NAME

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

SYNOPSIS

        #include <openssl/bn.h>

        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);

DESCRIPTION

       BN_generate_prime() generates a pseudo-random prime number of num bits.  If ret is not NULL, it will be
       used to store the number.

       If callback is not NULL, it is called as follows:

       •   callback(0, i, cb_arg) is called after generating the i-th potential prime number.

       •   While the number is being tested for primality, callback(1, j, cb_arg) is called as described below.

       •   When a prime has been found, callback(2, i, cb_arg) is called.

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

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

       If safe 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  a  is  prime.  The following tests are
       performed until one of them shows that a is composite; if a passes all  these  tests,  it  is  considered
       prime.

       BN_is_prime_fasttest(),  when  called  with  do_trial_division  ==  1, first attempts trial division by a
       number of small primes; if no divisors are found by this test and callback is not NULL,  callback(1,  -1,
       cb_arg) is called.  If do_trial_division == 0, this test is skipped.

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

       If  callback  is not NULL, callback(1, j, cb_arg) is called after the j-th iteration (j = 0, 1, ...). ctx
       is a pre-allocated BN_CTX (to save the overhead of allocating and freeing the structure in  a  loop),  or
       NULL.

RETURN VALUES

       BN_generate_prime() returns the prime number on success, NULL 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^checks, and -1 on error.

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

SEE ALSO

       bn(3), ERR_get_error(3), rand(3)

HISTORY

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

1.0.1f                                             2014-01-06                            BN_generate_prime(3SSL)