community.crypto/plugins/module_utils/crypto/math.py

# -*- coding: utf-8 -*-
#
# Copyright (c) 2019, Felix Fontein <felix@fontein.de>
# GNU General Public License v3.0+ (see LICENSES/GPL-3.0-or-later.txt or https://www.gnu.org/licenses/gpl-3.0.txt)
# SPDX-License-Identifier: GPL-3.0-or-later

from __future__ import absolute_import, division, print_function
__metaclass__ = type


import sys


def binary_exp_mod(f, e, m):
    '''Computes f^e mod m in O(log e) multiplications modulo m.'''
    # Compute len_e = floor(log_2(e))
    len_e = -1
    x = e
    while x > 0:
        x >>= 1
        len_e += 1
    # Compute f**e mod m
    result = 1
    for k in range(len_e, -1, -1):
        result = (result * result) % m
        if ((e >> k) & 1) != 0:
            result = (result * f) % m
    return result


def simple_gcd(a, b):
    '''Compute GCD of its two inputs.'''
    while b != 0:
        a, b = b, a % b
    return a


def quick_is_not_prime(n):
    '''Does some quick checks to see if we can poke a hole into the primality of n.

    A result of `False` does **not** mean that the number is prime; it just means
    that we could not detect quickly whether it is not prime.
    '''
    if n <= 2:
        return n < 2
    # The constant in the next line is the product of all primes < 200
    prime_product = 7799922041683461553249199106329813876687996789903550945093032474868511536164700810
    gcd = simple_gcd(n, prime_product)
    if gcd > 1:
        if n < 200 and gcd == n:
            # Explicitly check for all primes < 200
            return n not in (
                2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83,
                89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179,
                181, 191, 193, 197, 199,
            )
        return True
    # TODO: maybe do some iterations of Miller-Rabin to increase confidence
    # (https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test)
    return False


python_version = (sys.version_info[0], sys.version_info[1])
if python_version >= (2, 7) or python_version >= (3, 1):
    # Ansible still supports Python 2.6 on remote nodes

    def count_bytes(no):
        """
        Given an integer, compute the number of bytes necessary to store its absolute value.
        """
        no = abs(no)
        if no == 0:
            return 0
        return (no.bit_length() + 7) // 8

    def count_bits(no):
        """
        Given an integer, compute the number of bits necessary to store its absolute value.
        """
        no = abs(no)
        if no == 0:
            return 0
        return no.bit_length()
else:
    # Slow, but works
    def count_bytes(no):
        """
        Given an integer, compute the number of bytes necessary to store its absolute value.
        """
        no = abs(no)
        count = 0
        while no > 0:
            no >>= 8
            count += 1
        return count

    def count_bits(no):
        """
        Given an integer, compute the number of bits necessary to store its absolute value.
        """
        no = abs(no)
        count = 0
        while no > 0:
            no >>= 1
            count += 1
        return count

if sys.version_info[0] >= 3:
    # Python 3 (and newer)
    def _convert_int_to_bytes(count, no):
        return no.to_bytes(count, byteorder='big')

    def _to_hex(no):
        return hex(no)[2:]
else:
    # Python 2
    def _convert_int_to_bytes(count, n):
        if n == 0 and count == 0:
            return ''
        h = '%x' % n
        if len(h) > 2 * count:
            raise Exception('Number {1} needs more than {0} bytes!'.format(count, n))
        return ('0' * (2 * count - len(h)) + h).decode('hex')

    def _to_hex(no):
        return '%x' % no


def convert_int_to_bytes(no, count=None):
    """
    Convert the absolute value of an integer to a byte string in network byte order.

    If ``count`` is provided, it must be sufficiently large so that the integer's
    absolute value can be represented with these number of bytes. The resulting byte
    string will have length exactly ``count``.

    The value zero will be converted to an empty byte string if ``count`` is provided.
    """
    no = abs(no)
    if count is None:
        count = count_bytes(no)
    return _convert_int_to_bytes(count, no)


def convert_int_to_hex(no, digits=None):
    """
    Convert the absolute value of an integer to a string of hexadecimal digits.

    If ``digits`` is provided, the string will be padded on the left with ``0``s so
    that the returned value has length ``digits``. If ``digits`` is not sufficient,
    the string will be longer.
    """
    no = abs(no)
    value = _to_hex(no)
    if digits is not None and len(value) < digits:
        value = '0' * (digits - len(value)) + value
    return value