pycryptodome/lib/Crypto/Math/_Numbers_int.py

# ===================================================================
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# Copyright (c) 2014, Legrandin <helderijs@gmail.com>
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from Crypto.Util.number import long_to_bytes, bytes_to_long


class Natural(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")
        if value < 0:
            raise ValueError("A natural number is not negative")
        self._value = value

    def to_bytes(self, block_size=0):
        result = long_to_bytes(self._value, block_size)
        if len(result) > block_size > 0:
            raise ValueError("Value too large to encode")
        return result

    def __int__(self):
        return self._value

    def __str__(self):
        return str(int(self))

    @staticmethod
    def from_bytes(byte_string):
        return Natural(bytes_to_long(byte_string))

    # Arithmetic operations
    def __add__(self, term):
        try:
            return Natural(self._value + term._value)
        except AttributeError:
            return Natural(self._value + term)

    def __sub__(self, term):
        try:
            diff = self._value - term._value
        except AttributeError:
            diff = self._value - term
        if diff < 0:
            raise ValueError("Result of subtraction is not a natural value")
        return Natural(diff)

    def __mul__(self, factor):
        try:
            return Natural(self._value * factor._value)
        except AttributeError:
            return Natural(self._value * factor)

    def __mod__(self, divisor):
        try:
            return Natural(self._value % divisor._value)
        except AttributeError:
            return Natural(self._value % divisor)

    def __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 and mod_value < 0:
            raise ValueError("Modulus must be positive")
        return pow(self._value, exp_value, mod_value)

    # Boolean
    def __and__(self, term):
        try:
            return Natural(self._value & term._value)
        except AttributeError:
            return Natural(self._value % term)

    def __rshift__(self, pos):
        try:
            return Natural(self._value >> pos._value)
        except AttributeError:
            return Natural(self._value >> pos)

    def __irshift__(self, pos):
        try:
            self._value >>= pos._value
        except AttributeError:
            self._value >>= pos
        return self

    def size_in_bits(self):

        if self._value == 0:
            return 1

        bit_size = 0
        tmp = self._value
        while tmp:
            tmp >>= 1
            bit_size += 1

        return bit_size

    def is_odd(self):
        return (self._value & 1) == 1

    def is_even(self):
        return (self._value & 1) == 0

    # 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 __nonzero__(self):
        return self._value != 0

    # Extra
    def is_perfect_square(self):
        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

    @staticmethod
    def jacobi_symbol(a, n):
        if isinstance(a, Natural):
            a = a._value
        if isinstance(n, Natural):
            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 * Natural.jacobi_symbol(n1, a1)