74 lines
2.0 KiB
Python
74 lines
2.0 KiB
Python
# Pyrogram - Telegram MTProto API Client Library for Python
|
|
# Copyright (C) 2017-2018 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:
|
|
# 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
|