openssl/doc/crypto/BN_generate_prime.pod
Richard Levitte 6859cf7459 It makes more sense to refer to specific function manuals than the concept
manual when the specific function is refered to in the current manual text.
This correction was originally introduced in OpenBSD's tracking of OpenSSL.
2002-09-25 13:33:28 +00:00

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=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