Provided by: libssl-doc_1.1.1c-1ubuntu3_all

**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 lengthbits. Ifretis notNULL, it will be used to store the number. Ifcbis notNULL, 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 ofBN_generate_prime_ex()may callBN_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: Ifaddis notNULL, the prime will fulfill the condition p %add==rem(p %add== 1 ifrem==NULL) in order to suit a given generator. Ifsafeis true, it will be a safe prime (i.e. a prime p so that (p-1)/2 is also prime). The PRNG must be seeded prior to callingBN_generate_prime_ex(). The prime number generation has a negligible error probability.BN_is_prime_ex()andBN_is_prime_fasttest_ex()test if the numberpis prime. The following tests are performed until one of them shows thatpis composite; ifppasses all these tests, it is considered prime.BN_is_prime_fasttest_ex(), when called withdo_trial_division==1, first attempts trial division by a number of small primes; if no divisors are found by this test andcbis notNULL,BN_GENCB_call(cb,1,-1)is called. Ifdo_trial_division==0, this test is skipped. BothBN_is_prime_ex()andBN_is_prime_fasttest_ex()perform a Miller-Rabin probabilistic primality test withnchecksiterations. Ifnchecks==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,nchecksshould be set to 64. Ifcbis notNULL,BN_GENCB_call(cb,1,j)is called after the j-th iteration (j = 0, 1, ...).ctxis a pre-allocatedBN_CTX(to save the overhead of allocating and freeing the structure in a loop), orNULL.BN_GENCB_call()calls the callback function held in theBN_GENCBstructure and passes the intsaandbas arguments. There are two types ofBN_GENCBstructure 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. ABN_GENCBstructure should be created through a call toBN_GENCB_new(), and freed through a call toBN_GENCB_free(). For "new" style callbacks a BN_GENCB structure should be initialised with a call toBN_GENCB_set(), wheregencbis aBN_GENCB*,callbackis of typeint(*callback)(int,int,BN_GENCB*)andcb_argis avoid*. "Old" style callbacks are the same except they are initialised with a call toBN_GENCB_set_old()andcallbackis of typevoid(*callback)(int,int,void*). A callback is invoked through a call toBN_GENCB_call. This will check the type of the callback and will invokecallback(a,b,gencb)for new style callbacks orcallback(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 asBN_generate_prime_ex()but expects an old-style callback function directly in thecallbackparameter, and an argument to pass to it in thecb_arg.BN_is_prime()andBN_is_prime_fasttest()can similarly be compared toBN_is_prime_ex()andBN_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()andBN_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,NULLotherwise. BN_GENCB_new returns a pointer to a BN_GENCB structure on success, orNULLotherwise. 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 byERR_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)

**HISTORY**

TheBN_GENCB_new(),BN_GENCB_free(), andBN_GENCB_get_arg()functions were added in OpenSSL 1.1.0.

**COPYRIGHT**

Copyright 2000-2018 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>.