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
#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); #define BN_GENCB_set_old(gencb, callback, cb_arg) ... #define BN_GENCB_set(gencb, callback, cb_arg) ...
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);
BN_generate_prime_ex() generates a pseudo-random prime number of 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 PRNG must be seeded prior to calling BN_generate_prime_ex(). 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^-64 for random input. The error rate depends on the size of the prime and goes down for bigger primes. The rate is 2^-80 starting at 308 bits, 2^-112 at 852 bits, 2^-128 at 1080 bits, 2^-192 at 3747 bits and 2^-256 at 6394 bits.
When the source of the prime is not random or not trusted, the number of checks needs to be much higher to reach the same level of assurance: It should equal half of the targeted security level in bits (rounded up to the next integer if necessary). For instance, to reach the 128 bit security level, nchecks should be set to 64.
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 structure 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 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 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.
BN_generate_prime_ex() return 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).
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.