BN_generate_prime(3) OpenSSL BN_generate_prime(3)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);
DESCRIPTIONBN_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 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
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BN_generate_prime(3) OpenSSL BN_generate_prime(3)
== 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_check, 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 VALUESBN_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).
SEE ALSObn(3), err(3), rand(3)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.
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