=pod =head1 NAME BN_generate_prime, BN_is_prime, BN_is_prime_fasttest - Generate primes and test for primality =head1 SYNOPSIS #include 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() generates a pseudo-random prime number of B bits. If B is not B, it will be used to store the number. If B is not B, it is called 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(). The prime number generation has a negligible error probability. BN_is_prime() and BN_is_prime_fasttest() 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(), 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() and BN_is_prime_fasttest() 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. =head1 RETURN VALUES BN_generate_prime() returns the prime number on success, B 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^B, and -1 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