BN_generate_prime(3) OpenSSL BN_generate_prime(3)
BN_generate_prime, BN_is_prime, BN_is_prime_fasttest - generate primes
and test for primality
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 poten-
tial prime number.
o While the number is being tested for primality, callback(1, j,
cb_arg) is called as described below.
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 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
BN_generate_prime() returns the prime number on success, NULL other-
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).
openssl_bn(3), ERR_get_error(3), openssl_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
3rd Berkeley Distribution 0.9.7d BN_generate_prime(3)