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Diffstat (limited to 'frozen_deps/Crypto/Util/number.py')
| -rw-r--r-- | frozen_deps/Crypto/Util/number.py | 1456 |
1 files changed, 1456 insertions, 0 deletions
diff --git a/frozen_deps/Crypto/Util/number.py b/frozen_deps/Crypto/Util/number.py new file mode 100644 index 0000000..0e1baa0 --- /dev/null +++ b/frozen_deps/Crypto/Util/number.py @@ -0,0 +1,1456 @@ +# +# 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 = int +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 |= 2 ** (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 = int(u), int(v) + u1, v1 = 1, 0 + 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 range (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 range (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(int(N), int(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(14142135623730950489 * (2 ** (511 + 128*x)), + 10000000000000000000)[0] + upper_bound = (1 << (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 range ((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 >= 1 << 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(int(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 = int(n) + pack = struct.pack + while n > 0: + s = pack('>I', n & 0xffffffff) + 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 = 0 + 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, + 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, + 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, + 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, + 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, + 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, + 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, + 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, + 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, + 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, + 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, + 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, + 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, + 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, + 5641, 5647, 5651, 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