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=pod
=head1 NAME
BN_generate_prime_ex, BN_is_prime_ex, BN_is_prime_fasttest_ex, BN_GENCB_call,
BN_GENCB_set_old, BN_GENCB_set, BN_generate_prime, BN_is_prime,
BN_is_prime_fasttest - generate primes and test for primality
=head1 SYNOPSIS
#include <openssl/bn.h>
int BN_generate_prime_ex(BIGNUM *ret,int bits,int safe, const BIGNUM *add,
const BIGNUM *rem, BN_GENCB *cb);
int BN_is_prime_ex(const BIGNUM *p,int nchecks, BN_CTX *ctx, BN_GENCB *cb);
int BN_is_prime_fasttest_ex(const BIGNUM *p,int nchecks, BN_CTX *ctx,
int do_trial_division, BN_GENCB *cb);
int BN_GENCB_call(BN_GENCB *cb, int a, int b);
#define BN_GENCB_set_old(gencb, callback, cb_arg) ...
#define BN_GENCB_set(gencb, callback, cb_arg) ...
Deprecated:
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_ex() generates a pseudo-random prime number of
bit length B<bits>.
If B<ret> is not B<NULL>, it will be used to store the number.
If B<cb> is not B<NULL>, it is used as follows:
=over 4
=item *
B<BN_GENCB_call(cb, 0, i)> is called after generating the i-th
potential prime number.
=item *
While the number is being tested for primality,
B<BN_GENCB_call(cb, 1, j)> is called as described below.
=item *
When a prime has been found, B<BN_GENCB_call(cb, 2, i)> 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_ex().
The prime number generation has a negligible error probability.
BN_is_prime_ex() and BN_is_prime_fasttest_ex() test if the number B<p> is
prime. The following tests are performed until one of them shows that
B<p> is composite; if B<p> passes all these tests, it is considered
prime.
BN_is_prime_fasttest_ex(), 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<cb> is not B<NULL>,
B<BN_GENCB_call(cb, 1, -1)> is called.
If B<do_trial_division == 0>, this test is skipped.
Both BN_is_prime_ex() and BN_is_prime_fasttest_ex() perform a Miller-Rabin
probabilistic primality test with B<nchecks> iterations. If
B<nchecks == BN_prime_checks>, a number of iterations is used that
yields a false positive rate of at most 2^-80 for random input.
If B<cb> is not B<NULL>, B<BN_GENCB_call(cb, 1, j)> 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>.
BN_GENCB_call calls the callback function held in the B<BN_GENCB> structure
and passes the ints B<a> and B<b> as arguments. There are two types of
B<BN_GENCB> structure that are supported: "new" style and "old" style. New
programs should prefer the "new" style, whilst the "old" style is provided
for backwards compatibility purposes.
For "new" style callbacks a BN_GENCB structure should be initialised with a
call to BN_GENCB_set, where B<gencb> is a B<BN_GENCB *>, B<callback> is of
type B<int (*callback)(int, int, BN_GENCB *)> and B<cb_arg> is a B<void *>.
"Old" style callbacks are the same except they are initialised with a call
to BN_GENCB_set_old and B<callback> is of type
B<void (*callback)(int, int, void *)>.
A callback is invoked through a call to B<BN_GENCB_call>. This will check
the type of the callback and will invoke B<callback(a, b, gencb)> for new
style callbacks or B<callback(a, b, cb_arg)> for old style.
BN_generate_prime (deprecated) works in the same way as
BN_generate_prime_ex but expects an old style callback function
directly in the B<callback> parameter, and an argument to pass to it in
the B<cb_arg>. Similarly BN_is_prime and BN_is_prime_fasttest are
deprecated and can be compared to BN_is_prime_ex and
BN_is_prime_fasttest_ex respectively.
=head1 RETURN VALUES
BN_generate_prime_ex() return 1 on success or 0 on error.
BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime() and
BN_is_prime_fasttest() return 0 if the number is composite, 1 if it is
prime with an error probability of less than 0.25^B<nchecks>, and
-1 on error.
BN_generate_prime() returns the prime number on success, B<NULL> otherwise.
Callback functions should return 1 on success or 0 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
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