U ha@s"dZddlmZGdddZdS)z/ This module holds a fast Factorization class. )randintc@s(eZdZdZeddZeddZdS) FactorizationzB Simple module to factorize large numbers really quickly. c Csn|ddkrd|dfStd|dtd|dtd|d}}}d}}}d}} |dkr|}t|D]} t|d|||}qpd} | |kr|dkr|} tt||| D],} t|d|||}|t|||}q|||}| |7} q|d9}qZ||krFt| d|||} |t|| |}|dkr qFq |||} }| |krf| |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) clsZpqycmgrqxZysikprA/tmp/pip-unpacked-wheel-c81u5j2r/telethon/crypto/factorization.py factorize s2  .        zFactorization.factorizecCs|r|||}}q|S)z Calculates the Greatest Common Divisor. :param a: the first number. :param b: the second number. :return: GCD(a, b) r)abrrrr 7s zFactorization.gcdN)__name__ __module__ __qualname____doc__ classmethodr staticmethodr rrrrrs  +rN)rrandomrrrrrrs