mirror of
https://github.com/openssl/openssl.git
synced 2024-12-27 02:43:41 +08:00
103 lines
3.1 KiB
Plaintext
103 lines
3.1 KiB
Plaintext
=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(3)|err(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
|