generate primes and test for
*ret, int bits, int safe,
const BIGNUM *add, const BIGNUM
*rem, BN_GENCB *cb);
BN_is_prime_ex(const BIGNUM *p,
int nchecks, BN_CTX *ctx,
*p, int nchecks, BN_CTX
*ctx, int do_trial_division,
int a, int b);
*gencb, void (*callback)(int, int, void *),
int (*callback)(int, int, BN_GENCB *),
int num, int safe,
BIGNUM *add, BIGNUM *rem,
void (*callback)(int, int, void *),
BN_is_prime(const BIGNUM *a,
int checks, void (*callback)(int, int,
void *), BN_CTX *ctx, void
*a, int checks, void
(*callback)(int, int, void *), BN_CTX *ctx,
void *cb_arg, int
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
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
the prime will fulfill the condition p % add ==
rem (p % add == 1 if
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_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.
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
1, -1) is called. If do_trial_division == 0,
this test is skipped.
BN_is_prime_fasttest_ex() perform a Miller-Rabin
probabilistic primality test with nchecks iterations.
If nchecks ==
a number of iterations is used that yields a false positive rate of at most
2^-80 for random input.
If cb is not
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
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 structures 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 the macro
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 the macro
and callback is of type void
(*callback)(int, int, void *).
A callback is invoked through a call to
This will check the type of the callback and will invoke
b, gencb) for new style
b, cb_arg) for old style.
(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
are deprecated and can be compared to
BN_generate_prime_ex() returns 1 on
success or 0 on error.
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,
Callback functions should return 1 on success or 0 on error.
The error codes can be obtained by ERR_get_error(3).
BN_new(3), ERR_get_error(3), RAND_bytes(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