a db@sdZddlZddgZddZddZd d Zd dZd dZe d kre dddl Z e dD]4Z e \ZZertqe r\e ddkr\e de q\e ddS)zNumerical functions related to primes. Implementation based on the book Algorithm Design by Michael T. Goodrich and Roberto Tamassia, 2002. Ngetprimeare_relatively_primecCs|dkr|||}}q|S)zPReturns the greatest common divisor of p and q >>> gcd(48, 180) 12 r)pqrrZ/home/tom/ab/renpy-build/tmp/install.linux-x86_64/lib/python3.9/site-packages/rsa/prime.pygcdsrcCs|dkr dS|d}d}|d@s2|d7}|dL}qt|D]~}tj|dd}t|||}|dks:||dkrtq:t|dD]0}t|d|}|dkrdS||dkrq:qdSq:dS)a.Calculates whether n is composite (which is always correct) or prime (which theoretically is incorrect with error probability 4**-k), by applying Miller-Rabin primality testing. For reference and implementation example, see: https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test :param n: Integer to be tested for primality. :type n: int :param k: Number of rounds (witnesses) of Miller-Rabin testing. :type k: int :return: False if the number is composite, True if it's probably prime. :rtype: bool FrT)rangersarandnumrandintpow)nkdr_axrrrmiller_rabin_primality_testing(s(     rcCs&|dkr|dvS|d@sdSt|dS)aReturns True if the number is prime, and False otherwise. >>> is_prime(2) True >>> is_prime(42) False >>> is_prime(41) True >>> [x for x in range(901, 1000) if is_prime(x)] [907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997] )r r Fr)r)numberrrris_prime]s  rcCs*|dks Jtj|}t|r |Sq dS)aReturns a prime number that can be stored in 'nbits' bits. >>> p = getprime(128) >>> is_prime(p-1) False >>> is_prime(p) True >>> is_prime(p+1) False >>> from rsa import common >>> common.bit_size(p) == 128 True rN)r rZread_random_odd_intr)nbitsintegerrrrr|s  cCst||}|dkS)zReturns True if a and b are relatively prime, and False if they are not. >>> are_relatively_prime(2, 3) True >>> are_relatively_prime(2, 4) False r )r)rbrrrrrs __main__z'Running doctests 1000x or until failureidz%i timesz Doctests done)__doc__Z rsa.randnumr __all__rrrrr__name__printdoctestr counttestmodZfailurestestsrrrrs" 5