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Filename :
_IntegerNative.py
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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)