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


#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);


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.


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).


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.