NAME    [Toc]    [Back]

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

SYNOPSIS    [Toc]    [Back]

        #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    [Toc]    [Back]

       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:

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

       o   While the number is being tested for primality, call-
           back(1, j, cb_arg) is called as described below.

       o   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_gener-
       ate_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 preallocated
 BN_CTX (to save the overhead of allocating and
       freeing the structure in a loop), or NULL.

RETURN VALUES    [Toc]    [Back]

       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    [Toc]    [Back]

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

HISTORY    [Toc]    [Back]

       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.


OpenBSD 3.6                 2003-05-11                          2