## table of contents

other versions

- jessie 1.0.1t-1+deb8u8
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- testing 1.1.1a-1
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BN_generate_prime(3SSL) | OpenSSL | BN_generate_prime(3SSL) |

# NAME¶

BN_generate_prime, BN_is_prime, BN_is_prime_fasttest - generate primes and test for primality# SYNOPSIS¶

#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);

# DESCRIPTION¶

*BN_generate_prime()*generates a pseudo-random prime number of

**num**bits. If

**ret**is not

**NULL**, it will be used to store the number. If

**callback**is not

**NULL**, it is called as follows:

- •
**callback(0, i, cb_arg)**is called after generating the i-th potential prime number.

- •
- While the number is being tested for primality,
**callback(1, j,****cb_arg)**is called as described below.

- •
- When a prime has been found,
**callback(2, i, cb_arg)**is called.

**add**is not

**NULL**, the prime will fulfill the condition p %

**add**==

**rem**(p %

**add**== 1 if

**rem**==

**NULL**) in order to suit a given generator. If

**safe**is 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 number

**a**is prime. The following tests are performed until one of them shows that

**a**is composite; if

**a**passes all these tests, it is considered prime.

*BN_is_prime_fasttest()*, when called with

**do_trial_division == 1**, first attempts trial division by a number of small primes; if no divisors are found by this test and

**callback**is not

**NULL**,

**callback(1, -1, cb_arg)**is called. If

**do_trial_division == 0**, this test is skipped. Both

*BN_is_prime()*and

*BN_is_prime_fasttest()*perform a Miller-Rabin probabilistic primality test with

**checks**iterations. If

**checks == BN_prime_checks**, a number of iterations is used that yields a false positive rate of at most 2^-80 for random input. If

**callback**is not

**NULL**,

**callback(1, j, cb_arg)**is called after the j-th iteration (j = 0, 1, ...).

**ctx**is a pre-allocated

**BN_CTX**(to save the overhead of allocating and freeing the structure in a loop), or

**NULL**.

# RETURN VALUES¶

*BN_generate_prime()*returns the prime number on success,

**NULL**otherwise.

*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).

# SEE ALSO¶

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

The**cb_arg**arguments to

*BN_generate_prime()*and to

*BN_is_prime()*were added in SSLeay 0.9.0. The

**ret**argument to

*BN_generate_prime()*was added in SSLeay 0.9.1.

*BN_is_prime_fasttest()*was added in OpenSSL 0.9.5.

2016-05-03 | 1.0.1t |