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BN_generate_prime(3) OpenSSL BN_generate_prime(3)## NAME

BN_generate_prime_ex, BN_is_prime_ex, BN_is_prime_fasttest_ex, BN_GENCB_call, BN_GENCB_set_old, BN_GENCB_set, 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); #define BN_GENCB_set_old(gencb, callback, cb_arg) ... #define BN_GENCB_set(gencb, callback, cb_arg) ... Deprecated: 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);## DESCRIPTION

BN_generate_prime_ex()generates a pseudo-random prime number of bit lengthbits. Ifretis notNULL, it will be used to store the number. Ifcbis notNULL, it is used as follows: oBN_GENCB_call(cb,0,i)is called after generating the i-th potential prime number. o While the number is being tested for primality,BN_GENCB_call(cb,1,j)is called as described below. o When a prime has been found,BN_GENCB_call(cb,2,i)is called. 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^-80 for random input. 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. For "new" style callbacks a BN_GENCB structure should be initialised with a call to BN_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 to BN_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. BN_generate_prime (deprecated) works in the same way as BN_generate_prime_ex but expects an old style callback function directly in thecallbackparameter, and an argument to pass to it in thecb_arg. Similarly BN_is_prime and BN_is_prime_fasttest are deprecated and can 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()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. Callback functions should return 1 on success or 0 on error. The error codes can be obtained byERR_get_error(3).## SEE ALSO

bn(3),ERR_get_error(3),rand(3)## HISTORY

Thecb_argarguments toBN_generate_prime()and toBN_is_prime()were added in SSLeay 0.9.0. Theretargument toBN_generate_prime()was added in SSLeay 0.9.1.BN_is_prime_fasttest()was added in OpenSSL 0.9.5. 1.0.2h 2016-05-03 BN_generate_prime(3)

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