MTPyroger/pyrogram/crypto/prime.py

# Pyrogram - Telegram MTProto API Client Library for Python
# Copyright (C) 2017-2019 Dan Tès <https://github.com/delivrance>
#
# This file is part of Pyrogram.
#
# Pyrogram is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# Pyrogram is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with Pyrogram.  If not, see <http://www.gnu.org/licenses/>.

from random import randint


class Prime:
    CURRENT_DH_PRIME = int(
        "C71CAEB9C6B1C9048E6C522F70F13F73980D40238E3E21C14934D037563D930F"
        "48198A0AA7C14058229493D22530F4DBFA336F6E0AC925139543AED44CCE7C37"
        "20FD51F69458705AC68CD4FE6B6B13ABDC9746512969328454F18FAF8C595F64"
        "2477FE96BB2A941D5BCD1D4AC8CC49880708FA9B378E3C4F3A9060BEE67CF9A4"
        "A4A695811051907E162753B56B0F6B410DBA74D8A84B2A14B3144E0EF1284754"
        "FD17ED950D5965B4B9DD46582DB1178D169C6BC465B0D6FF9CA3928FEF5B9AE4"
        "E418FC15E83EBEA0F87FA9FF5EED70050DED2849F47BF959D956850CE929851F"
        "0D8115F635B105EE2E4E15D04B2454BF6F4FADF034B10403119CD8E3B92FCC5B",
        16
    )

    # Recursive variant
    # @classmethod
    # def gcd(cls, a: int, b: int) -> int:
    #     return cls.gcd(b, a % b) if b else a

    @staticmethod
    def gcd(a: int, b: int) -> int:
        while b:
            a, b = b, a % b

        return a

    @classmethod
    def decompose(cls, pq: int) -> int:
        # https://comeoncodeon.wordpress.com/2010/09/18/pollard-rho-brent-integer-factorization/
        if pq % 2 == 0:
            return 2

        y, c, m = randint(1, pq - 1), randint(1, pq - 1), randint(1, pq - 1)
        g = r = q = 1
        x = ys = 0

        while g == 1:
            x = y

            for i in range(r):
                y = (pow(y, 2, pq) + c) % pq

            k = 0

            while k < r and g == 1:
                ys = y

                for i in range(min(m, r - k)):
                    y = (pow(y, 2, pq) + c) % pq
                    q = q * (abs(x - y)) % pq

                g = cls.gcd(q, pq)
                k += m

            r *= 2

        if g == pq:
            while True:
                ys = (pow(ys, 2, pq) + c) % pq
                g = cls.gcd(abs(x - ys), pq)

                if g > 1:
                    break

        return g