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);
 #define BN_GENCB_set_old(gencb, callback, cb_arg) ...
 #define BN_GENCB_set(gencb, callback, 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 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^-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 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.

RETURN VALUES¶

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).

SEE ALSO¶

bn(3), ERR_get_error(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.