NAME¶
BN_generate_prime, BN_is_prime, BN_is_prime_fasttest - generate primes and test
for primality
SYNOPSIS¶
#include <openssl/bn.h>
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() generates a pseudo-random prime number of
num
bits. If
ret is not
NULL, it will be used to store the number.
If
callback is not
NULL, it is called as follows:
- •
- callback(0, i, cb_arg) is called after generating the i-th
potential prime number.
- •
- While the number is being tested for primality, callback(1, j,
cb_arg) is called as described below.
- •
- When a prime has been found, callback(2, i, cb_arg) 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(). The prime
number generation has a negligible error probability.
BN_is_prime() and
BN_is_prime_fasttest() test if the number
a is prime. The following tests are performed until one of them shows
that
a is composite; if
a passes all these tests, it is
considered prime.
BN_is_prime_fasttest(), 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
callback is not
NULL,
callback(1, -1,
cb_arg) is called. If
do_trial_division == 0, this test is skipped.
Both
BN_is_prime() and
BN_is_prime_fasttest() perform a
Miller-Rabin probabilistic primality test with
checks iterations. If
checks == BN_prime_checks, a number of iterations is used that yields a
false positive rate of at most 2^-80 for random input.
If
callback is not
NULL,
callback(1, j, cb_arg) 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.
RETURN VALUES¶
BN_generate_prime() returns the prime number on success,
NULL
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^
checks, and -1 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.