// 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
}
// 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...)
sig = append(sig, t2Bytes...)
sig = append(sig, t3Bytes...)
sig = appendN(sig, c)
sig = appendN(sig, salpha)
sig = appendN(sig, sbeta)
sig = appendN(sig, sx)
sig = appendN(sig, sdelta1)
sig = appendN(sig, sdelta2)
return sig, nil
}