str := fmt.Sprintf("hash of (R || m) is zero value")
return false, schnorrError(ErrSchnorrHashValue, str)
}
// Convert s to big int.
sBig := EncodedBytesToBigInt(copyBytes(sigS))
// We also can't have s greater than the order of the curve.
if sBig.Cmp(curve.N) >= 0 {
str := fmt.Sprintf("s value is too big")
return false, schnorrError(ErrInputValue, str)
}
// r can't be larger than the curve prime.
rBig := EncodedBytesToBigInt(copyBytes(sigR))
if rBig.Cmp(curve.P) == 1 {
str := fmt.Sprintf("given R was greater than curve prime")
return false, schnorrError(ErrBadSigRNotOnCurve, str)
}
// r' = hQ + sG
lx, ly := curve.ScalarMult(pubkey.GetX(), pubkey.GetY(), h)
rx, ry := curve.ScalarBaseMult(sigS)
rlx, rly := curve.Add(lx, ly, rx, ry)
if rly.Bit(0) == 1 {
str := fmt.Sprintf("calculated R y-value was odd")
return false, schnorrError(ErrBadSigRYValue, str)
}
if !curve.IsOnCurve(rlx, rly) {
str := fmt.Sprintf("calculated R point was not on curve")
return false, schnorrError(ErrBadSigRNotOnCurve, str)
}
rlxB := BigIntToEncodedBytes(rlx)
// r == r' --> valid signature
if !bytes.Equal(sigR, rlxB[:]) {
str := fmt.Sprintf("calculated R point was not given R")
return false, schnorrError(ErrUnequalRValues, str)
}
return true, nil
}