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[EDIT] FILE: _IntegerNative.py

# ===================================================================
#
# 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)

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