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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)