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