## table of contents

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

# NAME¶

BN_generate_prime_ex2, BN_generate_prime_ex, BN_is_prime_ex, BN_check_prime, 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_ex2(BIGNUM *ret, int bits, int safe, const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb, BN_CTX *ctx); int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb); int BN_check_prime(const BIGNUM *p, BN_CTX *ctx, 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);

The following functions have been deprecated since OpenSSL 0.9.8,
and can be hidden entirely by defining **OPENSSL_API_COMPAT** with a
suitable version value, see openssl_user_macros(7):

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 *p, int nchecks, void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg); int BN_is_prime_fasttest(const BIGNUM *p, int nchecks, void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg, int do_trial_division);

The following functions have been deprecated since OpenSSL 3.0,
and can be hidden entirely by defining **OPENSSL_API_COMPAT** with a
suitable version value, see openssl_user_macros(7):

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);

# DESCRIPTION¶

**BN_generate_prime_ex2()** generates a pseudo-random prime
number of at least bit length **bits** using the BN_CTX provided in
**ctx**. The value of **ctx** must not be NULL.

The returned number is probably prime with a negligible error. The maximum error rate is 2^-128. It's 2^-287 for a 512 bit prime, 2^-435 for a 1024 bit prime, 2^-648 for a 2048 bit prime, and lower than 2^-882 for primes larger than 2048 bit.

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. The random number generator configured for the
OSSL_LIB_CTX associated with **ctx** will be used.

**BN_generate_prime_ex()** is the same as
**BN_generate_prime_ex2()** except that no **ctx** parameter is
passed. In this case the random number generator associated with the default
OSSL_LIB_CTX will be used.

**BN_check_prime()**, **BN_is_prime_ex()**,
**BN_is_prime_fasttest_ex()**, **BN_is_prime()** and
**BN_is_prime_fasttest()** test if the number **p** is prime. The
functions tests until one of the tests shows that **p** is composite, or
all the tests passed. If **p** passes all these tests, it is considered a
probable prime.

The test performed on **p** are trial division by a number of
small primes and rounds of the of the Miller-Rabin probabilistic primality
test.

The functions do at least 64 rounds of the Miller-Rabin test
giving a maximum false positive rate of 2^-128. If the size of **p** is
more than 2048 bits, they do at least 128 rounds giving a maximum false
positive rate of 2^-256.

If **nchecks** is larger than the minimum above (64 or 128),
**nchecks** rounds of the Miller-Rabin test will be done.

If **do_trial_division** set to **0**, the trial division
will be skipped. **BN_is_prime_ex()** and **BN_is_prime()** always
skip the trial division.

**BN_is_prime_ex()**, **BN_is_prime_fasttest_ex()**,
**BN_is_prime()** and **BN_is_prime_fasttest()** are deprecated.

**BN_is_prime_fasttest()** and **BN_is_prime()** behave just
like **BN_is_prime_fasttest_ex()** and **BN_is_prime_ex()**
respectively, but with the old style call back.

**ctx** is a preallocated **BN_CTX** (to save the overhead
of allocating and freeing the structure in a loop), or **NULL**.

If the trial division is done, and no divisors are found and
**cb** is not **NULL**, **BN_GENCB_call(cb, 1, -1)** is called.

After each round of the Miller-Rabin probabilistic primality test,
if **cb** is not **NULL**, **BN_GENCB_call(cb, 1, j)** is called
with **j** the iteration (j = 0, 1, ...).

**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()**, **BN_is_prime_fasttest()** and BN_check_prime
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_is_prime_ex()** and **BN_is_prime_fasttest_ex()**
functions were deprecated in OpenSSL 3.0.

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

**BN_check_prime()** was added in OpenSSL 3.0.

# COPYRIGHT¶

Copyright 2000-2021 The OpenSSL Project Authors. All Rights Reserved.

Licensed under the Apache License 2.0 (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>.

2022-08-14 | 3.0.5 |