BN_generate_prime(3)        OpenSSL        BN_generate_prime(3)





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 num-
       ber 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,
           callback(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 negligi-
       ble 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_divi-
       sion == 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 allocat-
       ing 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 argu-
       ment to BN_generate_prime() was added in SSLeay 0.9.1.
       BN_is_prime_fasttest() was added in OpenSSL 0.9.5.



0.9.7c                     2003-01-13      BN_generate_prime(3)
