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       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

	#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);


	#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);

       BN_generate_prime_ex() generates	a pseudo-random	prime number of	at
       least bit length	bits. The returned number is probably prime with a
       negligible error.

       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

       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 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.

       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_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(),

       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

       BN_generate_prime() returns the prime number on success,	NULL

       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).

       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 *callback;
	callback = BN_GENCB_new();
	if (!callback)
	    /* error */

       DH_generate_parameters(3), DSA_generate_parameters(3),
       RSA_generate_key(3), ERR_get_error(3), RAND_bytes(3), RAND(7)

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

       Copyright 2000-2019 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

1.1.1d				  2019-09-10		  BN_GENERATE_PRIME(3)


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