Esempio n. 1
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func getServerSession(user string, password string, salt []byte, keyA *big.Int, keyB *big.Int, keyb *big.Int) []byte {
	prime, _, _ := getPrime()
	u := getScramble(keyA, keyB)
	v := getVerifier(user, password, salt)
	vu := mathutil.ModPowBigInt(v, u, prime)
	avu := new(big.Int).Mod(new(big.Int).Mul(keyA, vu), prime)
	sessionSecret := mathutil.ModPowBigInt(avu, keyb, prime)
	return bigToSha1(sessionSecret)
}
Esempio n. 2
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func getClientSession(user string, password string, salt []byte, keyA *big.Int, keyB *big.Int, keya *big.Int) []byte {
	prime, g, k := getPrime()
	u := getScramble(keyA, keyB)
	x := getUserHash(salt, user, password)
	gx := mathutil.ModPowBigInt(g, x, prime)                     // gx = pow(g, x, N)
	kgx := new(big.Int).Mod(new(big.Int).Mul(k, gx), prime)      // kgx = (k * gx) % N
	diff := new(big.Int).Mod(new(big.Int).Sub(keyB, kgx), prime) // diff = (B - kgx) % N
	ux := new(big.Int).Mod(new(big.Int).Mul(u, x), prime)        // ux = (u * x) % N
	aux := new(big.Int).Mod(new(big.Int).Add(keya, ux), prime)   // aux = (a + ux) % N
	sessionSecret := mathutil.ModPowBigInt(diff, aux, prime)     // (B - kg^x) ^ (a + ux)

	return bigToSha1(sessionSecret)
}
Esempio n. 3
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func getClientSeed() (keyA *big.Int, keya *big.Int) {
	prime, g, _ := getPrime()
	keya = new(big.Int).Rand(rand.New(rand.NewSource(time.Now().UnixNano())),
		bigFromString("340282366920938463463374607431768211456")) // 1 << 128
	keyA = mathutil.ModPowBigInt(g, keya, prime)
	return
}
Esempio n. 4
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func getServerSeed(v *big.Int) (keyB *big.Int, keyb *big.Int) {
	prime, g, k := getPrime()
	keyb = new(big.Int).Rand(rand.New(rand.NewSource(time.Now().UnixNano())),
		bigFromString("340282366920938463463374607431768211456")) // 1 << 128
	gb := mathutil.ModPowBigInt(g, keyb, prime)              // gb = pow(g, b, N)
	kv := new(big.Int).Mod(new(big.Int).Mul(k, v), prime)    // kv = (k * v) % N
	keyB = new(big.Int).Mod(new(big.Int).Add(kv, gb), prime) // B = (kv + gb) % N
	return
}
Esempio n. 5
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func benchmarkModPowBig(b *testing.B, base, e, m uint32) {
	b.StopTimer()
	bb := big.NewInt(int64(base))
	ee := New(e)
	mm := New(m)
	runtime.GC()
	b.StartTimer()
	for i := 0; i < b.N; i++ {
		mathutil.ModPowBigInt(bb, ee, mm)
	}
}
Esempio n. 6
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func main() {
	runtime.GOMAXPROCS(2)
	oClass := flag.Uint64("c", 2, `factor "class" number`)
	oDuration := flag.Duration("d", time.Second, "duration to spend on one class")
	flag.Parse()
	class := *oClass
	for class&1 != 0 {
		class >>= 1
	}
	class = mathutil.MaxUint64(class, 2)

	for {
		c := time.After(*oDuration)
		factor := big.NewInt(0)
		factor.SetUint64(class)
		exp := big.NewInt(0)
	oneClass:
		for {
			select {
			case <-c:
				break oneClass
			default:
			}

			exp.Set(factor)
			factor.Lsh(factor, 1)
			factor.Add(factor, _1)
			if !factor.ProbablyPrime(pp) {
				continue
			}

			if !exp.ProbablyPrime(pp) {
				continue
			}

			if mathutil.ModPowBigInt(_2, exp, factor).Cmp(_1) != 0 {
				continue
			}

			if !factor.ProbablyPrime(pp2) {
				continue
			}

			if !exp.ProbablyPrime(pp2) {
				continue
			}

			fmt.Printf("%d: %s | M%s (%d bits)\n", class, factor, exp, factor.BitLen())
		}

		class += 2
	}
}
Esempio n. 7
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func TestModPow(t *testing.T) {
	const N = 2e2
	data := []struct{ b, e, m, r uint32 }{
		{0, 1, 1, 0},
		{0, 2, 1, 0},
		{0, 3, 1, 0},

		{1, 0, 1, 0},
		{1, 1, 1, 0},
		{1, 2, 1, 0},
		{1, 3, 1, 0},

		{2, 0, 1, 0},
		{2, 1, 1, 0},
		{2, 2, 1, 0},
		{2, 3, 1, 0},

		{2, 3, 4, 8},
		{2, 3, 5, 4},
		{2, 4, 3, 1},
		{3, 3, 3, 3},
		{3, 4, 5, 30},
	}

	f := func(b, e, m uint32, expect *big.Int) {
		got := ModPow(b, e, m)
		if got.Cmp(expect) != 0 {
			t.Fatal(b, e, m, got, expect)
		}
	}

	var r big.Int
	for _, v := range data {
		r.SetInt64(int64(v.r))
		f(v.b, v.e, v.m, &r)
	}

	rg, _ := mathutil.NewFC32(2, 1<<10, true)
	var bb big.Int
	for i := 0; i < N; i++ {
		b, e, m := uint32(rg.Next()), uint32(rg.Next()), uint32(rg.Next())
		bb.SetInt64(int64(b))
		f(b, e, m, mathutil.ModPowBigInt(&bb, New(e), New(m)))
	}
}
Esempio n. 8
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func getClientProof(user string, password string, salt []byte, keyA *big.Int, keyB *big.Int, keya *big.Int) (keyM []byte, keyK []byte) {
	// M = H(H(N) xor H(g), H(I), s, A, B, K)
	prime, g, _ := getPrime()
	keyK = getClientSession(user, password, salt, keyA, keyB, keya)

	n1 := bytesToBig(bigToSha1(prime))
	n2 := bytesToBig(bigToSha1(g))
	n3 := mathutil.ModPowBigInt(n1, n2, prime)
	n4 := getStringHash(user)
	sha1 := sha1.New()
	sha1.Write(n3.Bytes())
	sha1.Write(n4.Bytes())
	sha1.Write(salt)
	sha1.Write(keyA.Bytes())
	sha1.Write(keyB.Bytes())
	sha1.Write(keyK)
	keyM = sha1.Sum(nil)

	return keyM, keyK
}
Esempio n. 9
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// HasFactorBigInt returns true if d | Mn, d > 0. Typical run time for a 128
// bit factor and a 32 bit exponent is < 75 µs.
func HasFactorBigInt(d *big.Int, n uint32) bool {
	return d.Cmp(_1) == 0 || d.Sign() > 0 && d.Bit(0) == 1 &&
		mathutil.ModPowBigInt(_2, big.NewInt(int64(n)), d).Cmp(_1) == 0
}
Esempio n. 10
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// HasFactorBigInt2 returns true if d | Mn, d > 0
func HasFactorBigInt2(d, n *big.Int) bool {
	return d.Cmp(_1) == 0 || d.Sign() > 0 && d.Bit(0) == 1 &&
		mathutil.ModPowBigInt(_2, n, d).Cmp(_1) == 0
}
Esempio n. 11
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func getVerifier(user string, password string, salt []byte) *big.Int {
	prime, g, _ := getPrime()
	x := getUserHash(salt, user, password)
	return mathutil.ModPowBigInt(g, x, prime)
}