.\" $OpenBSD: BN_generate_prime.3,v 1.18 2019/08/25 19:24:00 schwarze Exp $ .\" full merge up to: OpenSSL f987a4dd Jun 27 10:12:08 2019 +0200 .\" .\" This file was written by Ulf Moeller .\" Bodo Moeller , and Matt Caswell . .\" Copyright (c) 2000, 2003, 2013, 2014, 2018 The OpenSSL Project. .\" All rights reserved. .\" .\" Redistribution and use in source and binary forms, with or without .\" modification, are permitted provided that the following conditions .\" are met: .\" .\" 1. Redistributions of source code must retain the above copyright .\" notice, this list of conditions and the following disclaimer. .\" .\" 2. Redistributions in binary form must reproduce the above copyright .\" notice, this list of conditions and the following disclaimer in .\" the documentation and/or other materials provided with the .\" distribution. .\" .\" 3. 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Redistributions of any form whatsoever must retain the following .\" acknowledgment: .\" "This product includes software developed by the OpenSSL Project .\" for use in the OpenSSL Toolkit (http://www.openssl.org/)" .\" .\" THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY .\" EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE .\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR .\" PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR .\" ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, .\" SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT .\" NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; .\" LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) .\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, .\" STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) .\" ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED .\" OF THE POSSIBILITY OF SUCH DAMAGE. .\" .Dd $Mdocdate: August 25 2019 $ .Dt BN_GENERATE_PRIME 3 .Os .Sh NAME .Nm BN_generate_prime_ex , .Nm BN_is_prime_ex , .Nm BN_is_prime_fasttest_ex , .Nm BN_GENCB_call , .Nm BN_GENCB_new , .Nm BN_GENCB_free , .Nm BN_GENCB_set_old , .Nm BN_GENCB_set , .Nm BN_GENCB_get_arg , .Nm BN_generate_prime , .Nm BN_is_prime , .Nm BN_is_prime_fasttest .Nd generate primes and test for primality .Sh SYNOPSIS .In openssl/bn.h .Ft int .Fo BN_generate_prime_ex .Fa "BIGNUM *ret" .Fa "int bits" .Fa "int safe" .Fa "const BIGNUM *add" .Fa "const BIGNUM *rem" .Fa "BN_GENCB *cb" .Fc .Ft int .Fo BN_is_prime_ex .Fa "const BIGNUM *p" .Fa "int nchecks" .Fa "BN_CTX *ctx" .Fa "BN_GENCB *cb" .Fc .Ft int .Fo BN_is_prime_fasttest_ex .Fa "const BIGNUM *p" .Fa "int nchecks" .Fa "BN_CTX *ctx" .Fa "int do_trial_division" .Fa "BN_GENCB *cb" .Fc .Ft int .Fo BN_GENCB_call .Fa "BN_GENCB *cb" .Fa "int a" .Fa "int b" .Fc .Ft BN_GENCB * .Fn BN_GENCB_new void .Ft void .Fo BN_GENCB_free .Fa "BN_GENCB *cb" .Fc .Ft void .Fo BN_GENCB_set_old .Fa "BN_GENCB *gencb" .Fa "void (*callback)(int, int, void *)" .Fa "void *cb_arg" .Fc .Ft void .Fo BN_GENCB_set .Fa "BN_GENCB *gencb" .Fa "int (*callback)(int, int, BN_GENCB *)" .Fa "void *cb_arg" .Fc .Ft void * .Fo BN_GENCB_get_arg .Fa "BN_GENCB *cb" .Fc .Pp Deprecated: .Pp .Ft BIGNUM * .Fo BN_generate_prime .Fa "BIGNUM *ret" .Fa "int num" .Fa "int safe" .Fa "BIGNUM *add" .Fa "BIGNUM *rem" .Fa "void (*callback)(int, int, void *)" .Fa "void *cb_arg" .Fc .Ft int .Fo BN_is_prime .Fa "const BIGNUM *a" .Fa "int checks" .Fa "void (*callback)(int, int, void *)" .Fa "BN_CTX *ctx" .Fa "void *cb_arg" .Fc .Ft int .Fo BN_is_prime_fasttest .Fa "const BIGNUM *a" .Fa "int checks" .Fa "void (*callback)(int, int, void *)" .Fa "BN_CTX *ctx" .Fa "void *cb_arg" .Fa "int do_trial_division" .Fc .Sh DESCRIPTION .Fn BN_generate_prime_ex generates a pseudo-random prime number of at least bit length .Fa bits . The returned number is probably prime, but there is a very small probability of returning a non-prime number. If .Fa ret is not .Dv NULL , it will be used to store the number. .Pp If .Fa cb is not .Dv NULL , it is used as follows: .Bl -bullet .It .Fn BN_GENCB_call cb 0 i is called after generating the i-th potential prime number. .It While the number is being tested for primality, .Fn BN_GENCB_call cb 1 j is called as described below. .It When a prime has been found, .Fn BN_GENCB_call cb 2 i is called. .It The callers of .Fn BN_generate_prime_ex may call .Fn BN_GENCB_call with other values as described in their respective manual pages; see .Sx SEE ALSO . .El .Pp The prime may have to fulfill additional requirements for use in Diffie-Hellman key exchange: .Pp If .Fa add is not .Dv NULL , the prime will fulfill the condition p % .Fa add == .Fa rem (p % .Fa add == 1 if .Fa rem == .Dv NULL ) in order to suit a given generator. .Pp If .Fa safe is true, it will be a safe prime (i.e. a prime p so that (p-1)/2 is also prime). .Pp .Fn BN_is_prime_ex and .Fn BN_is_prime_fasttest_ex test if the number .Fa p is prime. The following tests are performed until one of them shows that .Fa p is composite; if .Fa p passes all these tests, it is considered prime. .Pp .Fn BN_is_prime_fasttest_ex , when called with .Fa do_trial_division == 1, first attempts trial division by a number of small primes; if no divisors are found by this test and .Fa cb is not .Dv NULL , .Sy BN_GENCB_call(cb, 1, -1) is called. If .Fa do_trial_division == 0, this test is skipped. .Pp Both .Fn BN_is_prime_ex and .Fn BN_is_prime_fasttest_ex perform a Miller-Rabin probabilistic primality test with .Fa nchecks iterations. If .Fa nchecks == .Dv BN_prime_checks , a number of iterations is used that yields a false positive rate of at most 2\(ha-64 for random input. The error rate depends on the size of the prime and goes down for bigger primes. The rate is 2\(ha-80 starting at 308 bits, 2\(ha-112 at 852 bits, 2\(ha-128 at 1080 bits, 2\(ha-192 at 3747 bits and 2\(ha-256 at 6394 bits. .Pp 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, .Fa nchecks should be set to 64. .Pp If .Fa cb is not .Dv NULL , .Fa BN_GENCB_call cb 1 j is called after the j-th iteration (j = 0, 1, ...). .Fa ctx is a pre-allocated .Vt BN_CTX (to save the overhead of allocating and freeing the structure in a loop), or .Dv NULL . .Pp .Fn BN_GENCB_call calls the callback function held in the .Vt BN_GENCB structure and passes the ints .Fa a and .Fa b as arguments. There are two types of .Vt 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. .Pp A .Vt BN_GENCB structure should be created through a call to .Fn BN_GENCB_new and freed through a call to .Fn BN_GENCB_free . .Pp For "new" style callbacks a .Vt BN_GENCB structure should be initialised with a call to .Fn BN_GENCB_set , where .Fa gencb is a .Vt BN_GENCB * , .Fa callback is of type .Vt int (*callback)(int, int, BN_GENCB *) and .Fa cb_arg is a .Vt void * . "Old" style callbacks are the same except they are initialised with a call to .Fn BN_GENCB_set_old and .Fa callback is of type .Vt void (*callback)(int, int, void *) . .Pp A callback is invoked through a call to .Fn BN_GENCB_call . This will check the type of the callback and will invoke .Fn callback a b gencb for new style callbacks or .Fn callback a b cb_arg for old style. .Pp It is possible to obtain the argument associated with a .Vt BN_GENCB structure (set via a call to .Fn BN_GENCB_set or .Fn BN_GENCB_set_old ) using .Fn BN_GENCB_get_arg . .Pp .Fn BN_generate_prime (deprecated) works in the same way as .Fn BN_generate_prime_ex but expects an old style callback function directly in the .Fa callback parameter, and an argument to pass to it in the .Fa cb_arg . Similarly .Fn BN_is_prime and .Fn BN_is_prime_fasttest are deprecated and can be compared to .Fn BN_is_prime_ex and .Fn BN_is_prime_fasttest_ex respectively. .Sh RETURN VALUES .Fn BN_generate_prime_ex returns 1 on success or 0 on error. .Pp .Fn BN_is_prime_ex , .Fn BN_is_prime_fasttest_ex , .Fn BN_is_prime , and .Fn BN_is_prime_fasttest return 0 if the number is composite, 1 if it is prime with an error probability of less than .Pf 0.25^ Fa nchecks , and -1 on error. .Pp .Fn BN_generate_prime returns the prime number on success, .Dv NULL otherwise. .Pp .Fn BN_GENCB_new returns a pointer to a .Vt BN_GENCB structure on success, or .Dv NULL otherwise. .Pp .Fn BN_GENCB_get_arg returns the argument previously associated with a .Vt BN_GENCB structure. .Pp Callback functions should return 1 on success or 0 on error. .Pp The error codes can be obtained by .Xr ERR_get_error 3 . .Sh SEE ALSO .Xr BN_new 3 , .Xr DH_generate_parameters 3 , .Xr DSA_generate_parameters 3 , .Xr RSA_generate_key 3 .Sh HISTORY .Fn BN_generate_prime and .Fn BN_is_prime first appeared in SSLeay 0.5.1 and had their .Fa cb_arg argument added in SSLeay 0.9.0. These two functions have been available since .Ox 2.4 . .Pp The .Fa ret argument to .Fn BN_generate_prime was added in SSLeay 0.9.1 and .Ox 2.6 . .Pp .Fn BN_is_prime_fasttest first appeared in OpenSSL 0.9.5 and has been available since .Ox 2.7 . .Pp .Fn BN_generate_prime_ex , .Fn BN_is_prime_ex , .Fn BN_is_prime_fasttest_ex , .Fn BN_GENCB_call , .Fn BN_GENCB_set_old , and .Fn BN_GENCB_set first appeared in OpenSSL 0.9.8 and have been available since .Ox 4.5 . .Pp .Fn BN_GENCB_new , .Fn BN_GENCB_free , and .Fn BN_GENCB_get_arg first appeared in OpenSSL 1.1.0 and have been available since .Ox 6.3 .