BN_generate_prime, BN_is_prime, BN_is_prime_fasttest — generate primes and test for primality
*BN_generate_prime(BIGNUM *ret, int num, int safe, BIGNUM *add,
BIGNUM *rem, void (*callback)(int, int, void *), void *cb_arg);
BN_is_prime(const BIGNUM *a, int checks, void (*callback)(int, int,
void *), BN_CTX *ctx, void *cb_arg);
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
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
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),
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).
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.