Documentation for BN_is_prime_fasttest.

     generation becomes much faster.

     This implies a change for the callback functions in DSA_is_prime

     and DSA_generate_parameters: They are now called once for each

     positive witness in the Rabin-Miller test, not just occasionally

     in the inner loop; and the parameters to the callback function now

     provide an iteration count for the outer loop rather than for the

     current invocation of the inner loop.

     and DSA_generate_parameters: The callback function is called once

     for each positive witness in the Rabin-Miller test, not just

     occasionally in the inner loop; and the parameters to the

     callback function now provide an iteration count for the outer

     loop rather than for the current invocation of the inner loop.

     DSA_generate_parameters additionally can call the callback

     function with an 'iteration count' of -1, meaning that a

     candidate has passed the trial division test (when q is generated 

     from an application-provided seed, trial division is skipped).

     [Bodo Moeller]

  *) New function BN_is_prime_fasttest that optionally does trial

=head1 NAME

BN_generate_prime, BN_is_prime - Generate primes and test for primality

BN_generate_prime, BN_is_prime, BN_is_prime_fasttest - Generate primes and test for primality

=head1 SYNOPSIS

 int BN_is_prime(BIGNUM *a, int checks, void (*callback)(int, int, 

     void *), BN_CTX *ctx, void *cb_arg);

 int BN_is_prime_fasttest(BIGNUM *a, int checks, void (*callback)(int, int, 

     void *), BN_CTX *ctx, BN_CTX *ctx2, 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 NULL, it will be used to store the number.

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:

The prime may have to fulfill additional requirements for use in

Diffie-Hellman key exchange:

If B<add> is not NULL, the prime will fulfill the condition p % B<add>

== B<rem> (p % B<add> == 1 if B<rem> == NULL) in order to suit a given

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

The PRNG must be seeded prior to calling BN_generate_prime().

The prime number generation has a negligible error probability.

BN_is_prime() tests if the number B<a> is prime. This is done by

performing a Miller-Rabin probabilistic primality test with B<checks>

iterations. If B<checks == BN_prime_check>, it uses a number

of iterations that yields a false positive rate of at most 2^-80 for

random input.

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.

=over 4

=item *

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.

=item *

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. B<ctx> is a pre-allocated B<BN_CTX> (to save

the overhead of allocating and freeing the structure in a loop), or

NULL.

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>. For

BN_is_prime_fasttest(), B<ctx2> is a second pre-allocated B<BN_CTX> or

B<NULL> (lacking this parameter, BN_is_prime() always has to allocated

an additional B<CN_CTX>).

=head1 RETURN VALUES

BN_generate_prime() returns the prime number on success, NULL otherwise.

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

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