### 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:

```
#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);
#endif
```

### DESCRIPTION

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 **add** is **NULL** the returned prime number will have exact bit length **bits** with the top most two bits set.

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(cb, i, j)**with other values as described in their respective man 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). If **safe** is true, and **rem** == **NULL** the condition will be p % **add** == 3. It is recommended that **add** is a multiple of 4.

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 preallocated **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_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**. BN_is_prime() and BN_is_prime_fasttest() can similarly be compared to BN_is_prime_ex() and BN_is_prime_fasttest_ex(), respectively.

### RETURN VALUES

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 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).

### REMOVED FUNCTIONALITY

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_new:

```
BN_GENCB *callback;
callback = BN_GENCB_new();
if (!callback)
/* error */
...
BN_GENCB_free(callback);
```

### SEE ALSO

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

### HISTORY

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

### COPYRIGHT

Copyright 2000-2020 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 https://www.openssl.org/source/license.html.