Golang bn256.G1類代碼示例

// Open reveals which member private key made the given signature. The return
// value will match the result of calling Tag on the member private key in
// question.
func (priv *PrivateKey) Open(sig []byte) ([]byte, bool) {
	if len(sig) != 12*32 {
		return nil, false
	}

	t1, ok := new(bn256.G1).Unmarshal(sig[:2*32])
	if !ok {
		return nil, false
	}
	t2, ok := new(bn256.G1).Unmarshal(sig[2*32 : 4*32])
	if !ok {
		return nil, false
	}
	t3, ok := new(bn256.G1).Unmarshal(sig[4*32 : 6*32])
	if !ok {
		return nil, false
	}

	a := new(bn256.G1).ScalarMult(t1, priv.xi1)
	b := new(bn256.G1).ScalarMult(t2, priv.xi2)
	a.Add(a, b)
	a.Neg(a)
	a.Add(t3, a)

	return a.Marshal(), true
}

// Update alters mem to create a member private key for an updated Group. (Note
// that the Group of mem must also be updated.) This functions returns false if
// mem is the member private key that has been revoked.
func (mem *MemberKey) Update(r *Revocation) bool {
	if mem.x.Cmp(r.x) == 0 {
		return false
	}

	d := new(big.Int).Sub(mem.x, r.x)
	d.Mod(d, bn256.Order)
	d.ModInverse(d, bn256.Order)

	newA := new(bn256.G1).ScalarMult(r.a, d)
	t := new(bn256.G1).ScalarMult(mem.a, d)
	t.Neg(t)
	newA.Add(newA, t)

	mem.a = newA
	return true
}

// Verify verifies that sig is a valid signature of digest using the given hash
// function.
func (g *Group) Verify(digest []byte, hashFunc hash.Hash, sig []byte) bool {
	if len(sig) != SignatureSize {
		return false
	}

	t1, ok := new(bn256.G1).Unmarshal(sig[:2*32])
	if !ok {
		return false
	}
	t2, ok := new(bn256.G1).Unmarshal(sig[2*32 : 4*32])
	if !ok {
		return false
	}
	t3, ok := new(bn256.G1).Unmarshal(sig[4*32 : 6*32])
	if !ok {
		return false
	}
	c := new(big.Int).SetBytes(sig[6*32 : 7*32])
	salpha := new(big.Int).SetBytes(sig[7*32 : 8*32])
	sbeta := new(big.Int).SetBytes(sig[8*32 : 9*32])
	sx := new(big.Int).SetBytes(sig[9*32 : 10*32])
	sdelta1 := new(big.Int).SetBytes(sig[10*32 : 11*32])
	sdelta2 := new(big.Int).SetBytes(sig[11*32 : 12*32])

	r1 := new(bn256.G1).ScalarMult(g.u, salpha)
	tmp := new(big.Int).Neg(c)
	tmp.Add(tmp, bn256.Order)
	tmpg := new(bn256.G1).ScalarMult(t1, tmp)
	r1.Add(r1, tmpg)

	r2 := new(bn256.G1).ScalarMult(g.v, sbeta)
	tmpg.ScalarMult(t2, tmp)
	r2.Add(r2, tmpg)

	r4 := new(bn256.G1).ScalarMult(t1, sx)
	tmp.Neg(sdelta1)
	tmp.Add(tmp, bn256.Order)
	tmpg.ScalarMult(g.u, tmp)
	r4.Add(r4, tmpg)

	r5 := new(bn256.G1).ScalarMult(t2, sx)
	tmp.Neg(sdelta2)
	tmp.Add(tmp, bn256.Order)
	tmpg.ScalarMult(g.v, tmp)
	r5.Add(r5, tmpg)

	r3 := bn256.Pair(t3, g.g2)
	r3.ScalarMult(r3, sx)

	tmp.Neg(salpha)
	tmp.Sub(tmp, sbeta)
	tmp.Mod(tmp, bn256.Order)
	tmpgt := new(bn256.GT).ScalarMult(g.ehw, tmp)
	r3.Add(r3, tmpgt)

	tmp.Neg(sdelta1)
	tmp.Sub(tmp, sdelta2)
	tmp.Mod(tmp, bn256.Order)
	tmpgt.ScalarMult(g.ehg2, tmp)
	r3.Add(r3, tmpgt)

	et3w := bn256.Pair(t3, g.w)
	et3w.Add(et3w, g.minusEg1g2)
	et3w.ScalarMult(et3w, c)
	r3.Add(r3, et3w)

	hashFunc.Reset()
	hashFunc.Write(digest)
	hashFunc.Write(t1.Marshal())
	hashFunc.Write(t2.Marshal())
	hashFunc.Write(t3.Marshal())
	hashFunc.Write(r1.Marshal())
	hashFunc.Write(r2.Marshal())
	hashFunc.Write(r3.Marshal())
	hashFunc.Write(r4.Marshal())
	hashFunc.Write(r5.Marshal())
	cprime := new(big.Int).SetBytes(hashFunc.Sum(nil))
	cprime.Mod(cprime, bn256.Order)

	return cprime.Cmp(c) == 0
}

// Sign computes a group signature of digest using the given hash function.
func (mem *MemberKey) Sign(r io.Reader, digest []byte, hashFunc hash.Hash) ([]byte, error) {
	var rnds [7]*big.Int
	for i := range rnds {
		var err error
		rnds[i], err = randomZp(r)
		if err != nil {
			return nil, err
		}
	}
	alpha := rnds[0]
	beta := rnds[1]

	t1 := new(bn256.G1).ScalarMult(mem.u, alpha)
	t2 := new(bn256.G1).ScalarMult(mem.v, beta)

	tmp := new(big.Int).Add(alpha, beta)
	t3 := new(bn256.G1).ScalarMult(mem.h, tmp)
	t3.Add(t3, mem.a)

	delta1 := new(big.Int).Mul(mem.x, alpha)
	delta1.Mod(delta1, bn256.Order)
	delta2 := new(big.Int).Mul(mem.x, beta)
	delta2.Mod(delta2, bn256.Order)

	ralpha := rnds[2]
	rbeta := rnds[3]
	rx := rnds[4]
	rdelta1 := rnds[5]
	rdelta2 := rnds[6]

	r1 := new(bn256.G1).ScalarMult(mem.u, ralpha)
	r2 := new(bn256.G1).ScalarMult(mem.v, rbeta)

	r3 := bn256.Pair(t3, mem.g2)
	r3.ScalarMult(r3, rx)

	tmp.Neg(ralpha)
	tmp.Sub(tmp, rbeta)
	tmp.Mod(tmp, bn256.Order)
	tmpgt := new(bn256.GT).ScalarMult(mem.ehw, tmp)
	r3.Add(r3, tmpgt)

	tmp.Neg(rdelta1)
	tmp.Sub(tmp, rdelta2)
	tmp.Mod(tmp, bn256.Order)
	tmpgt.ScalarMult(mem.ehg2, tmp)
	r3.Add(r3, tmpgt)

	r4 := new(bn256.G1).ScalarMult(t1, rx)
	tmp.Neg(rdelta1)
	tmp.Add(tmp, bn256.Order)
	tmpg := new(bn256.G1).ScalarMult(mem.u, tmp)
	r4.Add(r4, tmpg)

	r5 := new(bn256.G1).ScalarMult(t2, rx)
	tmp.Neg(rdelta2)
	tmp.Add(tmp, bn256.Order)
	tmpg.ScalarMult(mem.v, tmp)
	r5.Add(r5, tmpg)

	t1Bytes := t1.Marshal()
	t2Bytes := t2.Marshal()
	t3Bytes := t3.Marshal()

	hashFunc.Reset()
	hashFunc.Write(digest)
	hashFunc.Write(t1Bytes)
	hashFunc.Write(t2Bytes)
	hashFunc.Write(t3Bytes)
	hashFunc.Write(r1.Marshal())
	hashFunc.Write(r2.Marshal())
	hashFunc.Write(r3.Marshal())
	hashFunc.Write(r4.Marshal())
	hashFunc.Write(r5.Marshal())
	c := new(big.Int).SetBytes(hashFunc.Sum(nil))
	c.Mod(c, bn256.Order)

	salpha := new(big.Int).Mul(c, alpha)
	salpha.Add(salpha, ralpha)
	salpha.Mod(salpha, bn256.Order)

	sbeta := new(big.Int).Mul(c, beta)
	sbeta.Add(sbeta, rbeta)
	sbeta.Mod(sbeta, bn256.Order)

	sx := new(big.Int).Mul(c, mem.x)
	sx.Add(sx, rx)
	sx.Mod(sx, bn256.Order)

	sdelta1 := new(big.Int).Mul(c, delta1)
	sdelta1.Add(sdelta1, rdelta1)
	sdelta1.Mod(sdelta1, bn256.Order)

	sdelta2 := new(big.Int).Mul(c, delta2)
	sdelta2.Add(sdelta2, rdelta2)
	sdelta2.Mod(sdelta2, bn256.Order)

	sig := make([]byte, 0, SignatureSize)
	sig = append(sig, t1Bytes...)
//.........這裏部分代碼省略.........