BN_GENERATE_PRIME(3)

NAME
BN_generate_prime_ex, BN_is_prime_ex, BN_is_prime_fasttest_ex, BN_GENCB_call, BN_GENCB_set_old, BN_GENCB_set, BN_generate_prime, BN_is_prime, BN_is_prime_fasttest - generate primes and test for primality

SYNOPSIS
#include <openssl/bn.h>
int
BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb);
int
BN_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb);
int
BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, int do_trial_division, BN_GENCB *cb);
int
BN_GENCB_call(BN_GENCB *cb, int a, int b);
void
BN_GENCB_set_old(BN_GENCB *gencb, void (*callback)(int, int, void *), void *cb_arg);
void
BN_GENCB_set(BN_GENCB *gencb, int (*callback)(int, int, BN_GENCB *), void *cb_arg);

Deprecated:

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);

DESCRIPTION
BN_generate_prime_ex() generates a pseudo-random prime number of at least bit length bits. If ret is not NULL, it will be used to store the number.

If cb is not NULL, it is used as follows:

•   BN_GENCB_call(cb, 0, i) is called after generating the i-th potential prime number.

•   While the number is being tested for primality, BN_GENCB_call(cb, 1, j) is called as described below.

•   When a prime has been found, BN_GENCB_call(cb, 2, i) 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 prime number generation has a negligible error probability.

BN_is_prime_ex() and BN_is_prime_fasttest_ex() test if the number p is prime. The following tests are performed until one of them shows that p is composite; if p passes all these tests, it is considered prime.

BN_is_prime_fasttest_ex(), 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 cb is not NULL, BN_GENCB_call(cb, 1, -1) is called. If do_trial_division == 0, this test is skipped.

Both BN_is_prime_ex() and BN_is_prime_fasttest_ex() perform a Miller-Rabin probabilistic primality test with nchecks iterations. If nchecks == BN_prime_checks, a number of iterations is used that yields a false positive rate of at most 2^-80 for random input.

If cb is not NULL, BN_GENCB_call cb 1 j 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_GENCB_call() calls the callback function held in the BN_GENCB structure and passes the ints a and b as arguments. There are two types of BN_GENCB structures that are supported: "new" style and "old" style. New programs should prefer the "new" style, whilst the "old" style is provided for backwards compatibility purposes.

For "new" style callbacks a BN_GENCB structure should be initialised with a call to the macro BN_GENCB_set(), where gencb is a BN_GENCB *, callback is of type int (*callback)(int, int, BN_GENCB *) and cb_arg is a void *. "Old" style callbacks are the same except they are initialised with a call to the macro BN_GENCB_set_old() and callback is of type void (*callback)(int, int, void *).

A callback is invoked through a call to BN_GENCB_call(). This will check the type of the callback and will invoke callback(a, b, gencb) for new style callbacks or callback(a, b, cb_arg) for old style.

BN_generate_prime() (deprecated) works in the same way as BN_generate_prime_ex() but expects an old style callback function directly in the callback parameter, and an argument to pass to it in the cb_arg. Similarly BN_is_prime() and BN_is_prime_fasttest() are deprecated and can be compared to BN_is_prime_ex() and BN_is_prime_fasttest_ex() respectively.

RETURN VALUES
BN_generate_prime_ex() returns 1 on success or 0 on error.

BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime(), and BN_is_prime_fasttest() return 0 if the number is composite, 1 if it is prime with an error probability of less than 0.25^nchecks, and -1 on error.

BN_generate_prime() returns the prime number on success, NULL otherwise.

Callback functions should return 1 on success or 0 on error.

The error codes can be obtained by ERR_get_error(3).

SEE ALSO
BN_new(3), ERR_get_error(3), RAND_bytes(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.