=pod =head1 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 =head1 SYNOPSIS #include 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); =head1 DESCRIPTION BN_generate_prime_ex() generates a pseudo-random prime number of bit length B. If B is not B, it will be used to store the number. If B is not B, it is used as follows: =over 4 =item * B is called after generating the i-th potential prime number. =item * While the number is being tested for primality, B is called as described below. =item * When a prime has been found, B is called. =back The prime may have to fulfill additional requirements for use in Diffie-Hellman key exchange: If B is not B, the prime will fulfill the condition p % B == B (p % B == 1 if B == B) in order to suit a given generator. If B 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 B

is prime. The following tests are performed until one of them shows that B

is composite; if B

passes all these tests, it is considered prime. BN_is_prime_fasttest_ex(), when called with B, first attempts trial division by a number of small primes; if no divisors are found by this test and B is not B, B is called. If B, this test is skipped. Both BN_is_prime_ex() and BN_is_prime_fasttest_ex() perform a Miller-Rabin probabilistic primality test with B iterations. If B, a number of iterations is used that yields a false positive rate of at most 2^-80 for random input. If B is not B, B is called after the j-th iteration (j = 0, 1, ...). B is a pre-allocated B (to save the overhead of allocating and freeing the structure in a loop), or B. BN_GENCB_call calls the callback function held in the B structure and passes the ints B and B as arguments. There are two types of B 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 B is a B, B is of type B and B is a B. "Old" style callbacks are the same except they are initialised with a call to BN_GENCB_set_old and B is of type B. A callback is invoked through a call to B. This will check the type of the callback and will invoke B for new style callbacks or B 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 B parameter, and an argument to pass to it in the B. 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. =head1 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^B, and -1 on error. BN_generate_prime() returns the prime number on success, B otherwise. Callback functions should return 1 on success or 0 on error. The error codes can be obtained by L. =head1 SEE ALSO L, L, L =head1 HISTORY The B arguments to BN_generate_prime() and to BN_is_prime() were added in SSLeay 0.9.0. The B argument to BN_generate_prime() was added in SSLeay 0.9.1. BN_is_prime_fasttest() was added in OpenSSL 0.9.5. =cut