Add google-endpoints to third_party/.

third_party/google-endpoints/Crypto/Util/number.py

+#
+#   number.py : Number-theoretic functions
+#
+#  Part of the Python Cryptography Toolkit
+#
+#  Written by Andrew M. Kuchling, Barry A. Warsaw, and others
+#
+# ===================================================================
+# The contents of this file are dedicated to the public domain.  To
+# the extent that dedication to the public domain is not available,
+# everyone is granted a worldwide, perpetual, royalty-free,
+# non-exclusive license to exercise all rights associated with the
+# contents of this file for any purpose whatsoever.
+# No rights are reserved.
+#
+# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+# EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+# NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+# BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+# ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+# CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+# SOFTWARE.
+# ===================================================================
+#
+
+__revision__ = "$Id$"
+
+from Crypto.pct_warnings import GetRandomNumber_DeprecationWarning, PowmInsecureWarning
+from warnings import warn as _warn
+import math
+import sys
+from Crypto.Util.py3compat import *
+
+bignum = long
+try:
+    from Crypto.PublicKey import _fastmath
+except ImportError:
+    # For production, we are going to let import issues due to gmp/mpir shared
+    # libraries not loading slide silently and use slowmath. If you'd rather
+    # see an exception raised if _fastmath exists but cannot be imported,
+    # uncomment the below
+    #
+    # from distutils.sysconfig import get_config_var
+    # import inspect, os
+    # _fm_path = os.path.normpath(os.path.dirname(os.path.abspath(
+        # inspect.getfile(inspect.currentframe())))
+        # +"/../../PublicKey/_fastmath"+get_config_var("SO"))
+    # if os.path.exists(_fm_path):
+        # raise ImportError("While the _fastmath module exists, importing "+
+            # "it failed. This may point to the gmp or mpir shared library "+
+            # "not being in the path. _fastmath was found at "+_fm_path)
+    _fastmath = None
+
+# You need libgmp v5 or later to get mpz_powm_sec.  Warn if it's not available.
+if _fastmath is not None and not _fastmath.HAVE_DECL_MPZ_POWM_SEC:
+    _warn("Not using mpz_powm_sec.  You should rebuild using libgmp >= 5 to avoid timing attack vulnerability.", PowmInsecureWarning)
+
+# New functions
+from _number_new import *
+
+# Commented out and replaced with faster versions below
+## def long2str(n):
+##     s=''
+##     while n>0:
+##         s=chr(n & 255)+s
+##         n=n>>8
+##     return s
+
+## import types
+## def str2long(s):
+##     if type(s)!=types.StringType: return s   # Integers will be left alone
+##     return reduce(lambda x,y : x*256+ord(y), s, 0L)
+
+def size (N):
+    """size(N:long) : int
+    Returns the size of the number N in bits.
+    """
+    bits = 0
+    while N >> bits:
+        bits += 1
+    return bits
+
+def getRandomNumber(N, randfunc=None):
+    """Deprecated.  Use getRandomInteger or getRandomNBitInteger instead."""
+    warnings.warn("Crypto.Util.number.getRandomNumber has confusing semantics"+
+    "and has been deprecated.  Use getRandomInteger or getRandomNBitInteger instead.",
+        GetRandomNumber_DeprecationWarning)
+    return getRandomNBitInteger(N, randfunc)
+
+def getRandomInteger(N, randfunc=None):
+    """getRandomInteger(N:int, randfunc:callable):long
+    Return a random number with at most N bits.
+
+    If randfunc is omitted, then Random.new().read is used.
+
+    This function is for internal use only and may be renamed or removed in
+    the future.
+    """
+    if randfunc is None:
+        _import_Random()
+        randfunc = Random.new().read
+
+    S = randfunc(N>>3)
+    odd_bits = N % 8
+    if odd_bits != 0:
+        char = ord(randfunc(1)) >> (8-odd_bits)
+        S = bchr(char) + S
+    value = bytes_to_long(S)
+    return value
+
+def getRandomRange(a, b, randfunc=None):
+    """getRandomRange(a:int, b:int, randfunc:callable):long
+    Return a random number n so that a <= n < b.
+
+    If randfunc is omitted, then Random.new().read is used.
+
+    This function is for internal use only and may be renamed or removed in
+    the future.
+    """
+    range_ = b - a - 1
+    bits = size(range_)
+    value = getRandomInteger(bits, randfunc)
+    while value > range_:
+        value = getRandomInteger(bits, randfunc)
+    return a + value
+
+def getRandomNBitInteger(N, randfunc=None):
+    """getRandomInteger(N:int, randfunc:callable):long
+    Return a random number with exactly N-bits, i.e. a random number
+    between 2**(N-1) and (2**N)-1.
+
+    If randfunc is omitted, then Random.new().read is used.
+
+    This function is for internal use only and may be renamed or removed in
+    the future.
+    """
+    value = getRandomInteger (N-1, randfunc)
+    value |= 2L ** (N-1)                # Ensure high bit is set
+    assert size(value) >= N
+    return value
+
+def GCD(x,y):
+    """GCD(x:long, y:long): long
+    Return the GCD of x and y.
+    """
+    x = abs(x) ; y = abs(y)
+    while x > 0:
+        x, y = y % x, x
+    return y
+
+def inverse(u, v):
+    """inverse(u:long, v:long):long
+    Return the inverse of u mod v.
+    """
+    u3, v3 = long(u), long(v)
+    u1, v1 = 1L, 0L
+    while v3 > 0:
+        q=divmod(u3, v3)[0]
+        u1, v1 = v1, u1 - v1*q
+        u3, v3 = v3, u3 - v3*q
+    while u1<0:
+        u1 = u1 + v
+    return u1
+
+# Given a number of bits to generate and a random generation function,
+# find a prime number of the appropriate size.
+
+def getPrime(N, randfunc=None):
+    """getPrime(N:int, randfunc:callable):long
+    Return a random N-bit prime number.
+
+    If randfunc is omitted, then Random.new().read is used.
+    """
+    if randfunc is None:
+        _import_Random()
+        randfunc = Random.new().read
+
+    number=getRandomNBitInteger(N, randfunc) | 1
+    while (not isPrime(number, randfunc=randfunc)):
+        number=number+2
+    return number
+
+
+def _rabinMillerTest(n, rounds, randfunc=None):
+    """_rabinMillerTest(n:long, rounds:int, randfunc:callable):int
+    Tests if n is prime.
+    Returns 0 when n is definitly composite.
+    Returns 1 when n is probably prime.
+    Returns 2 when n is definitly prime.
+
+    If randfunc is omitted, then Random.new().read is used.
+
+    This function is for internal use only and may be renamed or removed in
+    the future.
+    """
+    # check special cases (n==2, n even, n < 2)
+    if n < 3 or (n & 1) == 0:
+        return n == 2
+    # n might be very large so it might be beneficial to precalculate n-1
+    n_1 = n - 1
+    # determine m and b so that 2**b * m = n - 1 and b maximal
+    b = 0
+    m = n_1
+    while (m & 1) == 0:
+        b += 1
+        m >>= 1
+
+    tested = []
+    # we need to do at most n-2 rounds.
+    for i in xrange (min (rounds, n-2)):
+        # randomly choose a < n and make sure it hasn't been tested yet
+        a = getRandomRange (2, n, randfunc)
+        while a in tested:
+            a = getRandomRange (2, n, randfunc)
+        tested.append (a)
+        # do the rabin-miller test
+        z = pow (a, m, n) # (a**m) % n
+        if z == 1 or z == n_1:
+            continue
+        composite = 1
+        for r in xrange (b):
+            z = (z * z) % n
+            if z == 1:
+                return 0
+            elif z == n_1:
+                composite = 0
+                break
+        if composite:
+            return 0
+    return 1
+
+def getStrongPrime(N, e=0, false_positive_prob=1e-6, randfunc=None):
+    """getStrongPrime(N:int, e:int, false_positive_prob:float, randfunc:callable):long
+    Return a random strong N-bit prime number.
+    In this context p is a strong prime if p-1 and p+1 have at
+    least one large prime factor.
+    N should be a multiple of 128 and > 512.
+
+    If e is provided the returned prime p-1 will be coprime to e
+    and thus suitable for RSA where e is the public exponent.
+
+    The optional false_positive_prob is the statistical probability
+    that true is returned even though it is not (pseudo-prime).
+    It defaults to 1e-6 (less than 1:1000000).
+    Note that the real probability of a false-positive is far less. This is
+    just the mathematically provable limit.
+
+    randfunc should take a single int parameter and return that
+    many random bytes as a string.
+    If randfunc is omitted, then Random.new().read is used.
+    """
+    # This function was implemented following the
+    # instructions found in the paper:
+    #   "FAST GENERATION OF RANDOM, STRONG RSA PRIMES"
+    #   by Robert D. Silverman
+    #   RSA Laboratories
+    #   May 17, 1997
+    # which by the time of writing could be freely downloaded here:
+    # http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.17.2713&rep=rep1&type=pdf
+
+    # Use the accelerator if available
+    if _fastmath is not None:
+        return _fastmath.getStrongPrime(long(N), long(e), false_positive_prob,
+            randfunc)
+
+    if (N < 512) or ((N % 128) != 0):
+        raise ValueError ("bits must be multiple of 128 and > 512")
+
+    rabin_miller_rounds = int(math.ceil(-math.log(false_positive_prob)/math.log(4)))
+
+    # calculate range for X
+    #   lower_bound = sqrt(2) * 2^{511 + 128*x}
+    #   upper_bound = 2^{512 + 128*x} - 1
+    x = (N - 512) >> 7;
+    # We need to approximate the sqrt(2) in the lower_bound by an integer
+    # expression because floating point math overflows with these numbers
+    lower_bound = divmod(14142135623730950489L * (2L ** (511 + 128*x)),
+                         10000000000000000000L)[0]
+    upper_bound = (1L << (512 + 128*x)) - 1
+    # Randomly choose X in calculated range
+    X = getRandomRange (lower_bound, upper_bound, randfunc)
+
+    # generate p1 and p2
+    p = [0, 0]
+    for i in (0, 1):
+        # randomly choose 101-bit y
+        y = getRandomNBitInteger (101, randfunc)
+        # initialize the field for sieving
+        field = [0] * 5 * len (sieve_base)
+        # sieve the field
+        for prime in sieve_base:
+            offset = y % prime
+            for j in xrange ((prime - offset) % prime, len (field), prime):
+                field[j] = 1
+
+        # look for suitable p[i] starting at y
+        result = 0
+        for j in range(len(field)):
+            composite = field[j]
+            # look for next canidate
+            if composite:
+                continue
+            tmp = y + j
+            result = _rabinMillerTest (tmp, rabin_miller_rounds)
+            if result > 0:
+                p[i] = tmp
+                break
+        if result == 0:
+            raise RuntimeError ("Couln't find prime in field. "
+                                "Developer: Increase field_size")
+
+    # Calculate R
+    #     R = (p2^{-1} mod p1) * p2 - (p1^{-1} mod p2) * p1
+    tmp1 = inverse (p[1], p[0]) * p[1]  # (p2^-1 mod p1)*p2
+    tmp2 = inverse (p[0], p[1]) * p[0]  # (p1^-1 mod p2)*p1
+    R = tmp1 - tmp2 # (p2^-1 mod p1)*p2 - (p1^-1 mod p2)*p1
+
+    # search for final prime number starting by Y0
+    #    Y0 = X + (R - X mod p1p2)
+    increment = p[0] * p[1]
+    X = X + (R - (X % increment))
+    while 1:
+        is_possible_prime = 1
+        # first check candidate against sieve_base
+        for prime in sieve_base:
+            if (X % prime) == 0:
+                is_possible_prime = 0
+                break
+        # if e is given make sure that e and X-1 are coprime
+        # this is not necessarily a strong prime criterion but useful when
+        # creating them for RSA where the p-1 and q-1 should be coprime to
+        # the public exponent e
+        if e and is_possible_prime:
+            if e & 1:
+                if GCD (e, X-1) != 1:
+                    is_possible_prime = 0
+            else:
+                if GCD (e, divmod((X-1),2)[0]) != 1:
+                    is_possible_prime = 0
+
+        # do some Rabin-Miller-Tests
+        if is_possible_prime:
+            result = _rabinMillerTest (X, rabin_miller_rounds)
+            if result > 0:
+                break
+        X += increment
+                # abort when X has more bits than requested
+                # TODO: maybe we shouldn't abort but rather start over.
+        if X >= 1L << N:
+            raise RuntimeError ("Couln't find prime in field. "
+                                "Developer: Increase field_size")
+    return X
+
+def isPrime(N, false_positive_prob=1e-6, randfunc=None):
+    """isPrime(N:long, false_positive_prob:float, randfunc:callable):bool
+    Return true if N is prime.
+
+    The optional false_positive_prob is the statistical probability
+    that true is returned even though it is not (pseudo-prime).
+    It defaults to 1e-6 (less than 1:1000000).
+    Note that the real probability of a false-positive is far less. This is
+    just the mathematically provable limit.
+
+    If randfunc is omitted, then Random.new().read is used.
+    """
+    if _fastmath is not None:
+        return _fastmath.isPrime(long(N), false_positive_prob, randfunc)
+
+    if N < 3 or N & 1 == 0:
+        return N == 2
+    for p in sieve_base:
+        if N == p:
+            return 1
+        if N % p == 0:
+            return 0
+
+    rounds = int(math.ceil(-math.log(false_positive_prob)/math.log(4)))
+    return _rabinMillerTest(N, rounds, randfunc)
+
+
+# Improved conversion functions contributed by Barry Warsaw, after
+# careful benchmarking
+
+import struct
+
+def long_to_bytes(n, blocksize=0):
+    """long_to_bytes(n:long, blocksize:int) : string
+    Convert a long integer to a byte string.
+
+    If optional blocksize is given and greater than zero, pad the front of the
+    byte string with binary zeros so that the length is a multiple of
+    blocksize.
+    """
+    # after much testing, this algorithm was deemed to be the fastest
+    s = b('')
+    n = long(n)
+    pack = struct.pack
+    while n > 0:
+        s = pack('>I', n & 0xffffffffL) + s
+        n = n >> 32
+    # strip off leading zeros
+    for i in range(len(s)):
+        if s[i] != b('\000')[0]:
+            break
+    else:
+        # only happens when n == 0
+        s = b('\000')
+        i = 0
+    s = s[i:]
+    # add back some pad bytes.  this could be done more efficiently w.r.t. the
+    # de-padding being done above, but sigh...
+    if blocksize > 0 and len(s) % blocksize:
+        s = (blocksize - len(s) % blocksize) * b('\000') + s
+    return s
+
+def bytes_to_long(s):
+    """bytes_to_long(string) : long
+    Convert a byte string to a long integer.
+
+    This is (essentially) the inverse of long_to_bytes().
+    """
+    acc = 0L
+    unpack = struct.unpack
+    length = len(s)
+    if length % 4:
+        extra = (4 - length % 4)
+        s = b('\000') * extra + s
+        length = length + extra
+    for i in range(0, length, 4):
+        acc = (acc << 32) + unpack('>I', s[i:i+4])[0]
+    return acc
+
+# For backwards compatibility...
+import warnings
+def long2str(n, blocksize=0):
+    warnings.warn("long2str() has been replaced by long_to_bytes()")
+    return long_to_bytes(n, blocksize)
+def str2long(s):
+    warnings.warn("str2long() has been replaced by bytes_to_long()")
+    return bytes_to_long(s)
+
+def _import_Random():
+    # This is called in a function instead of at the module level in order to
+    # avoid problems with recursive imports
+    global Random, StrongRandom
+    from Crypto import Random
+    from Crypto.Random.random import StrongRandom
+
+
+
+# The first 10000 primes used for checking primality.
+# This should be enough to eliminate most of the odd
+# numbers before needing to do a Rabin-Miller test at all.
+sieve_base = (
+     2,      3,      5,      7,     11,     13,     17,     19,     23,     29,
+    31,     37,     41,     43,     47,     53,     59,     61,     67,     71,
+    73,     79,     83,     89,     97,    101,    103,    107,    109,    113,
+   127,    131,    137,    139,    149,    151,    157,    163,    167,    173,
+   179,    181,    191,    193,    197,    199,    211,    223,    227,    229,
+   233,    239,    241,    251,    257,    263,    269,    271,    277,    281,
+   283,    293,    307,    311,    313,    317,    331,    337,    347,    349,
+   353,    359,    367,    373,    379,    383,    389,    397,    401,    409,
+   419,    421,    431,    433,    439,    443,    449,    457,    461,    463,
+   467,    479,    487,    491,    499,    503,    509,    521,    523,    541,
+   547,    557,    563,    569,    571,    577,    587,    593,    599,    601,
+   607,    613,    617,    619,    631,    641,    643,    647,    653,    659,
+   661,    673,    677,    683,    691,    701,    709,    719,    727,    733,
+   739,    743,    751,    757,    761,    769,    773,    787,    797,    809,
+   811,    821,    823,    827,    829,    839,    853,    857,    859,    863,
+   877,    881,    883,    887,    907,    911,    919,    929,    937,    941,
+   947,    953,    967,    971,    977,    983,    991,    997,   1009,   1013,
+  1019,   1021,   1031,   1033,   1039,   1049,   1051,   1061,   1063,   1069,
+  1087,   1091,   1093,   1097,   1103,   1109,   1117,   1123,   1129,   1151,
+  1153,   1163,   1171,   1181,   1187,   1193,   1201,   1213,   1217,   1223,
+  1229,   1231,   1237,   1249,   1259,   1277,   1279,   1283,   1289,   1291,
+  1297,   1301,   1303,   1307,   1319,   1321,   1327,   1361,   1367,   1373,
+  1381,   1399,   1409,   1423,   1427,   1429,   1433,   1439,   1447,   1451,
+  1453,   1459,   1471,   1481,   1483,   1487,   1489,   1493,   1499,   1511,
+  1523,   1531,   1543,   1549,   1553,   1559,   1567,   1571,   1579,   1583,
+  1597,   1601,   1607,   1609,   1613,   1619,   1621,   1627,   1637,   1657,
+  1663,   1667,   1669,   1693,   1697,   1699,   1709,   1721,   1723,   1733,
+  1741,   1747,   1753,   1759,   1777,   1783,   1787,   1789,   1801,   1811,
+  1823,   1831,   1847,   1861,   1867,   1871,   1873,   1877,   1879,   1889,
+  1901,   1907,   1913,   1931,   1933,   1949,   1951,   1973,   1979,   1987,
+  1993,   1997,   1999,   2003,   2011,   2017,   2027,   2029,   2039,   2053,
+  2063,   2069,   2081,   2083,   2087,   2089,   2099,   2111,   2113,   2129,
+  2131,   2137,   2141,   2143,   2153,   2161,   2179,   2203,   2207,   2213,
+  2221,   2237,   2239,   2243,   2251,   2267,   2269,   2273,   2281,   2287,
+  2293,   2297,   2309,   2311,   2333,   2339,   2341,   2347,   2351,   2357,
+  2371,   2377,   2381,   2383,   2389,   2393,   2399,   2411,   2417,   2423,
+  2437,   2441,   2447,   2459,   2467,   2473,   2477,   2503,   2521,   2531,
+  2539,   2543,   2549,   2551,   2557,   2579,   2591,   2593,   2609,   2617,
+  2621,   2633,   2647,   2657,   2659,   2663,   2671,   2677,   2683,   2687,
+  2689,   2693,   2699,   2707,   2711,   2713,   2719,   2729,   2731,   2741,
+  2749,   2753,   2767,   2777,   2789,   2791,   2797,   2801,   2803,   2819,
+  2833,   2837,   2843,   2851,   2857,   2861,   2879,   2887,   2897,   2903,
+  2909,   2917,   2927,   2939,   2953,   2957,   2963,   2969,   2971,   2999,
+  3001,   3011,   3019,   3023,   3037,   3041,   3049,   3061,   3067,   3079,
+  3083,   3089,   3109,   3119,   3121,   3137,   3163,   3167,   3169,   3181,
+  3187,   3191,   3203,   3209,   3217,   3221,   3229,   3251,   3253,   3257,
+  3259,   3271,   3299,   3301,   3307,   3313,   3319,   3323,   3329,   3331,
+  3343,   3347,   3359,   3361,   3371,   3373,   3389,   3391,   3407,   3413,
+  3433,   3449,   3457,   3461,   3463,   3467,   3469,   3491,   3499,   3511,
+  3517,   3527,   3529,   3533,   3539,   3541,   3547,   3557,   3559,   3571,
+  3581,   3583,   3593,   3607,   3613,   3617,   3623,   3631,   3637,   3643,
+  3659,   3671,   3673,   3677,   3691,   3697,   3701,   3709,   3719,   3727,
+  3733,   3739,   3761,   3767,   3769,   3779,   3793,   3797,   3803,   3821,
+  3823,   3833,   3847,   3851,   3853,   3863,   3877,   3881,   3889,   3907,
+  3911,   3917,   3919,   3923,   3929,   3931,   3943,   3947,   3967,   3989,
+  4001,   4003,   4007,   4013,   4019,   4021,   4027,   4049,   4051,   4057,
+  4073,   4079,   4091,   4093,   4099,   4111,   4127,   4129,   4133,   4139,
+  4153,   4157,   4159,   4177,   4201,   4211,   4217,   4219,   4229,   4231,
+  4241,   4243,   4253,   4259,   4261,   4271,   4273,   4283,   4289,   4297,
+  4327,   4337,   4339,   4349,   4357,   4363,   4373,   4391,   4397,   4409,
+  4421,   4423,   4441,   4447,   4451,   4457,   4463,   4481,   4483,   4493,
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