NAME

       BN_generate_prime_ex, BN_is_prime_ex, BN_is_prime_fasttest_ex, BN_GENCB_call,
       BN_GENCB_new, BN_GENCB_free, BN_GENCB_set_old, BN_GENCB_set, BN_GENCB_get_arg,
       BN_generate_prime, BN_is_prime, BN_is_prime_fasttest - generate primes and test for
       primality

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);

        BN_GENCB *BN_GENCB_new(void);

        void BN_GENCB_free(BN_GENCB *cb);

        void BN_GENCB_set_old(BN_GENCB *gencb,
                              void (*callback)(int, int, void *), void *cb_arg);

        void BN_GENCB_set(BN_GENCB *gencb,
                          int (*callback)(int, int, BN_GENCB *), void *cb_arg);

        void *BN_GENCB_get_arg(BN_GENCB *cb);

       Deprecated:

        #if OPENSSL_API_COMPAT < 0x00908000L
        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);
        #endif

DESCRIPTION

       BN_generate_prime_ex() generates a pseudo-random prime number of at least bit length bits.
       If ret is not NULL, it will be used to store the number.

       If cb is not NULL, it is used as follows:

       • BN_GENCB_call(cb, 0, i) is called after generating the i-th potential prime number.

       • While the number is being tested for primality, BN_GENCB_call(cb, 1, j) is called as
         described below.

       • When a prime has been found, BN_GENCB_call(cb, 2, i) is called.

       • The callers of BN_generate_prime_ex() may call BN_GENCB_call(cb, i, j) with other values
         as described in their respective man pages; see "SEE ALSO".

       The prime may have to fulfill additional requirements for use in Diffie-Hellman key
       exchange:

       If add is not NULL, the prime will fulfill the condition p % add == rem (p % add == 1 if
       rem == NULL) in order to suit a given generator.

       If 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 p is prime.  The
       following tests are performed until one of them shows that p is composite; if p passes all
       these tests, it is considered prime.

       BN_is_prime_fasttest_ex(), when called with do_trial_division == 1, first attempts trial
       division by a number of small primes; if no divisors are found by this test and cb is not
       NULL, BN_GENCB_call(cb, 1, -1) is called.  If 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 nchecks iterations. If nchecks == BN_prime_checks, a number of
       iterations is used that yields a false positive rate of at most 2^-64 for random input.
       The error rate depends on the size of the prime and goes down for bigger primes.  The rate
       is 2^-80 starting at 308 bits, 2^-112 at 852 bits, 2^-128 at 1080 bits, 2^-192 at 3747
       bits and 2^-256 at 6394 bits.

       When the source of the prime is not random or not trusted, the number of checks needs to
       be much higher to reach the same level of assurance: It should equal half of the targeted
       security level in bits (rounded up to the next integer if necessary).  For instance, to
       reach the 128 bit security level, nchecks should be set to 64.

       If cb is not NULL, BN_GENCB_call(cb, 1, j) is called after the j-th iteration (j = 0, 1,
       ...). ctx is a pre-allocated BN_CTX (to save the overhead of allocating and freeing the
       structure in a loop), or NULL.

       BN_GENCB_call() calls the callback function held in the BN_GENCB structure and passes the
       ints a and b as arguments. There are two types of 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.

       A BN_GENCB 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 gencb is a BN_GENCB *, callback is of type int (*callback)(int, int,
       BN_GENCB *) and cb_arg is a void *.  "Old" style callbacks are the same except they are
       initialised with a call to BN_GENCB_set_old() and callback is of type void
       (*callback)(int, int, void *).

       A callback is invoked through a call to BN_GENCB_call. This will check the type of the
       callback and will invoke callback(a, b, gencb) for new style callbacks or callback(a, b,
       cb_arg) 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 callback parameter, and an argument
       to pass to it in the cb_arg. BN_is_prime() and BN_is_prime_fasttest() can similarly be
       compared to BN_is_prime_ex() and BN_is_prime_fasttest_ex(), respectively.

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^nchecks, and -1 on error.

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

       BN_GENCB_new returns a pointer to a BN_GENCB structure on success, or NULL 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 ERR_get_error(3).

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);

SEE ALSO

       DH_generate_parameters(3), DSA_generate_parameters(3), RSA_generate_key(3),
       ERR_get_error(3), RAND_bytes(3)

HISTORY

       BN_GENCB_new(), BN_GENCB_free(), and BN_GENCB_get_arg() were added in OpenSSL 1.1.0

COPYRIGHT

       Copyright 2000-2018 The OpenSSL Project Authors. All Rights Reserved.

       Licensed under the OpenSSL license (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 <https://www.openssl.org/source/license.html>.