## table of contents

- buster 1.1.1d-0+deb10u3
- testing 1.1.1g-1
- unstable 1.1.1h-1
- experimental 3.0.0~~alpha4-1

BN_GENERATE_PRIME(3SSL) | OpenSSL | BN_GENERATE_PRIME(3SSL) |

# 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
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.

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>.

2020-04-21 | 1.1.1g |