=pod
=head1 NAME
BN_generate_prime, BN_is_prime, BN_is_prime_fasttest - generate primes and test for primality
=head1 SYNOPSIS
#include
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
bits.
If B is not B, it will be used to store the number.
If B is not B, it is called as follows:
=over 4
=item *
B is called after generating the i-th
potential prime number.
=item *
While the number is being tested for primality, B is called as described below.
=item *
When a prime has been found, B is called.
=back
The prime may have to fulfill additional requirements for use in
Diffie-Hellman key exchange:
If B is not B, the prime will fulfill the condition p % B
== B (p % B == 1 if B == B) in order to suit a given
generator.
If B 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 is
prime. The following tests are performed until one of them shows that
B is composite; if B passes all these tests, it is considered
prime.
BN_is_prime_fasttest(), when called with B,
first attempts trial division by a number of small primes;
if no divisors are found by this test and B is not B,
B is called.
If B, this test is skipped.
Both BN_is_prime() and BN_is_prime_fasttest() perform a Miller-Rabin
probabilistic primality test with B iterations. If
B, a number of iterations is used that
yields a false positive rate of at most 2^-80 for random input.
If B is not B, B is called
after the j-th iteration (j = 0, 1, ...). B is a
pre-allocated B (to save the overhead of allocating and
freeing the structure in a loop), or B.
=head1 RETURN VALUES
BN_generate_prime() returns the prime number on success, B 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, and
-1 on error.
The error codes can be obtained by L.
=head1 SEE ALSO
L, L, L
=head1 HISTORY
The B arguments to BN_generate_prime() and to BN_is_prime()
were added in SSLeay 0.9.0. The B argument to BN_generate_prime()
was added in SSLeay 0.9.1.
BN_is_prime_fasttest() was added in OpenSSL 0.9.5.
=cut