;Sia(dZddlmZGddZy)z/ This module holds a fast Factorization class. )randintc0eZdZdZedZedZy) FactorizationzB Simple module to factorize large numbers really quickly. c|dzdk(rd|dzfStd|dz td|dz td|dz }}}dx}x}}dx}} |dk(r|}t|D]} t|d||z|z}d} | |krm|dk(rh|} tt||| z D])} t|d||z|z}|t ||z z|z}+|j ||}| |z } | |kr|dk(rh|dz}|dk(r||k(r9 t| d||z|z} |j t || z |}|dkDrn8|||z}} | |kr| |fS|| fS)a Factorizes the given large integer. Implementation from https://comeoncodeon.wordpress.com/2010/09/18/pollard-rho-brent-integer-factorization/. :param pq: the prime pair pq. :return: a tuple containing the two factors p and q. r)rrangepowminabsgcd) clspqycmgrqxysikps b/var/www/OnlineNewsSite/project/venv/lib/python3.12/site-packages/telethon/crypto/factorization.py factorizezFactorization.factorize s 6Q;bAg: !R!V$gaa&8'!R!V:La1  A B1fA1X -Ar]Q&", -Aa%AFs1a!e}-.AQ2*b0ASQZ(2-A.GGArNQa%AF FA1f" 7"anq(B.GGCBK,q5  "'1Q1v*QF*c|r |||z}}|r |S)z Calculates the Greatest Common Divisor. :param a: the first number. :param b: the second number. :return: GCD(a, b) )abs rr zFactorization.gcd7s a!eqArN)__name__ __module__ __qualname____doc__ classmethodr staticmethodr rrrrrs0)+)+V  rrN)r%randomrrrrrr)s<<r