=pod

=head1 NAME

BN_generate_prime, BN_is_prime - 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(BIGNUM *a, int checks, void (*callback)(int, int, 
     void *), BN_CTX *ctx, void *cb_arg);

=head1 DESCRIPTION

BN_generate_prime() generates a pseudo-random prime number of B<num>
bits.
If B<ret> is not 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 NULL, the prime will fulfill the condition p % B<add>
== B<rem> (p % B<add> == 1 if B<rem> == 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() tests if the number B<a> is prime. This is done by
performing a Miller-Rabin probabilistic primality test with B<checks>
iterations. If B<checks == BN_prime_check>, it uses a number
of iterations 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. B<ctx> is a pre-allocated B<BN_CTX> (to save
the overhead of allocating and freeing the structure in a loop), or
NULL.

=head1 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^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.

=cut
