## 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 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:

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

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

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_generate_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 pre-allocated *BN_CTX* (to
save the overhead of allocating 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* argument
to BN_generate_prime() was added in SSLeay 0.9.1. BN_is_prime_fasttest()
was added in OpenSSL 0.9.5.