Exemplo n.º 1
0
// 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())
}
Exemplo n.º 2
0
// 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:]
		}
	}
}
Exemplo n.º 3
0
// 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:]
		}
	}
}