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BN_GENERATE_PRIME(3)	 BSD Library Functions Manual	  BN_GENERATE_PRIME(3)

NAME
     BN_generate_prime_ex, BN_is_prime_ex, BN_is_prime_fasttest_ex,
     BN_GENCB_call, BN_GENCB_set_old, BN_GENCB_set, BN_generate_prime,
     BN_is_prime, BN_is_prime_fasttest — generate primes and test for primal‐
     ity

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);

     #define BN_GENCB_set_old(gencb, callback, cb_arg) ...
     #define BN_GENCB_set(gencb, callback, cb_arg) ...

     Deprecated:

     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);

DESCRIPTION
     BN_generate_prime_ex() generates a pseudo-random prime number of 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 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 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^-80 for random input.

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

     BN_GENCB_call() calls the callback function held in the BN_GENCB struc‐
     ture and passes the ints a and b as arguments.  There are two types of
     BN_GENCB structures that are supported: "new" style and "old" style.  New
     programs should prefer the "new" style, whilst the "old" style is pro‐
     vided for backwards compatibility purposes.

     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.

     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.  Similarly BN_is_prime() and BN_is_prime_fasttest() are depre‐
     cated and can be compared to BN_is_prime_ex() and
     BN_is_prime_fasttest_ex() respectively.

RETURN VALUES
     BN_generate_prime_ex() returns 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.

     Callback functions should return 1 on success or 0 on error.

     The error codes can be obtained by ERR_get_error(3).

SEE ALSO
     bn(3), ERR_get_error(3), rand(3)

HISTORY
     The cb_arg arguments to BN_generate_prime() and to BN_is_prime() were
     added in SSLeay 0.9.0.  The ret argument to BN_generate_prime() was added
     in SSLeay 0.9.1.  BN_is_prime_fasttest() was added in OpenSSL 0.9.5.

BSD				March 28, 2024				   BSD
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