BN_generate_prime(3) OpenSSL BN_generate_prime(3)
BN_generate_prime, BN_is_prime, BN_is_prime_fasttest - generate primes and test for pri-
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,
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:
o callback(0, i, cb_arg) is called after generating the i-th potential prime number.
o While the number is being tested for primality, callback(1, j, cb_arg) is called as
o 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
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
Both BN_is_prime() and BN_is_prime_fasttest() perform a Miller-Rabin probabilistic primal-
ity 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 proba-
bility of less than 0.25^checks, and -1 on error.
The error codes can be obtained by ERR_get_error(3).
bn(3), ERR_get_error(3), rand(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.
0.9.7a 2003-01-13 BN_generate_prime(3)