U ڲg@sdZddlZddlZddgZeeedddZeedd d Zeeed d d Z eedddZ eedddZ eeedddZ e dkredddlZedD]4Ze\ZZerqeddkreredeqeddS)zNumerical functions related to primes. Implementation based on the book Algorithm Design by Michael T. Goodrich and Roberto Tamassia, 2002. Ngetprimeare_relatively_prime)pqreturncCs|dkr|||}}q|S)zPReturns the greatest common divisor of p and q >>> gcd(48, 180) 12 r)rrrr-/tmp/pip-unpacked-wheel-1z1vrokf/rsa/prime.pygcdsr )numberrcCs4tj|}|dkrdS|dkr$dS|dkr0dSdS)aReturns minimum number of rounds for Miller-Rabing primality testing, based on number bitsize. According to NIST FIPS 186-4, Appendix C, Table C.3, minimum number of rounds of M-R testing, using an error probability of 2 ** (-100), for different p, q bitsizes are: * p, q bitsize: 512; rounds: 7 * p, q bitsize: 1024; rounds: 4 * p, q bitsize: 1536; rounds: 3 See: http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf iii )rsacommonZbit_size)r Zbitsizerrrget_primality_testing_rounds's r)nkrcCs|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 Frr T)rangerrandnumrandintpow)rrdr_axrrrmiller_rabin_primality_testingAs(     rcCs2|dkr|dkS|d@sdSt|}t||dS)zReturns True if the number is prime, and False otherwise. >>> is_prime(2) True >>> is_prime(42) False >>> is_prime(41) True r>rr r rF)rr)r rrrris_primevs r!)nbitsrcCs*|dks ttj|}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 r N)AssertionErrorrrZread_random_odd_intr!)r"integerrrrrs  )rbrcCst||}|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 )rr%rrrrrs __main__z'Running doctests 1000x or until failureidz%i timesz Doctests done)__doc__Z rsa.commonrZ rsa.randnum__all__intr rboolrr!rr__name__printdoctestrcounttestmodZfailurestestsrrrrs& 5