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BN_generate_prime(3) OpenSSL BN_generate_prime(3)
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
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) ...
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,
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:
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.
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^-80 for random input.
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.
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
deprecated and can be compared to BN_is_prime_ex and
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
Callback functions should return 1 on success or 0 on error.
The error codes can be obtained by ERR_get_error(3).
bn(3), ERR_get_error(3), rand(3)
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
1.0.2h 2016-05-03 BN_generate_prime(3)