b3c1d18d03
manual when the specific function is refered to in the current manual text. This correction was originally introduced in OpenBSD's tracking of OpenSSL.
102 lines
3.1 KiB
Text
102 lines
3.1 KiB
Text
=pod
|
|
|
|
=head1 NAME
|
|
|
|
BN_generate_prime, BN_is_prime, BN_is_prime_fasttest - generate primes and test for primality
|
|
|
|
=head1 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);
|
|
|
|
=head1 DESCRIPTION
|
|
|
|
BN_generate_prime() generates a pseudo-random prime number of B<num>
|
|
bits.
|
|
If B<ret> is not B<NULL>, it will be used to store the number.
|
|
|
|
If B<callback> is not B<NULL>, it is called as follows:
|
|
|
|
=over 4
|
|
|
|
=item *
|
|
|
|
B<callback(0, i, cb_arg)> is called after generating the i-th
|
|
potential prime number.
|
|
|
|
=item *
|
|
|
|
While the number is being tested for primality, B<callback(1, j,
|
|
cb_arg)> is called as described below.
|
|
|
|
=item *
|
|
|
|
When a prime has been found, B<callback(2, i, cb_arg)> is called.
|
|
|
|
=back
|
|
|
|
The prime may have to fulfill additional requirements for use in
|
|
Diffie-Hellman key exchange:
|
|
|
|
If B<add> is not B<NULL>, the prime will fulfill the condition p % B<add>
|
|
== B<rem> (p % B<add> == 1 if B<rem> == B<NULL>) in order to suit a given
|
|
generator.
|
|
|
|
If B<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 B<a> is
|
|
prime. The following tests are performed until one of them shows that
|
|
B<a> is composite; if B<a> passes all these tests, it is considered
|
|
prime.
|
|
|
|
BN_is_prime_fasttest(), when called with B<do_trial_division == 1>,
|
|
first attempts trial division by a number of small primes;
|
|
if no divisors are found by this test and B<callback> is not B<NULL>,
|
|
B<callback(1, -1, cb_arg)> is called.
|
|
If B<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 B<checks> iterations. If
|
|
B<checks == BN_prime_check>, a number of iterations is used that
|
|
yields a false positive rate of at most 2^-80 for random input.
|
|
|
|
If B<callback> is not B<NULL>, B<callback(1, j, cb_arg)> is called
|
|
after the j-th iteration (j = 0, 1, ...). B<ctx> is a
|
|
pre-allocated B<BN_CTX> (to save the overhead of allocating and
|
|
freeing the structure in a loop), or B<NULL>.
|
|
|
|
=head1 RETURN VALUES
|
|
|
|
BN_generate_prime() returns the prime number on success, B<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^B<checks>, and
|
|
-1 on error.
|
|
|
|
The error codes can be obtained by L<ERR_get_error(3)|ERR_get_error(3)>.
|
|
|
|
=head1 SEE ALSO
|
|
|
|
L<bn(3)|bn(3)>, L<ERR_get_error(3)|ERR_get_error(3)>, L<rand(3)|rand(3)>
|
|
|
|
=head1 HISTORY
|
|
|
|
The B<cb_arg> arguments to BN_generate_prime() and to BN_is_prime()
|
|
were added in SSLeay 0.9.0. The B<ret> argument to BN_generate_prime()
|
|
was added in SSLeay 0.9.1.
|
|
BN_is_prime_fasttest() was added in OpenSSL 0.9.5.
|
|
|
|
=cut
|