Manual Pages for UNIX Operating System command usage for man BN_is_prime

OpenSSL                               BN_generate_prime(3openssl)



NNNNAAAAMMMMEEEE
     BN_generate_prime, BN_is_prime, BN_is_prime_fasttest -
     generate primes and test for primality

SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS
      #include 

      BIGNUM *BN_generate_prime(BIGNUM *ret, int num, int safe, BIGNUM *add,
          BIGNUM *rem, void (*callback)(int, int, void *), void *cb_arg);

      int BN_is_prime(const BIGNUM *a, int checks, void (*callback)(int, int,
          void *), BN_CTX *ctx, void *cb_arg);

      int BN_is_prime_fasttest(const BIGNUM *a, int checks,
          void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg,
          int do_trial_division);


DDDDEEEESSSSCCCCRRRRIIIIPPPPTTTTIIIIOOOONNNN
     BN_generate_prime() generates a pseudo-random prime number
     of nnnnuuuummmm bits.  If rrrreeeetttt is not NNNNUUUULLLLLLLL, it will be used to store
     the number.

     If ccccaaaallllllllbbbbaaaacccckkkk is not NNNNUUUULLLLLLLL, it is called as follows:

     +o   ccccaaaallllllllbbbbaaaacccckkkk((((0000,,,, iiii,,,, ccccbbbb_aaaarrrrgggg)))) is called after generating the
         i-th potential prime number.

     +o   While the number is being tested for primality,
         ccccaaaallllllllbbbbaaaacccckkkk((((1111,,,, jjjj,,,, ccccbbbb_aaaarrrrgggg)))) is called as described below.

     +o   When a prime has been found, ccccaaaallllllllbbbbaaaacccckkkk((((2222,,,, iiii,,,, ccccbbbb_aaaarrrrgggg)))) is
         called.

     The prime may have to fulfill additional requirements for
     use in Diffie-Hellman key exchange:

     If aaaadddddddd is not NNNNUUUULLLLLLLL, the prime will fulfill the condition p %
     aaaadddddddd == rrrreeeemmmm (p % aaaadddddddd == 1 if rrrreeeemmmm == NNNNUUUULLLLLLLL) in order to suit a
     given generator.

     If ssssaaaaffffeeee is true, it will be a safe prime (i.e. a prime p so
     that (p-1)/2 is also prime).

     The PRNG must be seeded prior to calling
     BN_generate_prime().  The prime number generation has a
     negligible error probability.

     BN_is_prime() and BN_is_prime_fasttest() test if the number
     aaaa is prime.  The following tests are performed until one of
     them shows that aaaa is composite; if aaaa passes all these tests,
     it is considered prime.



13/Jan/2003            Last change: 0.9.8o                      1






OpenSSL                               BN_generate_prime(3openssl)



     BN_is_prime_fasttest(), when called with ddddoooo_ttttrrrriiiiaaaallll_ddddiiiivvvviiiissssiiiioooonnnn
     ======== 1111, first attempts trial division by a number of small
     primes; if no divisors are found by this test and ccccaaaallllllllbbbbaaaacccckkkk
     is not NNNNUUUULLLLLLLL, ccccaaaallllllllbbbbaaaacccckkkk((((1111,,,, ----1111,,,, ccccbbbb_aaaarrrrgggg)))) is called.  If
     ddddoooo_ttttrrrriiiiaaaallll_ddddiiiivvvviiiissssiiiioooonnnn ======== 0000, this test is skipped.

     Both BN_is_prime() and BN_is_prime_fasttest() perform a
     Miller-Rabin probabilistic primality test with cccchhhheeeecccckkkkssss
     iterations. If cccchhhheeeecccckkkkssss ======== BBBBNNNN_pppprrrriiiimmmmeeee_cccchhhheeeecccckkkkssss, a number of
     iterations is used that yields a false positive rate of at
     most 2^-80 for random input.

     If ccccaaaallllllllbbbbaaaacccckkkk is not NNNNUUUULLLLLLLL, ccccaaaallllllllbbbbaaaacccckkkk((((1111,,,, jjjj,,,, ccccbbbb_aaaarrrrgggg)))) is called
     after the j-th iteration (j = 0, 1, ...). ccccttttxxxx is a pre-
     allocated BBBBNNNN_CCCCTTTTXXXX (to save the overhead of allocating and
     freeing the structure in a loop), or NNNNUUUULLLLLLLL.

RRRREEEETTTTUUUURRRRNNNN VVVVAAAALLLLUUUUEEEESSSS
     BN_generate_prime() returns the prime number on success,
     NNNNUUUULLLLLLLL otherwise.

     BN_is_prime() returns 0 if the number is composite, 1 if it
     is prime with an error probability of less than 0.25^cccchhhheeeecccckkkkssss,
     and -1 on error.

     The error codes can be obtained by ERR_get_error(3).

SSSSEEEEEEEE AAAALLLLSSSSOOOO
     bn(3), ERR_get_error(3), rand(3)

HHHHIIIISSSSTTTTOOOORRRRYYYY
     The ccccbbbb_aaaarrrrgggg arguments to BN_generate_prime() and to
     BN_is_prime() were added in SSLeay 0.9.0. The rrrreeeetttt argument
     to BN_generate_prime() was added in SSLeay 0.9.1.
     BN_is_prime_fasttest() was added in OpenSSL 0.9.5.




















13/Jan/2003            Last change: 0.9.8o                      2