Python Integer.size_in_bits方法代码示例

# 需要导入模块: from Crypto.Math.Numbers import Integer [as 别名]
# 或者: from Crypto.Math.Numbers.Integer import size_in_bits [as 别名]
def _generate_domain(L, randfunc):
    """Generate a new set of DSA domain parameters"""

    N = { 1024:160, 2048:224, 3072:256 }.get(L)
    if N is None:
        raise ValueError("Invalid modulus length (%d)" % L)

    outlen = SHA256.digest_size * 8
    n = (L + outlen - 1) // outlen - 1  # ceil(L/outlen) -1
    b_ = L - 1 - (n * outlen)

    # Generate q (A.1.1.2)
    q = Integer(4)
    upper_bit = 1 << (N - 1)
    while test_probable_prime(q, randfunc) != PROBABLY_PRIME:
        seed = randfunc(64)
        U = Integer.from_bytes(SHA256.new(seed).digest()) & (upper_bit - 1)
        q = U | upper_bit | 1

    assert(q.size_in_bits() == N)

    # Generate p (A.1.1.2)
    offset = 1
    upper_bit = 1 << (L - 1)
    while True:
        V = [ SHA256.new(seed + Integer(offset + j).to_bytes()).digest()
              for j in xrange(n + 1) ]
        V = [ Integer.from_bytes(v) for v in V ]
        W = sum([V[i] * (1 << (i * outlen)) for i in xrange(n)],
                (V[n] & (1 << b_ - 1)) * (1 << (n * outlen)))

        X = Integer(W + upper_bit) # 2^{L-1} < X < 2^{L}
        assert(X.size_in_bits() == L)

        c = X % (q * 2)
        p = X - (c - 1)  # 2q divides (p-1)
        if p.size_in_bits() == L and \
           test_probable_prime(p, randfunc) == PROBABLY_PRIME:
               break
        offset += n + 1

    # Generate g (A.2.3, index=1)
    e = (p - 1) // q
    for count in itertools.count(1):
        U = seed + b("ggen") + bchr(1) + Integer(count).to_bytes()
        W = Integer.from_bytes(SHA256.new(U).digest())
        g = pow(W, e, p)
        if g != 1:
            break

    return (p, q, g, seed)

# 需要导入模块: from Crypto.Math.Numbers import Integer [as 别名]
# 或者: from Crypto.Math.Numbers.Integer import size_in_bits [as 别名]
def test_probable_prime(candidate, randfunc=None):
    """Test if a number is prime.

    A number is qualified as prime if it passes a certain
    number of Miller-Rabin tests (dependent on the size
    of the number, but such that probability of a false
    positive is less than 10^-30) and a single Lucas test.

    For instance, a 1024-bit candidate will need to pass
    4 Miller-Rabin tests.

    :Parameters:
      candidate : integer
        The number to test for primality.
      randfunc : callable
        The routine to draw random bytes from to select Miller-Rabin bases.
    :Returns:
      ``PROBABLE_PRIME`` if the number if prime with very high probability.
      ``COMPOSITE`` if the number is a composite.
      For efficiency reasons, ``COMPOSITE`` is also returned for small primes.
    """

    if randfunc is None:
        randfunc = Random.new().read

    if not isinstance(candidate, Integer):
        candidate = Integer(candidate)

    # First, check trial division by the smallest primes
    if int(candidate) in _sieve_base:
        return PROBABLY_PRIME
    try:
        map(candidate.fail_if_divisible_by, _sieve_base)
    except ValueError:
        return COMPOSITE

    # These are the number of Miller-Rabin iterations s.t. p(k, t) < 1E-30,
    # with p(k, t) being the probability that a randomly chosen k-bit number
    # is composite but still survives t MR iterations.
    mr_ranges = ((220, 30), (280, 20), (390, 15), (512, 10),
                 (620, 7), (740, 6), (890, 5), (1200, 4),
                 (1700, 3), (3700, 2))

    bit_size = candidate.size_in_bits()
    try:
        mr_iterations = list(filter(lambda x: bit_size < x[0],
                                    mr_ranges))[0][1]
    except IndexError:
        mr_iterations = 1

    if miller_rabin_test(candidate, mr_iterations,
                         randfunc=randfunc) == COMPOSITE:
        return COMPOSITE
    if lucas_test(candidate) == COMPOSITE:
        return COMPOSITE
    return PROBABLY_PRIME

# 需要导入模块: from Crypto.Math.Numbers import Integer [as 别名]
# 或者: from Crypto.Math.Numbers.Integer import size_in_bits [as 别名]
    def _get_weak_domain(self):

        from Crypto.Math.Numbers import Integer
        from Crypto.Math import Primality

        p = Integer(4)
        while p.size_in_bits() != 1024 or Primality.test_probable_prime(p) != Primality.PROBABLY_PRIME:
            q1 = Integer.random(exact_bits=80)
            q2 = Integer.random(exact_bits=80)
            q = q1 * q2
            z = Integer.random(exact_bits=1024-160)
            p = z * q + 1

        h = Integer(2)
        g = 1
        while g == 1:
            g = pow(h, z, p)
            h += 1

        return (p, q, g)