parameter is passed.
In this case the random number generator associated with the default OPENSSL_CTX
will be used.
BN_check_prime(), BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime()
and BN_is_prime_fasttest() test if the number B is prime.
The functions tests until one of the tests shows that B

is composite,
or all the tests passed.
If B

passes all these tests, it is considered a probable prime.
The test performed on B

are trial division by a number of small primes
and rounds of the of the Miller-Rabin probabilistic primality test.
The functions do at least 64 rounds of the Miller-Rabin test giving a maximum
false positive rate of 2^-128.
If the size of B

is more than 2048 bits, they do at least 128 rounds
giving a maximum false positive rate of 2^-256.
If B is larger than the minimum above (64 or 128), B
rounds of the Miller-Rabin test will be done.
If B set to B<0>, the trial division will be skipped.
BN_is_prime_ex() and BN_is_prime() always skip the trial division.
BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime()
and BN_is_prime_fasttest() are deprecated.
BN_is_prime_fasttest() and BN_is_prime() behave just like
BN_is_prime_fasttest_ex() and BN_is_prime_ex() respectively, but with the old
style call back.
B is a pre-allocated B (to save the overhead of allocating and
freeing the structure in a loop), or B.
If the trial division is done, and no divisors are found and B
is not B, B is called.
After each round of the Miller-Rabin probabilistic primality test,
if B is not B, B is called
with B the iteration (j = 0, 1, ...).
BN_GENCB_call() calls the callback function held in the B structure
and passes the ints B and B** as arguments. There are two types of
B 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.
A B structure should be created through a call to BN_GENCB_new(),
and freed through a call to BN_GENCB_free().
For "new" style callbacks a BN_GENCB structure should be initialised with a
call to BN_GENCB_set(), where B is a B, B is of
type B and B is a B.
"Old" style callbacks are the same except they are initialised with a call
to BN_GENCB_set_old() and B is of type
B.
A callback is invoked through a call to B. This will check
the type of the callback and will invoke B for new
style callbacks or B for old style.
It is possible to obtain the argument associated with a BN_GENCB structure
(set via a call to BN_GENCB_set or BN_GENCB_set_old) using BN_GENCB_get_arg.
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 parameter, and an argument to pass to it in
the B. BN_is_prime() and BN_is_prime_fasttest()
can similarly 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(),
BN_is_prime_fasttest() and BN_check_prime return 0 if the number is composite,
1 if it is prime with an error probability of less than 0.25^B, and
-1 on error.
BN_generate_prime() returns the prime number on success, B otherwise.
BN_GENCB_new returns a pointer to a BN_GENCB structure on success, or B
otherwise.
BN_GENCB_get_arg returns the argument previously associated with a BN_GENCB
structure.
Callback functions should return 1 on success or 0 on error.
The error codes can be obtained by L.
=head1 REMOVED FUNCTIONALITY
As of OpenSSL 1.1.0 it is no longer possible to create a BN_GENCB structure
directly, as in:
BN_GENCB callback;
Instead applications should create a BN_GENCB structure using BN_GENCB_new:
BN_GENCB *callback;
callback = BN_GENCB_new();
if (!callback)
/* error */
...
BN_GENCB_free(callback);
=head1 SEE ALSO
L, L,
L, L, L,
L
=head1 HISTORY
The BN_GENCB_new(), BN_GENCB_free(),
and BN_GENCB_get_arg() functions were added in OpenSSL 1.1.0.
BN_check_prime() was added in OpenSSL 3.0.
=head1 COPYRIGHT
Copyright 2000-2019 The OpenSSL Project Authors. All Rights Reserved.
Licensed under the Apache License 2.0 (the "License"). You may not use
this file except in compliance with the License. You can obtain a copy
in the file LICENSE in the source distribution or at
L.
=cut
**