g8dZddlZddlZddgZdededefdZd edefd Zd ed edefd Z d edefdZ dedefdZ dededefdZ e dk(rQedddlZedD]1Zej$\ZZernedzdk(s$es'edez3edyy)zNumerical functions related to primes. Implementation based on the book Algorithm Design by Michael T. Goodrich and Roberto Tamassia, 2002. Ngetprimeare_relatively_primepqreturnc*|dk7r |||z}}|dk7r |S)zPReturns the greatest common divisor of p and q >>> gcd(48, 180) 12 r)rrs >/var/www/openai/venv/lib/python3.12/site-packages/rsa/prime.pygcdr s& q&QUA q& Hnumbercftjj|}|dk\ry|dk\ry|dk\ryy)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 )rsacommonbit_size)r bitsizes r get_primality_testing_roundsr's9jj!!&)G$$#~ r nkcN|dkry|dz }d}|dzs|dz }|dz}|dzst|D]u}tjj|dz dz}t |||}|dk(s||dz k(rCt|dz D]!}t |d|}|dk(ry||dz k(s!tyy)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 FrrT)rangerrandnumrandintpow)rrdr_axs r miller_rabin_primality_testingr&As" 1u AA A1u Q a1u 1X KK  A & * 1aL 6Q!a%Z q1uAAq! AAvAEz%( r cT|dkr|dvS|dzsyt|}t||dzS)zReturns True if the number is prime, and False otherwise. >>> is_prime(2) True >>> is_prime(42) False >>> is_prime(41) True r>rrrrF)rr&)r rs r is_primer)vsA{%% QJ %V,A *&!a% 88r nbitscl|dkDsJ tjj|}t|r|S-)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)rrread_random_odd_intr))r*integers r rrs; 199 ++11%8 G N r r$bc$t||}|dk(S)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 )r$r.r!s r rrs Aq A 6Mr __main__z'Running doctests 1000x or until failureidz%i timesz Doctests done)__doc__ rsa.commonr rsa.randnum__all__intr rboolr&r)rr__name__printdoctestrcounttestmodfailurestestsr r r r?s   - .  3  3  3  42c2c2d2j9S9T94CC8 C C D  z 34t+GOO-5   3;!  *u$ %  /r