Golang edwards25519.ExtendedGroupElement类代码示例

// EncodedBytesToBigIntPoint converts a 32 byte representation of a point
// on the elliptical curve into a big integer point. It returns an error
// if the point does not fall on the curve.
func (curve *TwistedEdwardsCurve) EncodedBytesToBigIntPoint(s *[32]byte) (*big.Int,
	*big.Int, error) {
	sCopy := new([32]byte)
	for i := 0; i < fieldIntSize; i++ {
		sCopy[i] = s[i]
	}

	xIsNegBytes := sCopy[31]>>7 == 1
	p := new(edwards25519.ExtendedGroupElement)
	if p.FromBytes(sCopy) == false {
		return nil, nil, fmt.Errorf("point not on curve")
	}

	// Normalize the X and Y coordinates in affine space.
	x, y, isNegative := curve.extendedToBigAffine(&p.X, &p.Y, &p.Z)

	// We got the wrong sign; flip the bit and recalculate.
	if xIsNegBytes != isNegative {
		x.Sub(curve.P, x)
	}

	// This should hopefully never happen, since the
	// library itself should never let us create a bad
	// point.
	if !curve.IsOnCurve(x, y) {
		return nil, nil, fmt.Errorf("point not on curve")
	}

	return x, y, nil
}

// Verify returns true iff sig is a valid signature of message by publicKey.
func Verify(publicKey *[PublicKeySize]byte, message []byte, sig *[SignatureSize]byte) bool {
	if sig[63]&224 != 0 {
		return false
	}

	var A edwards25519.ExtendedGroupElement
	if !A.FromBytes(publicKey) {
		return false
	}
	edwards25519.FeNeg(&A.X, &A.X)
	edwards25519.FeNeg(&A.T, &A.T)

	h := sha512.New()
	h.Write(sig[:32])
	h.Write(publicKey[:])
	h.Write(message)
	var digest [64]byte
	h.Sum(digest[:0])

	var hReduced [32]byte
	edwards25519.ScReduce(&hReduced, &digest)

	var R edwards25519.ProjectiveGroupElement
	var b [32]byte
	copy(b[:], sig[32:])
	edwards25519.GeDoubleScalarMultVartime(&R, &hReduced, &A, &b)

	var checkR [32]byte
	R.ToBytes(&checkR)
	return subtle.ConstantTimeCompare(sig[:32], checkR[:]) == 1
}

// GenerateKey generates a public/private key pair using randomness from rand.
func GenerateKey(rand io.Reader) (publicKey *[PublicKeySize]byte, privateKey *[PrivateKeySize]byte, err error) {
	privateKey = new([64]byte)
	publicKey = new([32]byte)
	_, err = io.ReadFull(rand, privateKey[:32])
	if err != nil {
		return nil, nil, err
	}

	h := sha512.New()
	h.Write(privateKey[:32])
	digest := h.Sum(nil)

	digest[0] &= 248
	digest[31] &= 127
	digest[31] |= 64

	var A edwards25519.ExtendedGroupElement
	var hBytes [32]byte
	copy(hBytes[:], digest)
	edwards25519.GeScalarMultBase(&A, &hBytes)
	A.ToBytes(publicKey)

	copy(privateKey[32:], publicKey[:])
	return
}

// 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
}

func TestUnmarshalMarshal(t *testing.T) {
	pub, _, _ := GenerateKey(rand.Reader)

	var A edwards25519.ExtendedGroupElement
	if !A.FromBytes(pub) {
		t.Fatalf("ExtendedGroupElement.FromBytes failed")
	}

	var pub2 [32]byte
	A.ToBytes(&pub2)

	if *pub != pub2 {
		t.Errorf("FromBytes(%v)->ToBytes does not round-trip, got %x\n", *pub, pub2)
	}
}

// Sign signs the message with privateKey and returns a signature.
func Sign(privateKey *[PrivateKeySize]byte, message []byte) *[SignatureSize]byte {
	h := sha512.New()
	h.Write(privateKey[:32])

	var digest1, messageDigest, hramDigest [64]byte
	var expandedSecretKey [32]byte
	h.Sum(digest1[:0])
	copy(expandedSecretKey[:], digest1[:])
	expandedSecretKey[0] &= 248
	expandedSecretKey[31] &= 63
	expandedSecretKey[31] |= 64

	h.Reset()
	h.Write(digest1[32:])
	h.Write(message)
	h.Sum(messageDigest[:0])

	var messageDigestReduced [32]byte
	edwards25519.ScReduce(&messageDigestReduced, &messageDigest)
	var R edwards25519.ExtendedGroupElement
	edwards25519.GeScalarMultBase(&R, &messageDigestReduced)

	var encodedR [32]byte
	R.ToBytes(&encodedR)

	h.Reset()
	h.Write(encodedR[:])
	h.Write(privateKey[32:])
	h.Write(message)
	h.Sum(hramDigest[:0])
	var hramDigestReduced [32]byte
	edwards25519.ScReduce(&hramDigestReduced, &hramDigest)

	var s [32]byte
	edwards25519.ScMulAdd(&s, &hramDigestReduced, &expandedSecretKey, &messageDigestReduced)

	signature := new([64]byte)
	copy(signature[:], encodedR[:])
	copy(signature[32:], s[:])
	return signature
}

// Add adds two points represented by pairs of big integers on the elliptical
// curve.
func (curve *TwistedEdwardsCurve) Add(x1, y1, x2, y2 *big.Int) (x, y *big.Int) {
	// Convert to extended from affine.
	a := BigIntPointToEncodedBytes(x1, y1)
	aEGE := new(edwards25519.ExtendedGroupElement)
	aEGE.FromBytes(a)

	b := BigIntPointToEncodedBytes(x2, y2)
	bEGE := new(edwards25519.ExtendedGroupElement)
	bEGE.FromBytes(b)

	// Cache b for use in group element addition.
	bCached := new(cachedGroupElement)
	toCached(bCached, bEGE)

	p := aEGE
	q := bCached

	// geAdd(r*CompletedGroupElement, p*ExtendedGroupElement,
	//   q*CachedGroupElement)
	// r is the result.
	r := new(edwards25519.CompletedGroupElement)
	var t0 edwards25519.FieldElement

	edwards25519.FeAdd(&r.X, &p.Y, &p.X)
	edwards25519.FeSub(&r.Y, &p.Y, &p.X)
	edwards25519.FeMul(&r.Z, &r.X, &q.yPlusX)
	edwards25519.FeMul(&r.Y, &r.Y, &q.yMinusX)
	edwards25519.FeMul(&r.T, &q.T2d, &p.T)
	edwards25519.FeMul(&r.X, &p.Z, &q.Z)
	edwards25519.FeAdd(&t0, &r.X, &r.X)
	edwards25519.FeSub(&r.X, &r.Z, &r.Y)
	edwards25519.FeAdd(&r.Y, &r.Z, &r.Y)
	edwards25519.FeAdd(&r.Z, &t0, &r.T)
	edwards25519.FeSub(&r.T, &t0, &r.T)

	rEGE := new(edwards25519.ExtendedGroupElement)
	r.ToExtended(rEGE)

	s := new([32]byte)
	rEGE.ToBytes(s)

	x, y, _ = curve.EncodedBytesToBigIntPoint(s)

	return
}

// Double adds the same pair of big integer coordinates to itself on the
// elliptical curve.
func (curve *TwistedEdwardsCurve) Double(x1, y1 *big.Int) (x, y *big.Int) {
	// Convert to extended projective coordinates.
	a := BigIntPointToEncodedBytes(x1, y1)
	aEGE := new(edwards25519.ExtendedGroupElement)
	aEGE.FromBytes(a)

	r := new(edwards25519.CompletedGroupElement)
	aEGE.Double(r)
	rEGE := new(edwards25519.ExtendedGroupElement)
	r.ToExtended(rEGE)

	s := new([32]byte)
	rEGE.ToBytes(s)
	x, y, _ = curve.EncodedBytesToBigIntPoint(s)

	return
}

// SignFromScalar signs a message 'hash' using the given private scalar priv.
// It uses RFC6979 to generate a deterministic nonce. Considered experimental.
// r = kG, where k is the RFC6979 nonce
// s = r + hash512(k || A || M) * a
func SignFromScalar(curve *TwistedEdwardsCurve, priv *PrivateKey,
	nonce []byte, hash []byte) (r, s *big.Int, err error) {
	publicKey := new([PubKeyBytesLen]byte)
	var A edwards25519.ExtendedGroupElement
	privateScalar := copyBytes(priv.Serialize())
	reverse(privateScalar) // BE --> LE
	edwards25519.GeScalarMultBase(&A, privateScalar)
	A.ToBytes(publicKey)

	// For signing from a scalar, r = nonce.
	nonceLE := copyBytes(nonce)
	reverse(nonceLE)
	var R edwards25519.ExtendedGroupElement
	edwards25519.GeScalarMultBase(&R, nonceLE)

	var encodedR [32]byte
	R.ToBytes(&encodedR)

	// h = hash512(k || A || M)
	h := sha512.New()
	h.Reset()
	h.Write(encodedR[:])
	h.Write(publicKey[:])
	h.Write(hash)

	// s = r + h * a
	var hramDigest [64]byte
	h.Sum(hramDigest[:0])
	var hramDigestReduced [32]byte
	edwards25519.ScReduce(&hramDigestReduced, &hramDigest)

	var localS [32]byte
	edwards25519.ScMulAdd(&localS, &hramDigestReduced, privateScalar,
		nonceLE)

	signature := new([64]byte)
	copy(signature[:], encodedR[:])
	copy(signature[32:], localS[:])
	sigEd, err := ParseSignature(curve, signature[:])
	if err != nil {
		return nil, nil, err
	}

	return sigEd.GetR(), sigEd.GetS(), nil
}

// ScalarMult returns k*(Bx,By) where k is a number in big-endian form. This
// uses the repeated doubling method, which is variable time.
// TODO use a constant time method to prevent side channel attacks.
func (curve *TwistedEdwardsCurve) ScalarMult(x1, y1 *big.Int,
	k []byte) (x, y *big.Int) {
	// Convert the scalar to a big int.
	s := new(big.Int).SetBytes(k)

	// Get a new group element to do cached doubling
	// calculations in.
	dEGE := new(edwards25519.ExtendedGroupElement)
	dEGE.Zero()

	// Use the doubling method for the multiplication.
	// p := given point
	// q := point(zero)
	// for each bit in the scalar, descending:
	//   double(q)
	//   if bit == 1:
	//     add(q, p)
	// return q
	//
	// Note that the addition is skipped for zero bits,
	// making this variable time and thus vulnerable to
	// side channel attack vectors.
	for i := s.BitLen() - 1; i >= 0; i-- {
		dCGE := new(edwards25519.CompletedGroupElement)
		dEGE.Double(dCGE)
		dCGE.ToExtended(dEGE)
		if s.Bit(i) == 1 {
			ss := new([32]byte)
			dEGE.ToBytes(ss)
			var err error
			xi, yi, err := curve.EncodedBytesToBigIntPoint(ss)
			if err != nil {
				return nil, nil
			}
			xAdd, yAdd := curve.Add(xi, yi, x1, y1)
			dTempBytes := BigIntPointToEncodedBytes(xAdd, yAdd)
			dEGE.FromBytes(dTempBytes)
		}
	}

	finalBytes := new([32]byte)
	dEGE.ToBytes(finalBytes)

	var err error
	x, y, err = curve.EncodedBytesToBigIntPoint(finalBytes)
	if err != nil {
		return nil, nil
	}

	return
}