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# =================================================================== # # Copyright (c) 2018, Helder Eijs <helderijs@gmail.com> # All rights reserved. # # Redistribution and use in source and binary forms, with or without # modification, are permitted provided that the following conditions # are met: # # 1. Redistributions of source code must retain the above copyright # notice, this list of conditions and the following disclaimer. # 2. Redistributions in binary form must reproduce the above copyright # notice, this list of conditions and the following disclaimer in # the documentation and/or other materials provided with the # distribution. # # THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS # "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT # LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS # FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE # COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, # INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, # BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; # LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER # CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT # LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN # ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE # POSSIBILITY OF SUCH DAMAGE. # =================================================================== import abc from Cryptodome.Util.py3compat import iter_range, bord, bchr, ABC from Cryptodome import Random class IntegerBase(ABC): # Conversions @abc.abstractmethod def __int__(self): pass @abc.abstractmethod def __str__(self): pass @abc.abstractmethod def __repr__(self): pass @abc.abstractmethod def to_bytes(self, block_size=0, byteorder='big'): pass @staticmethod @abc.abstractmethod def from_bytes(byte_string, byteorder='big'): pass # Relations @abc.abstractmethod def __eq__(self, term): pass @abc.abstractmethod def __ne__(self, term): pass @abc.abstractmethod def __lt__(self, term): pass @abc.abstractmethod def __le__(self, term): pass @abc.abstractmethod def __gt__(self, term): pass @abc.abstractmethod def __ge__(self, term): pass @abc.abstractmethod def __nonzero__(self): pass __bool__ = __nonzero__ @abc.abstractmethod def is_negative(self): pass # Arithmetic operations @abc.abstractmethod def __add__(self, term): pass @abc.abstractmethod def __sub__(self, term): pass @abc.abstractmethod def __mul__(self, factor): pass @abc.abstractmethod def __floordiv__(self, divisor): pass @abc.abstractmethod def __mod__(self, divisor): pass @abc.abstractmethod def inplace_pow(self, exponent, modulus=None): pass @abc.abstractmethod def __pow__(self, exponent, modulus=None): pass @abc.abstractmethod def __abs__(self): pass @abc.abstractmethod def sqrt(self, modulus=None): pass @abc.abstractmethod def __iadd__(self, term): pass @abc.abstractmethod def __isub__(self, term): pass @abc.abstractmethod def __imul__(self, term): pass @abc.abstractmethod def __imod__(self, term): pass # Boolean/bit operations @abc.abstractmethod def __and__(self, term): pass @abc.abstractmethod def __or__(self, term): pass @abc.abstractmethod def __rshift__(self, pos): pass @abc.abstractmethod def __irshift__(self, pos): pass @abc.abstractmethod def __lshift__(self, pos): pass @abc.abstractmethod def __ilshift__(self, pos): pass @abc.abstractmethod def get_bit(self, n): pass # Extra @abc.abstractmethod def is_odd(self): pass @abc.abstractmethod def is_even(self): pass @abc.abstractmethod def size_in_bits(self): pass @abc.abstractmethod def size_in_bytes(self): pass @abc.abstractmethod def is_perfect_square(self): pass @abc.abstractmethod def fail_if_divisible_by(self, small_prime): pass @abc.abstractmethod def multiply_accumulate(self, a, b): pass @abc.abstractmethod def set(self, source): pass @abc.abstractmethod def inplace_inverse(self, modulus): pass @abc.abstractmethod def inverse(self, modulus): pass @abc.abstractmethod def gcd(self, term): pass @abc.abstractmethod def lcm(self, term): pass @staticmethod @abc.abstractmethod def jacobi_symbol(a, n): pass @staticmethod def _tonelli_shanks(n, p): """Tonelli-shanks algorithm for computing the square root of n modulo a prime p. n must be in the range [0..p-1]. p must be at least even. The return value r is the square root of modulo p. If non-zero, another solution will also exist (p-r). Note we cannot assume that p is really a prime: if it's not, we can either raise an exception or return the correct value. """ # See https://rosettacode.org/wiki/Tonelli-Shanks_algorithm if n in (0, 1): return n if p % 4 == 3: root = pow(n, (p + 1) // 4, p) if pow(root, 2, p) != n: raise ValueError("Cannot compute square root") return root s = 1 q = (p - 1) // 2 while not (q & 1): s += 1 q >>= 1 z = n.__class__(2) while True: euler = pow(z, (p - 1) // 2, p) if euler == 1: z += 1 continue if euler == p - 1: break # Most probably p is not a prime raise ValueError("Cannot compute square root") m = s c = pow(z, q, p) t = pow(n, q, p) r = pow(n, (q + 1) // 2, p) while t != 1: for i in iter_range(0, m): if pow(t, 2**i, p) == 1: break if i == m: raise ValueError("Cannot compute square root of %d mod %d" % (n, p)) b = pow(c, 2**(m - i - 1), p) m = i c = b**2 % p t = (t * b**2) % p r = (r * b) % p if pow(r, 2, p) != n: raise ValueError("Cannot compute square root") return r @classmethod def random(cls, **kwargs): """Generate a random natural integer of a certain size. :Keywords: exact_bits : positive integer The length in bits of the resulting random Integer number. The number is guaranteed to fulfil the relation: 2^bits > result >= 2^(bits - 1) max_bits : positive integer The maximum length in bits of the resulting random Integer number. The number is guaranteed to fulfil the relation: 2^bits > result >=0 randfunc : callable A function that returns a random byte string. The length of the byte string is passed as parameter. Optional. If not provided (or ``None``), randomness is read from the system RNG. :Return: a Integer object """ exact_bits = kwargs.pop("exact_bits", None) max_bits = kwargs.pop("max_bits", None) randfunc = kwargs.pop("randfunc", None) if randfunc is None: randfunc = Random.new().read if exact_bits is None and max_bits is None: raise ValueError("Either 'exact_bits' or 'max_bits' must be specified") if exact_bits is not None and max_bits is not None: raise ValueError("'exact_bits' and 'max_bits' are mutually exclusive") bits = exact_bits or max_bits bytes_needed = ((bits - 1) // 8) + 1 significant_bits_msb = 8 - (bytes_needed * 8 - bits) msb = bord(randfunc(1)[0]) if exact_bits is not None: msb |= 1 << (significant_bits_msb - 1) msb &= (1 << significant_bits_msb) - 1 return cls.from_bytes(bchr(msb) + randfunc(bytes_needed - 1)) @classmethod def random_range(cls, **kwargs): """Generate a random integer within a given internal. :Keywords: min_inclusive : integer The lower end of the interval (inclusive). max_inclusive : integer The higher end of the interval (inclusive). max_exclusive : integer The higher end of the interval (exclusive). randfunc : callable A function that returns a random byte string. The length of the byte string is passed as parameter. Optional. If not provided (or ``None``), randomness is read from the system RNG. :Returns: An Integer randomly taken in the given interval. """ min_inclusive = kwargs.pop("min_inclusive", None) max_inclusive = kwargs.pop("max_inclusive", None) max_exclusive = kwargs.pop("max_exclusive", None) randfunc = kwargs.pop("randfunc", None) if kwargs: raise ValueError("Unknown keywords: " + str(kwargs.keys)) if None not in (max_inclusive, max_exclusive): raise ValueError("max_inclusive and max_exclusive cannot be both" " specified") if max_exclusive is not None: max_inclusive = max_exclusive - 1 if None in (min_inclusive, max_inclusive): raise ValueError("Missing keyword to identify the interval") if randfunc is None: randfunc = Random.new().read norm_maximum = max_inclusive - min_inclusive bits_needed = cls(norm_maximum).size_in_bits() norm_candidate = -1 while not 0 <= norm_candidate <= norm_maximum: norm_candidate = cls.random( max_bits=bits_needed, randfunc=randfunc ) return norm_candidate + min_inclusive @staticmethod @abc.abstractmethod def _mult_modulo_bytes(term1, term2, modulus): """Multiply two integers, take the modulo, and encode as big endian. This specialized method is used for RSA decryption. Args: term1 : integer The first term of the multiplication, non-negative. term2 : integer The second term of the multiplication, non-negative. modulus: integer The modulus, a positive odd number. :Returns: A byte string, with the result of the modular multiplication encoded in big endian mode. It is as long as the modulus would be, with zero padding on the left if needed. """ pass