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Dongho Kim
2024-12-01 04:19:04 +09:00
parent 00b0afd17a
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47
env/lib/python3.12/site-packages/Crypto/Math/Numbers.py vendored Normal file
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# ===================================================================
#
# Copyright (c) 2014, Legrandin <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.
# ===================================================================
__all__ = ["Integer"]
import os
try:
if os.getenv("PYCRYPTODOME_DISABLE_GMP"):
raise ImportError()
from Crypto.Math._IntegerGMP import IntegerGMP as Integer
from Crypto.Math._IntegerGMP import implementation as _implementation
except (ImportError, OSError, AttributeError):
try:
from Crypto.Math._IntegerCustom import IntegerCustom as Integer
from Crypto.Math._IntegerCustom import implementation as _implementation
except (ImportError, OSError):
from Crypto.Math._IntegerNative import IntegerNative as Integer
_implementation = {}

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env/lib/python3.12/site-packages/Crypto/Math/Numbers.pyi vendored Normal file
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from Crypto.Math._IntegerBase import IntegerBase as Integer
__all__ = ['Integer']

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env/lib/python3.12/site-packages/Crypto/Math/Primality.py vendored Normal file
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# ===================================================================
#
# Copyright (c) 2014, Legrandin <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.
# ===================================================================
"""Functions to create and test prime numbers.
:undocumented: __package__
"""
from Crypto import Random
from Crypto.Math.Numbers import Integer
from Crypto.Util.py3compat import iter_range
COMPOSITE = 0
PROBABLY_PRIME = 1
def miller_rabin_test(candidate, iterations, randfunc=None):
"""Perform a Miller-Rabin primality test on an integer.
The test is specified in Section C.3.1 of `FIPS PUB 186-4`__.
:Parameters:
candidate : integer
The number to test for primality.
iterations : integer
The maximum number of iterations to perform before
declaring a candidate a probable prime.
randfunc : callable
An RNG function where bases are taken from.
:Returns:
``Primality.COMPOSITE`` or ``Primality.PROBABLY_PRIME``.
.. __: http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf
"""
if not isinstance(candidate, Integer):
candidate = Integer(candidate)
if candidate in (1, 2, 3, 5):
return PROBABLY_PRIME
if candidate.is_even():
return COMPOSITE
one = Integer(1)
minus_one = Integer(candidate - 1)
if randfunc is None:
randfunc = Random.new().read
# Step 1 and 2
m = Integer(minus_one)
a = 0
while m.is_even():
m >>= 1
a += 1
# Skip step 3
# Step 4
for i in iter_range(iterations):
# Step 4.1-2
base = 1
while base in (one, minus_one):
base = Integer.random_range(min_inclusive=2,
max_inclusive=candidate - 2,
randfunc=randfunc)
assert(2 <= base <= candidate - 2)
# Step 4.3-4.4
z = pow(base, m, candidate)
if z in (one, minus_one):
continue
# Step 4.5
for j in iter_range(1, a):
z = pow(z, 2, candidate)
if z == minus_one:
break
if z == one:
return COMPOSITE
else:
return COMPOSITE
# Step 5
return PROBABLY_PRIME
def lucas_test(candidate):
"""Perform a Lucas primality test on an integer.
The test is specified in Section C.3.3 of `FIPS PUB 186-4`__.
:Parameters:
candidate : integer
The number to test for primality.
:Returns:
``Primality.COMPOSITE`` or ``Primality.PROBABLY_PRIME``.
.. __: http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf
"""
if not isinstance(candidate, Integer):
candidate = Integer(candidate)
# Step 1
if candidate in (1, 2, 3, 5):
return PROBABLY_PRIME
if candidate.is_even() or candidate.is_perfect_square():
return COMPOSITE
# Step 2
def alternate():
value = 5
while True:
yield value
if value > 0:
value += 2
else:
value -= 2
value = -value
for D in alternate():
if candidate in (D, -D):
continue
js = Integer.jacobi_symbol(D, candidate)
if js == 0:
return COMPOSITE
if js == -1:
break
# Found D. P=1 and Q=(1-D)/4 (note that Q is guaranteed to be an integer)
# Step 3
# This is \delta(n) = n - jacobi(D/n)
K = candidate + 1
# Step 4
r = K.size_in_bits() - 1
# Step 5
# U_1=1 and V_1=P
U_i = Integer(1)
V_i = Integer(1)
U_temp = Integer(0)
V_temp = Integer(0)
# Step 6
for i in iter_range(r - 1, -1, -1):
# Square
# U_temp = U_i * V_i % candidate
U_temp.set(U_i)
U_temp *= V_i
U_temp %= candidate
# V_temp = (((V_i ** 2 + (U_i ** 2 * D)) * K) >> 1) % candidate
V_temp.set(U_i)
V_temp *= U_i
V_temp *= D
V_temp.multiply_accumulate(V_i, V_i)
if V_temp.is_odd():
V_temp += candidate
V_temp >>= 1
V_temp %= candidate
# Multiply
if K.get_bit(i):
# U_i = (((U_temp + V_temp) * K) >> 1) % candidate
U_i.set(U_temp)
U_i += V_temp
if U_i.is_odd():
U_i += candidate
U_i >>= 1
U_i %= candidate
# V_i = (((V_temp + U_temp * D) * K) >> 1) % candidate
V_i.set(V_temp)
V_i.multiply_accumulate(U_temp, D)
if V_i.is_odd():
V_i += candidate
V_i >>= 1
V_i %= candidate
else:
U_i.set(U_temp)
V_i.set(V_temp)
# Step 7
if U_i == 0:
return PROBABLY_PRIME
return COMPOSITE
from Crypto.Util.number import sieve_base as _sieve_base_large
## The optimal number of small primes to use for the sieve
## is probably dependent on the platform and the candidate size
_sieve_base = set(_sieve_base_large[:100])
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
def generate_probable_prime(**kwargs):
"""Generate a random probable prime.
The prime will not have any specific properties
(e.g. it will not be a *strong* prime).
Random numbers are evaluated for primality until one
passes all tests, consisting of a certain number of
Miller-Rabin tests with random bases followed by
a single Lucas test.
The number of Miller-Rabin iterations is chosen such that
the probability that the output number is a non-prime is
less than 1E-30 (roughly 2^{-100}).
This approach is compliant to `FIPS PUB 186-4`__.
:Keywords:
exact_bits : integer
The desired size in bits of the probable prime.
It must be at least 160.
randfunc : callable
An RNG function where candidate primes are taken from.
prime_filter : callable
A function that takes an Integer as parameter and returns
True if the number can be passed to further primality tests,
False if it should be immediately discarded.
:Return:
A probable prime in the range 2^exact_bits > p > 2^(exact_bits-1).
.. __: http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf
"""
exact_bits = kwargs.pop("exact_bits", None)
randfunc = kwargs.pop("randfunc", None)
prime_filter = kwargs.pop("prime_filter", lambda x: True)
if kwargs:
raise ValueError("Unknown parameters: " + kwargs.keys())
if exact_bits is None:
raise ValueError("Missing exact_bits parameter")
if exact_bits < 160:
raise ValueError("Prime number is not big enough.")
if randfunc is None:
randfunc = Random.new().read
result = COMPOSITE
while result == COMPOSITE:
candidate = Integer.random(exact_bits=exact_bits,
randfunc=randfunc) | 1
if not prime_filter(candidate):
continue
result = test_probable_prime(candidate, randfunc)
return candidate
def generate_probable_safe_prime(**kwargs):
"""Generate a random, probable safe prime.
Note this operation is much slower than generating a simple prime.
:Keywords:
exact_bits : integer
The desired size in bits of the probable safe prime.
randfunc : callable
An RNG function where candidate primes are taken from.
:Return:
A probable safe prime in the range
2^exact_bits > p > 2^(exact_bits-1).
"""
exact_bits = kwargs.pop("exact_bits", None)
randfunc = kwargs.pop("randfunc", None)
if kwargs:
raise ValueError("Unknown parameters: " + kwargs.keys())
if randfunc is None:
randfunc = Random.new().read
result = COMPOSITE
while result == COMPOSITE:
q = generate_probable_prime(exact_bits=exact_bits - 1, randfunc=randfunc)
candidate = q * 2 + 1
if candidate.size_in_bits() != exact_bits:
continue
result = test_probable_prime(candidate, randfunc=randfunc)
return candidate

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env/lib/python3.12/site-packages/Crypto/Math/Primality.pyi vendored Normal file
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from typing import Callable, Optional, Union, Set
PrimeResult = int
COMPOSITE: PrimeResult
PROBABLY_PRIME: PrimeResult
def miller_rabin_test(candidate: int, iterations: int, randfunc: Optional[Callable[[int],bytes]]=None) -> PrimeResult: ...
def lucas_test(candidate: int) -> PrimeResult: ...
_sieve_base: Set[int]
def test_probable_prime(candidate: int, randfunc: Optional[Callable[[int],bytes]]=None) -> PrimeResult: ...
def generate_probable_prime(*,
exact_bits: int = ...,
randfunc: Callable[[int],bytes] = ...,
prime_filter: Callable[[int],bool] = ...) -> int: ...
def generate_probable_safe_prime(*,
exact_bits: int = ...,
randfunc: Callable[[int],bytes] = ...) -> int: ...

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env/lib/python3.12/site-packages/Crypto/Math/_IntegerBase.py vendored Normal file
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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 Crypto.Util.py3compat import iter_range, bord, bchr, ABC
from Crypto 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

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from typing import Optional, Union, Callable
RandFunc = Callable[[int],int]
class IntegerBase:
def __init__(self, value: Union[IntegerBase, int]): ...
def __int__(self) -> int: ...
def __str__(self) -> str: ...
def __repr__(self) -> str: ...
def to_bytes(self, block_size: Optional[int]=0, byteorder: str= ...) -> bytes: ...
@staticmethod
def from_bytes(byte_string: bytes, byteorder: Optional[str] = ...) -> IntegerBase: ...
def __eq__(self, term: object) -> bool: ...
def __ne__(self, term: object) -> bool: ...
def __lt__(self, term: Union[IntegerBase, int]) -> bool: ...
def __le__(self, term: Union[IntegerBase, int]) -> bool: ...
def __gt__(self, term: Union[IntegerBase, int]) -> bool: ...
def __ge__(self, term: Union[IntegerBase, int]) -> bool: ...
def __nonzero__(self) -> bool: ...
def is_negative(self) -> bool: ...
def __add__(self, term: Union[IntegerBase, int]) -> IntegerBase: ...
def __sub__(self, term: Union[IntegerBase, int]) -> IntegerBase: ...
def __mul__(self, term: Union[IntegerBase, int]) -> IntegerBase: ...
def __floordiv__(self, divisor: Union[IntegerBase, int]) -> IntegerBase: ...
def __mod__(self, divisor: Union[IntegerBase, int]) -> IntegerBase: ...
def inplace_pow(self, exponent: int, modulus: Optional[Union[IntegerBase, int]]=None) -> IntegerBase: ...
def __pow__(self, exponent: int, modulus: Optional[int]) -> IntegerBase: ...
def __abs__(self) -> IntegerBase: ...
def sqrt(self, modulus: Optional[int]) -> IntegerBase: ...
def __iadd__(self, term: Union[IntegerBase, int]) -> IntegerBase: ...
def __isub__(self, term: Union[IntegerBase, int]) -> IntegerBase: ...
def __imul__(self, term: Union[IntegerBase, int]) -> IntegerBase: ...
def __imod__(self, divisor: Union[IntegerBase, int]) -> IntegerBase: ...
def __and__(self, term: Union[IntegerBase, int]) -> IntegerBase: ...
def __or__(self, term: Union[IntegerBase, int]) -> IntegerBase: ...
def __rshift__(self, pos: Union[IntegerBase, int]) -> IntegerBase: ...
def __irshift__(self, pos: Union[IntegerBase, int]) -> IntegerBase: ...
def __lshift__(self, pos: Union[IntegerBase, int]) -> IntegerBase: ...
def __ilshift__(self, pos: Union[IntegerBase, int]) -> IntegerBase: ...
def get_bit(self, n: int) -> bool: ...
def is_odd(self) -> bool: ...
def is_even(self) -> bool: ...
def size_in_bits(self) -> int: ...
def size_in_bytes(self) -> int: ...
def is_perfect_square(self) -> bool: ...
def fail_if_divisible_by(self, small_prime: Union[IntegerBase, int]) -> None: ...
def multiply_accumulate(self, a: Union[IntegerBase, int], b: Union[IntegerBase, int]) -> IntegerBase: ...
def set(self, source: Union[IntegerBase, int]) -> IntegerBase: ...
def inplace_inverse(self, modulus: Union[IntegerBase, int]) -> IntegerBase: ...
def inverse(self, modulus: Union[IntegerBase, int]) -> IntegerBase: ...
def gcd(self, term: Union[IntegerBase, int]) -> IntegerBase: ...
def lcm(self, term: Union[IntegerBase, int]) -> IntegerBase: ...
@staticmethod
def jacobi_symbol(a: Union[IntegerBase, int], n: Union[IntegerBase, int]) -> IntegerBase: ...
@staticmethod
def _tonelli_shanks(n: Union[IntegerBase, int], p: Union[IntegerBase, int]) -> IntegerBase : ...
@classmethod
def random(cls, **kwargs: Union[int,RandFunc]) -> IntegerBase : ...
@classmethod
def random_range(cls, **kwargs: Union[int,RandFunc]) -> IntegerBase : ...
@staticmethod
def _mult_modulo_bytes(term1: Union[IntegerBase, int],
term2: Union[IntegerBase, int],
modulus: Union[IntegerBase, int]) -> bytes: ...

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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.
# ===================================================================
from ._IntegerNative import IntegerNative
from Crypto.Util.number import long_to_bytes, bytes_to_long
from Crypto.Util._raw_api import (load_pycryptodome_raw_lib,
create_string_buffer,
get_raw_buffer, backend,
c_size_t, c_ulonglong)
from Crypto.Random.random import getrandbits
c_defs = """
int monty_pow(uint8_t *out,
const uint8_t *base,
const uint8_t *exp,
const uint8_t *modulus,
size_t len,
uint64_t seed);
int monty_multiply(uint8_t *out,
const uint8_t *term1,
const uint8_t *term2,
const uint8_t *modulus,
size_t len);
"""
_raw_montgomery = load_pycryptodome_raw_lib("Crypto.Math._modexp", c_defs)
implementation = {"library": "custom", "api": backend}
class IntegerCustom(IntegerNative):
@staticmethod
def from_bytes(byte_string, byteorder='big'):
if byteorder == 'big':
pass
elif byteorder == 'little':
byte_string = bytearray(byte_string)
byte_string.reverse()
else:
raise ValueError("Incorrect byteorder")
return IntegerCustom(bytes_to_long(byte_string))
def inplace_pow(self, exponent, modulus=None):
exp_value = int(exponent)
if exp_value < 0:
raise ValueError("Exponent must not be negative")
# No modular reduction
if modulus is None:
self._value = pow(self._value, exp_value)
return self
# With modular reduction
mod_value = int(modulus)
if mod_value < 0:
raise ValueError("Modulus must be positive")
if mod_value == 0:
raise ZeroDivisionError("Modulus cannot be zero")
# C extension only works with odd moduli
if (mod_value & 1) == 0:
self._value = pow(self._value, exp_value, mod_value)
return self
# C extension only works with bases smaller than modulus
if self._value >= mod_value:
self._value %= mod_value
max_len = len(long_to_bytes(max(self._value, exp_value, mod_value)))
base_b = long_to_bytes(self._value, max_len)
exp_b = long_to_bytes(exp_value, max_len)
modulus_b = long_to_bytes(mod_value, max_len)
out = create_string_buffer(max_len)
error = _raw_montgomery.monty_pow(
out,
base_b,
exp_b,
modulus_b,
c_size_t(max_len),
c_ulonglong(getrandbits(64))
)
if error:
raise ValueError("monty_pow failed with error: %d" % error)
result = bytes_to_long(get_raw_buffer(out))
self._value = result
return self
@staticmethod
def _mult_modulo_bytes(term1, term2, modulus):
# With modular reduction
mod_value = int(modulus)
if mod_value < 0:
raise ValueError("Modulus must be positive")
if mod_value == 0:
raise ZeroDivisionError("Modulus cannot be zero")
# C extension only works with odd moduli
if (mod_value & 1) == 0:
raise ValueError("Odd modulus is required")
# C extension only works with non-negative terms smaller than modulus
if term1 >= mod_value or term1 < 0:
term1 %= mod_value
if term2 >= mod_value or term2 < 0:
term2 %= mod_value
modulus_b = long_to_bytes(mod_value)
numbers_len = len(modulus_b)
term1_b = long_to_bytes(term1, numbers_len)
term2_b = long_to_bytes(term2, numbers_len)
out = create_string_buffer(numbers_len)
error = _raw_montgomery.monty_multiply(
out,
term1_b,
term2_b,
modulus_b,
c_size_t(numbers_len)
)
if error:
raise ValueError("monty_multiply failed with error: %d" % error)
return get_raw_buffer(out)

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from typing import Any
from ._IntegerNative import IntegerNative
_raw_montgomery = Any
class IntegerCustom(IntegerNative):
pass

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# ===================================================================
#
# Copyright (c) 2014, Legrandin <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 sys
import struct
from Crypto.Util.py3compat import is_native_int
from Crypto.Util._raw_api import (backend, load_lib,
c_ulong, c_size_t, c_uint8_ptr)
from ._IntegerBase import IntegerBase
gmp_defs = """typedef unsigned long UNIX_ULONG;
typedef struct { int a; int b; void *c; } MPZ;
typedef MPZ mpz_t[1];
typedef UNIX_ULONG mp_bitcnt_t;
void __gmpz_init (mpz_t x);
void __gmpz_init_set (mpz_t rop, const mpz_t op);
void __gmpz_init_set_ui (mpz_t rop, UNIX_ULONG op);
UNIX_ULONG __gmpz_get_ui (const mpz_t op);
void __gmpz_set (mpz_t rop, const mpz_t op);
void __gmpz_set_ui (mpz_t rop, UNIX_ULONG op);
void __gmpz_add (mpz_t rop, const mpz_t op1, const mpz_t op2);
void __gmpz_add_ui (mpz_t rop, const mpz_t op1, UNIX_ULONG op2);
void __gmpz_sub_ui (mpz_t rop, const mpz_t op1, UNIX_ULONG op2);
void __gmpz_addmul (mpz_t rop, const mpz_t op1, const mpz_t op2);
void __gmpz_addmul_ui (mpz_t rop, const mpz_t op1, UNIX_ULONG op2);
void __gmpz_submul_ui (mpz_t rop, const mpz_t op1, UNIX_ULONG op2);
void __gmpz_import (mpz_t rop, size_t count, int order, size_t size,
int endian, size_t nails, const void *op);
void * __gmpz_export (void *rop, size_t *countp, int order,
size_t size,
int endian, size_t nails, const mpz_t op);
size_t __gmpz_sizeinbase (const mpz_t op, int base);
void __gmpz_sub (mpz_t rop, const mpz_t op1, const mpz_t op2);
void __gmpz_mul (mpz_t rop, const mpz_t op1, const mpz_t op2);
void __gmpz_mul_ui (mpz_t rop, const mpz_t op1, UNIX_ULONG op2);
int __gmpz_cmp (const mpz_t op1, const mpz_t op2);
void __gmpz_powm (mpz_t rop, const mpz_t base, const mpz_t exp, const
mpz_t mod);
void __gmpz_powm_ui (mpz_t rop, const mpz_t base, UNIX_ULONG exp,
const mpz_t mod);
void __gmpz_pow_ui (mpz_t rop, const mpz_t base, UNIX_ULONG exp);
void __gmpz_sqrt(mpz_t rop, const mpz_t op);
void __gmpz_mod (mpz_t r, const mpz_t n, const mpz_t d);
void __gmpz_neg (mpz_t rop, const mpz_t op);
void __gmpz_abs (mpz_t rop, const mpz_t op);
void __gmpz_and (mpz_t rop, const mpz_t op1, const mpz_t op2);
void __gmpz_ior (mpz_t rop, const mpz_t op1, const mpz_t op2);
void __gmpz_clear (mpz_t x);
void __gmpz_tdiv_q_2exp (mpz_t q, const mpz_t n, mp_bitcnt_t b);
void __gmpz_fdiv_q (mpz_t q, const mpz_t n, const mpz_t d);
void __gmpz_mul_2exp (mpz_t rop, const mpz_t op1, mp_bitcnt_t op2);
int __gmpz_tstbit (const mpz_t op, mp_bitcnt_t bit_index);
int __gmpz_perfect_square_p (const mpz_t op);
int __gmpz_jacobi (const mpz_t a, const mpz_t b);
void __gmpz_gcd (mpz_t rop, const mpz_t op1, const mpz_t op2);
UNIX_ULONG __gmpz_gcd_ui (mpz_t rop, const mpz_t op1,
UNIX_ULONG op2);
void __gmpz_lcm (mpz_t rop, const mpz_t op1, const mpz_t op2);
int __gmpz_invert (mpz_t rop, const mpz_t op1, const mpz_t op2);
int __gmpz_divisible_p (const mpz_t n, const mpz_t d);
int __gmpz_divisible_ui_p (const mpz_t n, UNIX_ULONG d);
size_t __gmpz_size (const mpz_t op);
UNIX_ULONG __gmpz_getlimbn (const mpz_t op, size_t n);
"""
if sys.platform == "win32":
raise ImportError("Not using GMP on Windows")
lib = load_lib("gmp", gmp_defs)
implementation = {"library": "gmp", "api": backend}
if hasattr(lib, "__mpir_version"):
raise ImportError("MPIR library detected")
# Lazy creation of GMP methods
class _GMP(object):
def __getattr__(self, name):
if name.startswith("mpz_"):
func_name = "__gmpz_" + name[4:]
elif name.startswith("gmp_"):
func_name = "__gmp_" + name[4:]
else:
raise AttributeError("Attribute %s is invalid" % name)
func = getattr(lib, func_name)
setattr(self, name, func)
return func
_gmp = _GMP()
# In order to create a function that returns a pointer to
# a new MPZ structure, we need to break the abstraction
# and know exactly what ffi backend we have
if implementation["api"] == "ctypes":
from ctypes import Structure, c_int, c_void_p, byref
class _MPZ(Structure):
_fields_ = [('_mp_alloc', c_int),
('_mp_size', c_int),
('_mp_d', c_void_p)]
def new_mpz():
return byref(_MPZ())
_gmp.mpz_getlimbn.restype = c_ulong
else:
# We are using CFFI
from Crypto.Util._raw_api import ffi
def new_mpz():
return ffi.new("MPZ*")
# Size of a native word
_sys_bits = 8 * struct.calcsize("P")
class IntegerGMP(IntegerBase):
"""A fast, arbitrary precision integer"""
_zero_mpz_p = new_mpz()
_gmp.mpz_init_set_ui(_zero_mpz_p, c_ulong(0))
def __init__(self, value):
"""Initialize the integer to the given value."""
self._mpz_p = new_mpz()
self._initialized = False
if isinstance(value, float):
raise ValueError("A floating point type is not a natural number")
if is_native_int(value):
_gmp.mpz_init(self._mpz_p)
self._initialized = True
if value == 0:
return
tmp = new_mpz()
_gmp.mpz_init(tmp)
try:
positive = value >= 0
reduce = abs(value)
slots = (reduce.bit_length() - 1) // 32 + 1
while slots > 0:
slots = slots - 1
_gmp.mpz_set_ui(tmp,
c_ulong(0xFFFFFFFF & (reduce >> (slots * 32))))
_gmp.mpz_mul_2exp(tmp, tmp, c_ulong(slots * 32))
_gmp.mpz_add(self._mpz_p, self._mpz_p, tmp)
finally:
_gmp.mpz_clear(tmp)
if not positive:
_gmp.mpz_neg(self._mpz_p, self._mpz_p)
elif isinstance(value, IntegerGMP):
_gmp.mpz_init_set(self._mpz_p, value._mpz_p)
self._initialized = True
else:
raise NotImplementedError
# Conversions
def __int__(self):
tmp = new_mpz()
_gmp.mpz_init_set(tmp, self._mpz_p)
try:
value = 0
slot = 0
while _gmp.mpz_cmp(tmp, self._zero_mpz_p) != 0:
lsb = _gmp.mpz_get_ui(tmp) & 0xFFFFFFFF
value |= lsb << (slot * 32)
_gmp.mpz_tdiv_q_2exp(tmp, tmp, c_ulong(32))
slot = slot + 1
finally:
_gmp.mpz_clear(tmp)
if self < 0:
value = -value
return int(value)
def __str__(self):
return str(int(self))
def __repr__(self):
return "Integer(%s)" % str(self)
# Only Python 2.x
def __hex__(self):
return hex(int(self))
# Only Python 3.x
def __index__(self):
return int(self)
def to_bytes(self, block_size=0, byteorder='big'):
"""Convert the number into a byte string.
This method encodes the number in network order and prepends
as many zero bytes as required. It only works for non-negative
values.
:Parameters:
block_size : integer
The exact size the output byte string must have.
If zero, the string has the minimal length.
byteorder : string
'big' for big-endian integers (default), 'little' for litte-endian.
:Returns:
A byte string.
:Raise ValueError:
If the value is negative or if ``block_size`` is
provided and the length of the byte string would exceed it.
"""
if self < 0:
raise ValueError("Conversion only valid for non-negative numbers")
num_limbs = _gmp.mpz_size(self._mpz_p)
if _sys_bits == 32:
spchar = "L"
num_limbs = max(1, num_limbs, (block_size + 3) // 4)
elif _sys_bits == 64:
spchar = "Q"
num_limbs = max(1, num_limbs, (block_size + 7) // 8)
else:
raise ValueError("Unknown limb size")
# mpz_getlimbn returns 0 if i is larger than the number of actual limbs
limbs = [_gmp.mpz_getlimbn(self._mpz_p, num_limbs - i - 1) for i in range(num_limbs)]
result = struct.pack(">" + spchar * num_limbs, *limbs)
cutoff_len = len(result) - block_size
if block_size == 0:
result = result.lstrip(b'\x00')
elif cutoff_len > 0:
if result[:cutoff_len] != b'\x00' * (cutoff_len):
raise ValueError("Number is too big to convert to "
"byte string of prescribed length")
result = result[cutoff_len:]
elif cutoff_len < 0:
result = b'\x00' * (-cutoff_len) + result
if byteorder == 'little':
result = result[::-1]
elif byteorder == 'big':
pass
else:
raise ValueError("Incorrect byteorder")
if len(result) == 0:
result = b'\x00'
return result
@staticmethod
def from_bytes(byte_string, byteorder='big'):
"""Convert a byte string into a number.
:Parameters:
byte_string : byte string
The input number, encoded in network order.
It can only be non-negative.
byteorder : string
'big' for big-endian integers (default), 'little' for litte-endian.
:Return:
The ``Integer`` object carrying the same value as the input.
"""
result = IntegerGMP(0)
if byteorder == 'big':
pass
elif byteorder == 'little':
byte_string = bytearray(byte_string)
byte_string.reverse()
else:
raise ValueError("Incorrect byteorder")
_gmp.mpz_import(
result._mpz_p,
c_size_t(len(byte_string)), # Amount of words to read
1, # Big endian
c_size_t(1), # Each word is 1 byte long
0, # Endianess within a word - not relevant
c_size_t(0), # No nails
c_uint8_ptr(byte_string))
return result
# Relations
def _apply_and_return(self, func, term):
if not isinstance(term, IntegerGMP):
term = IntegerGMP(term)
return func(self._mpz_p, term._mpz_p)
def __eq__(self, term):
if not (isinstance(term, IntegerGMP) or is_native_int(term)):
return False
return self._apply_and_return(_gmp.mpz_cmp, term) == 0
def __ne__(self, term):
if not (isinstance(term, IntegerGMP) or is_native_int(term)):
return True
return self._apply_and_return(_gmp.mpz_cmp, term) != 0
def __lt__(self, term):
return self._apply_and_return(_gmp.mpz_cmp, term) < 0
def __le__(self, term):
return self._apply_and_return(_gmp.mpz_cmp, term) <= 0
def __gt__(self, term):
return self._apply_and_return(_gmp.mpz_cmp, term) > 0
def __ge__(self, term):
return self._apply_and_return(_gmp.mpz_cmp, term) >= 0
def __nonzero__(self):
return _gmp.mpz_cmp(self._mpz_p, self._zero_mpz_p) != 0
__bool__ = __nonzero__
def is_negative(self):
return _gmp.mpz_cmp(self._mpz_p, self._zero_mpz_p) < 0
# Arithmetic operations
def __add__(self, term):
result = IntegerGMP(0)
if not isinstance(term, IntegerGMP):
try:
term = IntegerGMP(term)
except NotImplementedError:
return NotImplemented
_gmp.mpz_add(result._mpz_p,
self._mpz_p,
term._mpz_p)
return result
def __sub__(self, term):
result = IntegerGMP(0)
if not isinstance(term, IntegerGMP):
try:
term = IntegerGMP(term)
except NotImplementedError:
return NotImplemented
_gmp.mpz_sub(result._mpz_p,
self._mpz_p,
term._mpz_p)
return result
def __mul__(self, term):
result = IntegerGMP(0)
if not isinstance(term, IntegerGMP):
try:
term = IntegerGMP(term)
except NotImplementedError:
return NotImplemented
_gmp.mpz_mul(result._mpz_p,
self._mpz_p,
term._mpz_p)
return result
def __floordiv__(self, divisor):
if not isinstance(divisor, IntegerGMP):
divisor = IntegerGMP(divisor)
if _gmp.mpz_cmp(divisor._mpz_p,
self._zero_mpz_p) == 0:
raise ZeroDivisionError("Division by zero")
result = IntegerGMP(0)
_gmp.mpz_fdiv_q(result._mpz_p,
self._mpz_p,
divisor._mpz_p)
return result
def __mod__(self, divisor):
if not isinstance(divisor, IntegerGMP):
divisor = IntegerGMP(divisor)
comp = _gmp.mpz_cmp(divisor._mpz_p,
self._zero_mpz_p)
if comp == 0:
raise ZeroDivisionError("Division by zero")
if comp < 0:
raise ValueError("Modulus must be positive")
result = IntegerGMP(0)
_gmp.mpz_mod(result._mpz_p,
self._mpz_p,
divisor._mpz_p)
return result
def inplace_pow(self, exponent, modulus=None):
if modulus is None:
if exponent < 0:
raise ValueError("Exponent must not be negative")
# Normal exponentiation
if exponent > 256:
raise ValueError("Exponent is too big")
_gmp.mpz_pow_ui(self._mpz_p,
self._mpz_p, # Base
c_ulong(int(exponent))
)
else:
# Modular exponentiation
if not isinstance(modulus, IntegerGMP):
modulus = IntegerGMP(modulus)
if not modulus:
raise ZeroDivisionError("Division by zero")
if modulus.is_negative():
raise ValueError("Modulus must be positive")
if is_native_int(exponent):
if exponent < 0:
raise ValueError("Exponent must not be negative")
if exponent < 65536:
_gmp.mpz_powm_ui(self._mpz_p,
self._mpz_p,
c_ulong(exponent),
modulus._mpz_p)
return self
exponent = IntegerGMP(exponent)
elif exponent.is_negative():
raise ValueError("Exponent must not be negative")
_gmp.mpz_powm(self._mpz_p,
self._mpz_p,
exponent._mpz_p,
modulus._mpz_p)
return self
def __pow__(self, exponent, modulus=None):
result = IntegerGMP(self)
return result.inplace_pow(exponent, modulus)
def __abs__(self):
result = IntegerGMP(0)
_gmp.mpz_abs(result._mpz_p, self._mpz_p)
return result
def sqrt(self, modulus=None):
"""Return the largest Integer that does not
exceed the square root"""
if modulus is None:
if self < 0:
raise ValueError("Square root of negative value")
result = IntegerGMP(0)
_gmp.mpz_sqrt(result._mpz_p,
self._mpz_p)
else:
if modulus <= 0:
raise ValueError("Modulus must be positive")
modulus = int(modulus)
result = IntegerGMP(self._tonelli_shanks(int(self) % modulus, modulus))
return result
def __iadd__(self, term):
if is_native_int(term):
if 0 <= term < 65536:
_gmp.mpz_add_ui(self._mpz_p,
self._mpz_p,
c_ulong(term))
return self
if -65535 < term < 0:
_gmp.mpz_sub_ui(self._mpz_p,
self._mpz_p,
c_ulong(-term))
return self
term = IntegerGMP(term)
_gmp.mpz_add(self._mpz_p,
self._mpz_p,
term._mpz_p)
return self
def __isub__(self, term):
if is_native_int(term):
if 0 <= term < 65536:
_gmp.mpz_sub_ui(self._mpz_p,
self._mpz_p,
c_ulong(term))
return self
if -65535 < term < 0:
_gmp.mpz_add_ui(self._mpz_p,
self._mpz_p,
c_ulong(-term))
return self
term = IntegerGMP(term)
_gmp.mpz_sub(self._mpz_p,
self._mpz_p,
term._mpz_p)
return self
def __imul__(self, term):
if is_native_int(term):
if 0 <= term < 65536:
_gmp.mpz_mul_ui(self._mpz_p,
self._mpz_p,
c_ulong(term))
return self
if -65535 < term < 0:
_gmp.mpz_mul_ui(self._mpz_p,
self._mpz_p,
c_ulong(-term))
_gmp.mpz_neg(self._mpz_p, self._mpz_p)
return self
term = IntegerGMP(term)
_gmp.mpz_mul(self._mpz_p,
self._mpz_p,
term._mpz_p)
return self
def __imod__(self, divisor):
if not isinstance(divisor, IntegerGMP):
divisor = IntegerGMP(divisor)
comp = _gmp.mpz_cmp(divisor._mpz_p,
divisor._zero_mpz_p)
if comp == 0:
raise ZeroDivisionError("Division by zero")
if comp < 0:
raise ValueError("Modulus must be positive")
_gmp.mpz_mod(self._mpz_p,
self._mpz_p,
divisor._mpz_p)
return self
# Boolean/bit operations
def __and__(self, term):
result = IntegerGMP(0)
if not isinstance(term, IntegerGMP):
term = IntegerGMP(term)
_gmp.mpz_and(result._mpz_p,
self._mpz_p,
term._mpz_p)
return result
def __or__(self, term):
result = IntegerGMP(0)
if not isinstance(term, IntegerGMP):
term = IntegerGMP(term)
_gmp.mpz_ior(result._mpz_p,
self._mpz_p,
term._mpz_p)
return result
def __rshift__(self, pos):
result = IntegerGMP(0)
if pos < 0:
raise ValueError("negative shift count")
if pos > 65536:
if self < 0:
return -1
else:
return 0
_gmp.mpz_tdiv_q_2exp(result._mpz_p,
self._mpz_p,
c_ulong(int(pos)))
return result
def __irshift__(self, pos):
if pos < 0:
raise ValueError("negative shift count")
if pos > 65536:
if self < 0:
return -1
else:
return 0
_gmp.mpz_tdiv_q_2exp(self._mpz_p,
self._mpz_p,
c_ulong(int(pos)))
return self
def __lshift__(self, pos):
result = IntegerGMP(0)
if not 0 <= pos < 65536:
raise ValueError("Incorrect shift count")
_gmp.mpz_mul_2exp(result._mpz_p,
self._mpz_p,
c_ulong(int(pos)))
return result
def __ilshift__(self, pos):
if not 0 <= pos < 65536:
raise ValueError("Incorrect shift count")
_gmp.mpz_mul_2exp(self._mpz_p,
self._mpz_p,
c_ulong(int(pos)))
return self
def get_bit(self, n):
"""Return True if the n-th bit is set to 1.
Bit 0 is the least significant."""
if self < 0:
raise ValueError("no bit representation for negative values")
if n < 0:
raise ValueError("negative bit count")
if n > 65536:
return 0
return bool(_gmp.mpz_tstbit(self._mpz_p,
c_ulong(int(n))))
# Extra
def is_odd(self):
return _gmp.mpz_tstbit(self._mpz_p, 0) == 1
def is_even(self):
return _gmp.mpz_tstbit(self._mpz_p, 0) == 0
def size_in_bits(self):
"""Return the minimum number of bits that can encode the number."""
if self < 0:
raise ValueError("Conversion only valid for non-negative numbers")
return _gmp.mpz_sizeinbase(self._mpz_p, 2)
def size_in_bytes(self):
"""Return the minimum number of bytes that can encode the number."""
return (self.size_in_bits() - 1) // 8 + 1
def is_perfect_square(self):
return _gmp.mpz_perfect_square_p(self._mpz_p) != 0
def fail_if_divisible_by(self, small_prime):
"""Raise an exception if the small prime is a divisor."""
if is_native_int(small_prime):
if 0 < small_prime < 65536:
if _gmp.mpz_divisible_ui_p(self._mpz_p,
c_ulong(small_prime)):
raise ValueError("The value is composite")
return
small_prime = IntegerGMP(small_prime)
if _gmp.mpz_divisible_p(self._mpz_p,
small_prime._mpz_p):
raise ValueError("The value is composite")
def multiply_accumulate(self, a, b):
"""Increment the number by the product of a and b."""
if not isinstance(a, IntegerGMP):
a = IntegerGMP(a)
if is_native_int(b):
if 0 < b < 65536:
_gmp.mpz_addmul_ui(self._mpz_p,
a._mpz_p,
c_ulong(b))
return self
if -65535 < b < 0:
_gmp.mpz_submul_ui(self._mpz_p,
a._mpz_p,
c_ulong(-b))
return self
b = IntegerGMP(b)
_gmp.mpz_addmul(self._mpz_p,
a._mpz_p,
b._mpz_p)
return self
def set(self, source):
"""Set the Integer to have the given value"""
if not isinstance(source, IntegerGMP):
source = IntegerGMP(source)
_gmp.mpz_set(self._mpz_p,
source._mpz_p)
return self
def inplace_inverse(self, modulus):
"""Compute the inverse of this number in the ring of
modulo integers.
Raise an exception if no inverse exists.
"""
if not isinstance(modulus, IntegerGMP):
modulus = IntegerGMP(modulus)
comp = _gmp.mpz_cmp(modulus._mpz_p,
self._zero_mpz_p)
if comp == 0:
raise ZeroDivisionError("Modulus cannot be zero")
if comp < 0:
raise ValueError("Modulus must be positive")
result = _gmp.mpz_invert(self._mpz_p,
self._mpz_p,
modulus._mpz_p)
if not result:
raise ValueError("No inverse value can be computed")
return self
def inverse(self, modulus):
result = IntegerGMP(self)
result.inplace_inverse(modulus)
return result
def gcd(self, term):
"""Compute the greatest common denominator between this
number and another term."""
result = IntegerGMP(0)
if is_native_int(term):
if 0 < term < 65535:
_gmp.mpz_gcd_ui(result._mpz_p,
self._mpz_p,
c_ulong(term))
return result
term = IntegerGMP(term)
_gmp.mpz_gcd(result._mpz_p, self._mpz_p, term._mpz_p)
return result
def lcm(self, term):
"""Compute the least common multiplier between this
number and another term."""
result = IntegerGMP(0)
if not isinstance(term, IntegerGMP):
term = IntegerGMP(term)
_gmp.mpz_lcm(result._mpz_p, self._mpz_p, term._mpz_p)
return result
@staticmethod
def jacobi_symbol(a, n):
"""Compute the Jacobi symbol"""
if not isinstance(a, IntegerGMP):
a = IntegerGMP(a)
if not isinstance(n, IntegerGMP):
n = IntegerGMP(n)
if n <= 0 or n.is_even():
raise ValueError("n must be positive odd for the Jacobi symbol")
return _gmp.mpz_jacobi(a._mpz_p, n._mpz_p)
@staticmethod
def _mult_modulo_bytes(term1, term2, modulus):
if not isinstance(term1, IntegerGMP):
term1 = IntegerGMP(term1)
if not isinstance(term2, IntegerGMP):
term2 = IntegerGMP(term2)
if not isinstance(modulus, IntegerGMP):
modulus = IntegerGMP(modulus)
if modulus < 0:
raise ValueError("Modulus must be positive")
if modulus == 0:
raise ZeroDivisionError("Modulus cannot be zero")
if (modulus & 1) == 0:
raise ValueError("Odd modulus is required")
product = (term1 * term2) % modulus
return product.to_bytes(modulus.size_in_bytes())
# Clean-up
def __del__(self):
try:
if self._mpz_p is not None:
if self._initialized:
_gmp.mpz_clear(self._mpz_p)
self._mpz_p = None
except AttributeError:
pass

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env/lib/python3.12/site-packages/Crypto/Math/_IntegerGMP.pyi vendored Normal file
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from ._IntegerBase import IntegerBase
class IntegerGMP(IntegerBase):
pass

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# ===================================================================
#
# Copyright (c) 2014, Legrandin <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.
# ===================================================================
from ._IntegerBase import IntegerBase
from Crypto.Util.number import long_to_bytes, bytes_to_long, inverse, GCD
class IntegerNative(IntegerBase):
"""A class to model a natural integer (including zero)"""
def __init__(self, value):
if isinstance(value, float):
raise ValueError("A floating point type is not a natural number")
try:
self._value = value._value
except AttributeError:
self._value = value
# Conversions
def __int__(self):
return self._value
def __str__(self):
return str(int(self))
def __repr__(self):
return "Integer(%s)" % str(self)
# Only Python 2.x
def __hex__(self):
return hex(self._value)
# Only Python 3.x
def __index__(self):
return int(self._value)
def to_bytes(self, block_size=0, byteorder='big'):
if self._value < 0:
raise ValueError("Conversion only valid for non-negative numbers")
result = long_to_bytes(self._value, block_size)
if len(result) > block_size > 0:
raise ValueError("Value too large to encode")
if byteorder == 'big':
pass
elif byteorder == 'little':
result = bytearray(result)
result.reverse()
result = bytes(result)
else:
raise ValueError("Incorrect byteorder")
return result
@classmethod
def from_bytes(cls, byte_string, byteorder='big'):
if byteorder == 'big':
pass
elif byteorder == 'little':
byte_string = bytearray(byte_string)
byte_string.reverse()
else:
raise ValueError("Incorrect byteorder")
return cls(bytes_to_long(byte_string))
# Relations
def __eq__(self, term):
if term is None:
return False
return self._value == int(term)
def __ne__(self, term):
return not self.__eq__(term)
def __lt__(self, term):
return self._value < int(term)
def __le__(self, term):
return self.__lt__(term) or self.__eq__(term)
def __gt__(self, term):
return not self.__le__(term)
def __ge__(self, term):
return not self.__lt__(term)
def __nonzero__(self):
return self._value != 0
__bool__ = __nonzero__
def is_negative(self):
return self._value < 0
# Arithmetic operations
def __add__(self, term):
try:
return self.__class__(self._value + int(term))
except (ValueError, AttributeError, TypeError):
return NotImplemented
def __sub__(self, term):
try:
return self.__class__(self._value - int(term))
except (ValueError, AttributeError, TypeError):
return NotImplemented
def __mul__(self, factor):
try:
return self.__class__(self._value * int(factor))
except (ValueError, AttributeError, TypeError):
return NotImplemented
def __floordiv__(self, divisor):
return self.__class__(self._value // int(divisor))
def __mod__(self, divisor):
divisor_value = int(divisor)
if divisor_value < 0:
raise ValueError("Modulus must be positive")
return self.__class__(self._value % divisor_value)
def inplace_pow(self, exponent, modulus=None):
exp_value = int(exponent)
if exp_value < 0:
raise ValueError("Exponent must not be negative")
if modulus is not None:
mod_value = int(modulus)
if mod_value < 0:
raise ValueError("Modulus must be positive")
if mod_value == 0:
raise ZeroDivisionError("Modulus cannot be zero")
else:
mod_value = None
self._value = pow(self._value, exp_value, mod_value)
return self
def __pow__(self, exponent, modulus=None):
result = self.__class__(self)
return result.inplace_pow(exponent, modulus)
def __abs__(self):
return abs(self._value)
def sqrt(self, modulus=None):
value = self._value
if modulus is None:
if value < 0:
raise ValueError("Square root of negative value")
# http://stackoverflow.com/questions/15390807/integer-square-root-in-python
x = value
y = (x + 1) // 2
while y < x:
x = y
y = (x + value // x) // 2
result = x
else:
if modulus <= 0:
raise ValueError("Modulus must be positive")
result = self._tonelli_shanks(self % modulus, modulus)
return self.__class__(result)
def __iadd__(self, term):
self._value += int(term)
return self
def __isub__(self, term):
self._value -= int(term)
return self
def __imul__(self, term):
self._value *= int(term)
return self
def __imod__(self, term):
modulus = int(term)
if modulus == 0:
raise ZeroDivisionError("Division by zero")
if modulus < 0:
raise ValueError("Modulus must be positive")
self._value %= modulus
return self
# Boolean/bit operations
def __and__(self, term):
return self.__class__(self._value & int(term))
def __or__(self, term):
return self.__class__(self._value | int(term))
def __rshift__(self, pos):
try:
return self.__class__(self._value >> int(pos))
except OverflowError:
if self._value >= 0:
return 0
else:
return -1
def __irshift__(self, pos):
try:
self._value >>= int(pos)
except OverflowError:
if self._value >= 0:
return 0
else:
return -1
return self
def __lshift__(self, pos):
try:
return self.__class__(self._value << int(pos))
except OverflowError:
raise ValueError("Incorrect shift count")
def __ilshift__(self, pos):
try:
self._value <<= int(pos)
except OverflowError:
raise ValueError("Incorrect shift count")
return self
def get_bit(self, n):
if self._value < 0:
raise ValueError("no bit representation for negative values")
try:
try:
result = (self._value >> n._value) & 1
if n._value < 0:
raise ValueError("negative bit count")
except AttributeError:
result = (self._value >> n) & 1
if n < 0:
raise ValueError("negative bit count")
except OverflowError:
result = 0
return result
# Extra
def is_odd(self):
return (self._value & 1) == 1
def is_even(self):
return (self._value & 1) == 0
def size_in_bits(self):
if self._value < 0:
raise ValueError("Conversion only valid for non-negative numbers")
if self._value == 0:
return 1
return self._value.bit_length()
def size_in_bytes(self):
return (self.size_in_bits() - 1) // 8 + 1
def is_perfect_square(self):
if self._value < 0:
return False
if self._value in (0, 1):
return True
x = self._value // 2
square_x = x ** 2
while square_x > self._value:
x = (square_x + self._value) // (2 * x)
square_x = x ** 2
return self._value == x ** 2
def fail_if_divisible_by(self, small_prime):
if (self._value % int(small_prime)) == 0:
raise ValueError("Value is composite")
def multiply_accumulate(self, a, b):
self._value += int(a) * int(b)
return self
def set(self, source):
self._value = int(source)
def inplace_inverse(self, modulus):
self._value = inverse(self._value, int(modulus))
return self
def inverse(self, modulus):
result = self.__class__(self)
result.inplace_inverse(modulus)
return result
def gcd(self, term):
return self.__class__(GCD(abs(self._value), abs(int(term))))
def lcm(self, term):
term = int(term)
if self._value == 0 or term == 0:
return self.__class__(0)
return self.__class__(abs((self._value * term) // self.gcd(term)._value))
@staticmethod
def jacobi_symbol(a, n):
a = int(a)
n = int(n)
if n <= 0:
raise ValueError("n must be a positive integer")
if (n & 1) == 0:
raise ValueError("n must be odd for the Jacobi symbol")
# Step 1
a = a % n
# Step 2
if a == 1 or n == 1:
return 1
# Step 3
if a == 0:
return 0
# Step 4
e = 0
a1 = a
while (a1 & 1) == 0:
a1 >>= 1
e += 1
# Step 5
if (e & 1) == 0:
s = 1
elif n % 8 in (1, 7):
s = 1
else:
s = -1
# Step 6
if n % 4 == 3 and a1 % 4 == 3:
s = -s
# Step 7
n1 = n % a1
# Step 8
return s * IntegerNative.jacobi_symbol(n1, a1)
@staticmethod
def _mult_modulo_bytes(term1, term2, modulus):
if modulus < 0:
raise ValueError("Modulus must be positive")
if modulus == 0:
raise ZeroDivisionError("Modulus cannot be zero")
if (modulus & 1) == 0:
raise ValueError("Odd modulus is required")
number_len = len(long_to_bytes(modulus))
return long_to_bytes((term1 * term2) % modulus, number_len)

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from ._IntegerBase import IntegerBase
class IntegerNative(IntegerBase):
pass

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