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.