Example #1
0
// 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
}
Example #2
0
// 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
}