=pod

=head1 NAME

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

=head1 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);

=head1 DESCRIPTION

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

If B<callback> is not B<NULL>, it is called as follows:

=over 4

=item *

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

=item *

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

=item *

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

=back

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

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

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

BN_is_prime_fasttest(), when called with B<do_trial_division == 1>,
first attempts trial division by a number of small primes;
if no divisors are found by this test and B<callback> is not B<NULL>,
B<callback(1, -1, cb_arg)> is called.
If B<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 B<checks> iterations. If
B<checks == BN_prime_check>, a number of iterations is used that
yields a false positive rate of at most 2^-80 for random input.

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

=head1 RETURN VALUES

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

The error codes can be obtained by L<ERR_get_error(3)|ERR_get_error(3)>.

=head1 SEE ALSO

L<bn(3)|bn(3)>, L<err(3)|err(3)>, L<rand(3)|rand(3)>

=head1 HISTORY

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

=cut
