+ oiPRt^RIt^RItRR.tRRltRRltRR ltR R ltR R lt RRlt ] R8Xdm] !R4^RI t ]!R4FJt] P !4wtt]'dM-]^d,^8XgK1]'gK;] !R],4KL ] !R4R#R#)zNumerical functions related to primes. Implementation based on the book Algorithm Design by Michael T. Goodrich and Roberto Tamassia, 2002. Ngetprimeare_relatively_primec<V^8dQhR\R\R\/#)pqreturnint)formats"l/Users/tonyclaw/.openclaw/workspace/scripts/youtube-playlists/venv/lib/python3.14/site-packages/rsa/prime.py __annotate__r s!   3  3  3  c*V^8wd YV,rKV#)zDReturns the greatest common divisor of p and q >>> gcd(48, 180) 12 )rrs&&r gcdrs q&UA Hrc0V^8dQhR\R\/#rnumberrr )r s"r r r 'srcz\PPV4pVR8d^#VR8d^#VR8d^#^ #)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)rbitsizes& r get_primality_testing_roundsr's9jj!!&)G$$#~ rc<V^8dQhR\R\R\/#)rnkrr bool)r s"r r r As!22c2c2d2rcV^8dR#V^, p^pV^,'gV^, pV^,pK#\V4Fp\PPV^, 4^,p\ WRV4pV^8XgW`^, 8XdKR\V^, 4F+p\ V^V4pV^8XdR#W`^, 8XgK*K R# R#)aCalculates 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 FT)rangerrandnumrandintpow)rrdr_axs&& r miller_rabin_primality_testingr*As" 1u AA A1uu Q a1X KK  A & * aL 6Qa%Z q1uAAq! AAvEz%( rc0V^8dQhR\R\/#rr)r s"r r r vs99S9T9rcvV^ 8dVR9#V^,'gR#\V4p\W^,4#)z}Returns True if the number is prime, and False otherwise. >>> is_prime(2) True >>> is_prime(42) False >>> is_prime(41) True F>r)rr*)rrs& r is_primer0vsA{%% QJJ %V,A *&a% 88rc0V^8dQhR\R\/#)rnbitsrr )r s"r r r sCCrc~V^8gQh\PPV4p\V4'gK3V#)zReturns 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 )rr"read_random_odd_intr0)r2integers& r rrs9 199 ++11%8 G  Nrc<V^8dQhR\R\R\/#)rr(brr)r s"r r r s!  C C D rc"\W4pV^8H#)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(r7r%s&& r rrs A A 6Mr__main__z'Running doctests 1000x or until failureiz%i timesz Doctests done)__doc__ rsa.commonr rsa.randnum__all__rrr*r0rr__name__printdoctestr!counttestmodfailurestestsrrr rEs  - .  42j948  z 34t#OO-5   3;!  *u$ %  /r