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BN_generate_prime(3) OpenSSL BN_generate_prime(3)NAMEBN_generate_prime, BN_is_prime, BN_is_prime_fasttest - generate primes and test for primalityLIBRARYlibcrypto, -lcryptoSYNOPSIS#include <openssl/bn.h> 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);DESCRIPTIONBN_generate_prime() generates a pseudo-random prime number ofnumbits. Ifretis notNULL, it will be used to store the number. Ifcallbackis notNULL, it is called as follows: ocallback(0,i,cb_arg)is called after generating the i-th potential prime number. o While the number is being tested for primality,callback(1,j,cb_arg)is called as described below. o When a prime has been found,callback(2,i,cb_arg)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 calling BN_generate_prime(). The prime number generation has a negligible error probability. BN_is_prime() and BN_is_prime_fasttest() test if the numberais prime. The following tests are performed until one of them shows thatais composite; ifapasses all these tests, it is considered prime. BN_is_prime_fasttest(), when called withdo_trial_division==1, first attempts trial division by a number of small primes; if no divisors are found by this test andcallbackis notNULL,callback(1,-1,cb_arg)is called. Ifdo_trial_division==0, this test is skipped. Both BN_is_prime() and BN_is_prime_fasttest() perform a Miller-Rabin probabilistic primality test withchecksiterations. Ifchecks==BN_prime_checks, a number of iterations is used that yields a false positive rate of at most 2^-80 for random input. Ifcallbackis notNULL,callback(1,j,cb_arg)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.RETURNVALUESBN_generate_prime() returns the prime number on success,NULLotherwise. BN_is_prime() returns 0 if the number is composite, 1 if it is prime with an error probability of less than 0.25^checks, and -1 on error. The error codes can be obtained by ERR_get_error(3).SEEALSOopenssl_bn(3), ERR_get_error(3), openssl_rand(3)HISTORYThecb_argarguments to BN_generate_prime() and to BN_is_prime() were added in SSLeay 0.9.0. Theretargument to BN_generate_prime() was added in SSLeay 0.9.1. BN_is_prime_fasttest() was added in OpenSSL 0.9.5. 1.0.1u 2009-07-19 BN_generate_prime(3)