/usr/lib/python3/dist-packages/Cryptodome/Math/_Numbers_int.py is in python3-pycryptodome 3.4.7-1ubuntu1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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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 Cryptodome.Util.number import long_to_bytes, bytes_to_long
from Cryptodome.Util.py3compat import maxint
class Integer(object):
"""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)
def to_bytes(self, block_size=0):
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")
return result
@staticmethod
def from_bytes(byte_string):
return Integer(bytes_to_long(byte_string))
# Relations
def __eq__(self, term):
try:
result = self._value == term._value
except AttributeError:
result = self._value == term
return result
def __ne__(self, term):
return not self.__eq__(term)
def __lt__(self, term):
try:
result = self._value < term._value
except AttributeError:
result = self._value < term
return result
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 __bool__(self):
return self._value != 0
def is_negative(self):
return self._value < 0
# Arithmetic operations
def __add__(self, term):
try:
return Integer(self._value + term._value)
except AttributeError:
return Integer(self._value + term)
def __sub__(self, term):
try:
diff = self._value - term._value
except AttributeError:
diff = self._value - term
return Integer(diff)
def __mul__(self, factor):
try:
return Integer(self._value * factor._value)
except AttributeError:
return Integer(self._value * factor)
def __floordiv__(self, divisor):
try:
divisor_value = divisor._value
except AttributeError:
divisor_value = divisor
return Integer(self._value // divisor_value)
def __mod__(self, divisor):
try:
divisor_value = divisor._value
except AttributeError:
divisor_value = divisor
if divisor_value < 0:
raise ValueError("Modulus must be positive")
return Integer(self._value % divisor_value)
def inplace_pow(self, exponent, modulus=None):
try:
exp_value = exponent._value
except AttributeError:
exp_value = exponent
if exp_value < 0:
raise ValueError("Exponent must not be negative")
try:
mod_value = modulus._value
except AttributeError:
mod_value = modulus
if mod_value is not None:
if mod_value < 0:
raise ValueError("Modulus must be positive")
if mod_value == 0:
raise ZeroDivisionError("Modulus cannot be zero")
self._value = pow(self._value, exp_value, mod_value)
return self
def __pow__(self, exponent, modulus=None):
result = Integer(self)
return result.inplace_pow(exponent, modulus)
def __abs__(self):
return abs(self._value)
def sqrt(self):
# http://stackoverflow.com/questions/15390807/integer-square-root-in-python
if self._value < 0:
raise ValueError("Square root of negative value")
x = self._value
y = (x + 1) // 2
while y < x:
x = y
y = (x + self._value // x) // 2
return Integer(x)
def __iadd__(self, term):
try:
self._value += term._value
except AttributeError:
self._value += term
return self
def __isub__(self, term):
try:
self._value -= term._value
except AttributeError:
self._value -= term
return self
def __imul__(self, term):
try:
self._value *= term._value
except AttributeError:
self._value *= term
return self
def __imod__(self, term):
try:
modulus = term._value
except AttributeError:
modulus = 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):
try:
return Integer(self._value & term._value)
except AttributeError:
return Integer(self._value & term)
def __or__(self, term):
try:
return Integer(self._value | term._value)
except AttributeError:
return Integer(self._value | term)
def __rshift__(self, pos):
try:
try:
return Integer(self._value >> pos._value)
except AttributeError:
return Integer(self._value >> pos)
except OverflowError:
raise ValueError("Incorrect shift count")
def __irshift__(self, pos):
try:
try:
self._value >>= pos._value
except AttributeError:
self._value >>= pos
except OverflowError:
raise ValueError("Incorrect shift count")
return self
def __lshift__(self, pos):
try:
try:
return Integer(self._value << pos._value)
except AttributeError:
return Integer(self._value << pos)
except OverflowError:
raise ValueError("Incorrect shift count")
def __ilshift__(self, pos):
try:
try:
self._value <<= pos._value
except AttributeError:
self._value <<= pos
except OverflowError:
raise ValueError("Incorrect shift count")
return self
def get_bit(self, n):
try:
try:
return (self._value >> n._value) & 1
except AttributeError:
return (self._value >> n) & 1
except OverflowError:
raise ValueError("Incorrect bit position")
# 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
bit_size = 0
tmp = self._value
while tmp:
tmp >>= 1
bit_size += 1
return bit_size
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):
try:
if (self._value % small_prime._value) == 0:
raise ValueError("Value is composite")
except AttributeError:
if (self._value % small_prime) == 0:
raise ValueError("Value is composite")
def multiply_accumulate(self, a, b):
if type(a) == Integer:
a = a._value
if type(b) == Integer:
b = b._value
self._value += a * b
return self
def set(self, source):
if type(source) == Integer:
self._value = source._value
else:
self._value = source
def inplace_inverse(self, modulus):
try:
modulus = modulus._value
except AttributeError:
pass
if modulus == 0:
raise ZeroDivisionError("Modulus cannot be zero")
if modulus < 0:
raise ValueError("Modulus cannot be negative")
r_p, r_n = self._value, modulus
s_p, s_n = 1, 0
while r_n > 0:
q = r_p // r_n
r_p, r_n = r_n, r_p - q * r_n
s_p, s_n = s_n, s_p - q * s_n
if r_p != 1:
raise ValueError("No inverse value can be computed" + str(r_p))
while s_p < 0:
s_p += modulus
self._value = s_p
return self
def inverse(self, modulus):
result = Integer(self)
result.inplace_inverse(modulus)
return result
def gcd(self, term):
try:
term = term._value
except AttributeError:
pass
r_p, r_n = abs(self._value), abs(term)
while r_n > 0:
q = r_p // r_n
r_p, r_n = r_n, r_p - q * r_n
return Integer(r_p)
def lcm(self, term):
try:
term = term._value
except AttributeError:
pass
if self._value == 0 or term == 0:
return Integer(0)
return Integer(abs((self._value * term) // self.gcd(term)._value))
@staticmethod
def jacobi_symbol(a, n):
if isinstance(a, Integer):
a = a._value
if isinstance(n, Integer):
n = n._value
if (n & 1) == 0:
raise ValueError("n must be even 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 * Integer.jacobi_symbol(n1, a1)
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