is true, it will be a safe prime (i.e. a prime p so
that (p1)/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 is
prime. The following tests are performed until one of them shows that
B
is composite; if B
passes all these tests, it is considered
prime.

BN_is_prime_fasttest_ex(), when called with B,
first attempts trial division by a number of small primes;
if no divisors are found by this test and B is not B,
B is called.
If B, this test is skipped.

Both BN_is_prime_ex() and BN_is_prime_fasttest_ex() perform a MillerRabin
probabilistic primality test with B iterations. If
B, a number of iterations is used that
yields a false positive rate of at most 2^80 for random input.

If B is not B, B is called
after the jth iteration (j = 0, 1, ...). B is a
preallocated B (to save the overhead of allocating and
+that (p1)/2 is also prime). If B is true, and B == B
+the condition will be p % B == 3.
+It is recommended that B is a multiple of 4.
+
+The random generator must be seeded prior to calling BN_generate_prime_ex().
+If the automatic seeding or reseeding of the OpenSSL CSPRNG fails due to
+external circumstances (see L), the operation will fail.
+The random number generator configured for the OPENSSL_CTX associated with
+B will be used.
+
+BN_generate_prime_ex() is the same as BN_generate_prime_ex2() except that no
+B 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 MillerRabin probabilistic primality test.
+
+The functions do at least 64 rounds of the MillerRabin 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 MillerRabin 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 preallocated B (to save the overhead of allocating and
freeing the structure in a loop), or B.
BN_GENCB_call calls the callback function held in the B structure
+If the trial division is done, and no divisors are found and B
+is not B, B is called.
+
+After each round of the MillerRabin 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 BN_GENCB structure should be created through a call to BN_GENCB_new(),
+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
@@ 127,23 +178,23 @@ 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 obtained the argument associated with a BN_GENCB structure
+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
+BN_generate_prime() (deprecated) works in the same way as
+BN_generate_prime_ex() but expects an oldstyle callback function
directly in the B parameter, and an argument to pass to it in
the B. 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.
+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() 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, and
+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.
@@ 169,24 +220,29 @@ Instead applications should create a BN_GENCB structure using BN_GENCB_new:
BN_GENCB *callback;
callback = BN_GENCB_new();
 if(!callback) /* handle error */
+ if (!callback)
+ /* error */
...
BN_GENCB_free(callback);
=head1 SEE ALSO
L, L
+L, L,
+L, L, L,
+L
=head1 HISTORY
BN_GENCB_new(), BN_GENCB_free(),
and BN_GENCB_get_arg() were added in OpenSSL 1.1.0
+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 20002017 The OpenSSL Project Authors. All Rights Reserved.
+Copyright 20002019 The OpenSSL Project Authors. All Rights Reserved.
Licensed under the OpenSSL license (the "License"). You may not use
+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.