.ds Aq ’

*Manual Reference Pages - *BN_generate_prime (3SSL)

### NAME

### CONTENTS

### SYNOPSIS

### DESCRIPTION

### RETURN VALUES

### SEE ALSO

### HISTORY

blog comments powered by Disqus

BN_generate_prime, BN_is_prime, BN_is_prime_fasttest - generate primes and test for primality

#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);

BN_generate_prime()generates a pseudo-random prime number ofnumbits. Ifretis notNULL, it will be used to store the number.If

callbackis notNULL, it is called as follows:The prime may have to fulfill additional requirements for use in Diffie-Hellman key exchange:

o callback(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.If

addis notNULL, the prime will fulfill the condition p %add==rem(p %add== 1 ifrem==NULL) in order to suit a given generator.If

safeis 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()andBN_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()andBN_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.If

callbackis 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.

BN_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).

bn(3),ERR_get_error(3),rand(3)

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.

1.0.1e |
BN_generate_prime (3SSL) | 2013-02-11 |