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BN_GENERATE_PRIME(3ossl)            OpenSSL           BN_GENERATE_PRIME(3ossl)




NAME

       BN_generate_prime_ex2, BN_generate_prime_ex, BN_is_prime_ex,
       BN_check_prime, 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_ex2(BIGNUM *ret, int bits, int safe,
                                  const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb,
                                  BN_CTX *ctx);

        int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add,
                                 const BIGNUM *rem, BN_GENCB *cb);

        int BN_check_prime(const BIGNUM *p, BN_CTX *ctx, 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);

       The following functions have been deprecated since OpenSSL 0.9.8, and
       can be hidden entirely by defining OPENSSL_API_COMPAT with a suitable
       version value, see openssl_user_macros(7):

        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 *p, int nchecks,
                        void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg);

        int BN_is_prime_fasttest(const BIGNUM *p, int nchecks,
                                 void (*callback)(int, int, void *), BN_CTX *ctx,
                                 void *cb_arg, int do_trial_division);

       The following functions have been deprecated since OpenSSL 3.0, and can
       be hidden entirely by defining OPENSSL_API_COMPAT with a suitable
       version value, see openssl_user_macros(7):

        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);


DESCRIPTION

       BN_generate_prime_ex2() generates a pseudo-random prime number of at
       least bit length bits using the BN_CTX provided in ctx. The value of
       ctx must not be NULL.

       The returned number is probably prime with a negligible error.  The
       maximum error rate is 2^-128.  It's 2^-287 for a 512 bit prime, 2^-435
       for a 1024 bit prime, 2^-648 for a 2048 bit prime, and lower than
       2^-882 for primes larger than 2048 bit.

       If add is NULL the returned prime number will have exact bit length
       bits with the top most two bits set.

       If ret is not NULL, it will be used to store the number.

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

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

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

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

       o 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). If safe is true, and rem == NULL the condition
       will be p % add == 3.  It is recommended that add 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 RAND(7)), the
       operation will fail.  The random number generator configured for the
       OSSL_LIB_CTX associated with ctx will be used.

       BN_generate_prime_ex() is the same as BN_generate_prime_ex2() except
       that no ctx parameter is passed.  In this case the random number
       generator associated with the default OSSL_LIB_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 p is prime.
       The functions tests until one of the tests shows that p is composite,
       or all the tests passed.  If p passes all these tests, it is considered
       a probable prime.

       The test performed on p 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 p is more than
       2048 bits, they do at least 128 rounds giving a maximum false positive
       rate of 2^-256.

       If nchecks is larger than the minimum above (64 or 128), nchecks rounds
       of the Miller-Rabin test will be done.

       If do_trial_division set to 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.

       ctx is a preallocated BN_CTX (to save the overhead of allocating and
       freeing the structure in a loop), or NULL.

       If the trial division is done, and no divisors are found and cb is not
       NULL, BN_GENCB_call(cb, 1, -1) is called.

       After each round of the Miller-Rabin probabilistic primality test, if
       cb is not NULL, BN_GENCB_call(cb, 1, j) is called with j the iteration
       (j = 0, 1, ...).

       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(3) (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(),
       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^nchecks, and -1 on error.

       BN_generate_prime(3) 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), RAND(7)


HISTORY

       The BN_is_prime_ex() and BN_is_prime_fasttest_ex() functions were
       deprecated in OpenSSL 3.0.

       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.


COPYRIGHT

       Copyright 2000-2021 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
       <https://www.openssl.org/source/license.html>.



3.0.1                             2021-12-14          BN_GENERATE_PRIME(3ossl)

openssl 3.0.1 - Generated Mon Dec 20 19:32:08 CST 2021
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