- NAME
- SYNOPSIS
- DESCRIPTION
- RETURN VALUES
- SEE ALSO
- HISTORY

# 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.

# SEE ALSO

bn, ERR_get_error, rand

# 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.