## NAME

`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

## 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`);

`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`);

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 at least bit length
`bits`. The returned number is probably prime, but there
is a very small probability of returning a non-prime number. 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 callers of
`BN_generate_prime_ex`

() may call`BN_GENCB_call`

() with other values as described in their respective manual 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).

`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` 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.

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`

()
(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_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.

`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).

## SEE ALSO

BN_new(3), DH_generate_parameters(3), DSA_generate_parameters(3), RSA_generate_key(3)

## HISTORY

`BN_generate_prime`

() and
`BN_is_prime`

() first appeared in SSLeay 0.5.1 and had
their `cb_arg` argument added in SSLeay 0.9.0. These two
functions have been available since OpenBSD 2.4.

The `ret` argument to
`BN_generate_prime`

() was added in SSLeay 0.9.1 and
OpenBSD 2.6.

`BN_is_prime_fasttest`

() first appeared in
OpenSSL 0.9.5 and has been available since OpenBSD
2.7.

`BN_generate_prime_ex`

(),
`BN_is_prime_ex`

(),
`BN_is_prime_fasttest_ex`

(),
`BN_GENCB_call`

(),
`BN_GENCB_set_old`

(), and
`BN_GENCB_set`

() first appeared in OpenSSL 0.9.8 and
have been available since OpenBSD 4.5.

`BN_GENCB_new`

(),
`BN_GENCB_free`

(), and
`BN_GENCB_get_arg`

() first appeared in OpenSSL 1.1.0
and have been available since OpenBSD 6.3.