// Initialize Residue group parameters for a quadratic residue group,
// by picking primes P and Q such that P=2Q+1
// and the smallest valid generator G for this group.
func (g *ResidueGroup) QuadraticResidueGroup(bitlen uint, rand cipher.Stream) {
g.R = two
// pick primes p,q such that p = 2q+1
fmt.Printf("Generating %d-bit QR group", bitlen)
for i := 0; ; i++ {
if i > 1000 {
print(".")
i = 0
}
// First pick a prime Q
b := random.Bits(bitlen-1, true, rand)
b[len(b)-1] |= 1 // must be odd
g.Q = new(big.Int).SetBytes(b)
//println("q?",hex.EncodeToString(g.Q.Bytes()))
if !isPrime(g.Q) {
continue
}
// Does the corresponding P come out prime too?
g.P = new(big.Int)
g.P.Mul(g.Q, two)
g.P.Add(g.P, one)
//println("p?",hex.EncodeToString(g.P.Bytes()))
if uint(g.P.BitLen()) == bitlen && isPrime(g.P) {
break
}
}
println()
println("p", g.P.String())
println("q", g.Q.String())
// pick standard generator G
h := new(big.Int).Set(two)
g.G = new(big.Int)
for {
g.G.Exp(h, two, g.P)
if g.G.Cmp(one) != 0 {
break
}
h.Add(h, one)
}
println("g", g.G.String())
}
// Pick a curve point containing a variable amount of embedded data.
// Remaining bits comprising the point are chosen randomly.
func (p *curvePoint) Pick(data []byte, rand cipher.Stream) (abstract.Point, []byte) {
l := p.c.coordLen()
dl := p.PickLen()
if dl > len(data) {
dl = len(data)
}
for {
b := random.Bits(uint(p.c.p.P.BitLen()), false, rand)
if data != nil {
b[l-1] = byte(dl) // Encode length in low 8 bits
copy(b[l-dl-1:l-1], data) // Copy in data to embed
}
if p.genPoint(new(big.Int).SetBytes(b), rand) {
return p, data[dl:]
}
}
}
// Pick a point containing a variable amount of embedded data.
// Remaining bits comprising the point are chosen randomly.
// This will only work efficiently for quadratic residue groups!
func (p *residuePoint) Pick(data []byte, rand cipher.Stream) (abstract.Point, []byte) {
l := p.g.PointLen()
dl := p.PickLen()
if dl > len(data) {
dl = len(data)
}
for {
b := random.Bits(uint(p.g.P.BitLen()), false, rand)
if data != nil {
b[l-1] = byte(dl) // Encode length in low 16 bits
b[l-2] = byte(dl >> 8)
copy(b[l-dl-2:l-2], data) // Copy in embedded data
}
p.Int.SetBytes(b)
if p.Valid() {
return p, data[dl:]
}
}
}