BN_GENERATE_PRIME(3)

NAME
BN_is_prime_ex, BN_is_prime_fasttest_ex, BN_generate_prime_ex, BN_GENCB_call, BN_GENCB_new, BN_GENCB_free, BN_GENCB_set, BN_GENCB_get_arg, BN_GENCB_set_old - generate primes and test for primality

SYNOPSIS
#include <openssl/bn.h>
int
BN_is_prime_ex(const BIGNUM *a, int nchecks, BN_CTX *ctx, BN_GENCB *cb);
int
BN_is_prime_fasttest_ex(const BIGNUM *a, int nchecks, BN_CTX *ctx, int do_trial_division, BN_GENCB *cb);
int
BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *modulus, const BIGNUM *remainder, BN_GENCB *cb);
int
BN_GENCB_call(BN_GENCB *cb, int state_code, int serial_number);
BN_GENCB *
BN_GENCB_new(void);
void
BN_GENCB_free(BN_GENCB *cb);
void
BN_GENCB_set(BN_GENCB *cb, int (*cb_fp)(int, int, BN_GENCB *), void *cb_arg);
void *
BN_GENCB_get_arg(BN_GENCB *cb);

Deprecated:

void
BN_GENCB_set_old(BN_GENCB *cb, void (*cb_fp)(int, int, void *), void *cb_arg);

DESCRIPTION
BN_is_prime_ex() and BN_is_prime_fasttest_ex() test whether the number a is prime. In LibreSSL, both functions behave identically and use the Baillie-Pomerance-Selfridge-Wagstaff algorithm combined with checks Miller-Rabin rounds. The do_trial_division argument is ignored.

It is unknown whether any composite number exists that the Baillie-PSW algorithm misclassifies as a prime. Some suspect that there may be infinitely many such numbers, but not a single one is currently known. It is known that no such number exists below 2^64.

In order to reduce the likelihood of a composite number passing the primality tests BN_is_prime_fasttest_ex() and BN_is_prime_ex(), a number of rounds of the probabilistic Miller-Rabin test is performed. If checks is positive, it is used as the number of rounds; if it is zero or the special value BN_prime_checks, a suitable number of rounds is calculated from the bit length of a.

If NULL is passed for the ctx argument, these function allocate a BN_CTX object internally when they need one and free it before returning. Alternatively, to save the overhead of allocating and freeing that object for each call, the caller can pre-allocate a BN_CTX object and pass it in the ctx argument.

BN_generate_prime_ex() generates a pseudo-random prime number of at least bit length bits and places it in ret. Primality of ret is tested internally using BN_is_prime_ex(). Consequently, for bits larger than 64, it is theoretically possible that this function might place a composite number into ret; the probability of such an event is unknown but very small.

The prime may have to fulfill additional requirements for use in Diffie-Hellman key exchange:

•   If modulus is not NULL, a prime is generated that fulfills the condition ret % modulus = remainder. If the remainder argument is NULL, 1 is used as the desired remainder.

•   If the safe argument is non-zero, a safe prime is generated, that is, (ret - 1)/2 is also prime.

If cb is not NULL, it is used as follows:

•   BN_GENCB_call(cb, 0, serial_number) is called after generating a potential prime number.

•   The state_code of 1 is reserved for callbacks during primality testing, but LibreSSL performs no such callbacks.

•   When safe is non-zero and a safe prime has been found, BN_GENCB_call(cb, 2, serial_number) is called.

•   The callers of BN_generate_prime_ex() may call BN_GENCB_call() with other values as described in their respective manual pages; see SEE ALSO.

In all cases, the serial_number is the number of candidates that have already been discarded for not being prime; that is, serial_number is 0 for the first candidate and then incremented whenever a new candidate is generated.

BN_GENCB_call() calls the callback function held in cb and passes the state_code and the serial_number as arguments. If cb is NULL or does not contain a callback function, no action occurs.

BN_GENCB_new() allocates a new BN_GENCB object.

BN_GENCB_free() frees cb. If cb is NULL, no action occurs.

BN_GENCB_set() initialises cb to use the callback function pointer cb_fp and the additional callback argument cb_arg.

The deprecated function BN_GENCB_set_old() initialises cb to use the old-style callback function pointer cb_fp and the additional callback argument cb_arg.

RETURN VALUES
BN_is_prime_ex() and BN_is_prime_fasttest_ex() return 0 if the number is composite, 1 if it is prime with a very small error probability, or -1 on error.

BN_generate_prime_ex() returns 1 on success or 0 on error.

BN_GENCB_call() returns 1 on success, including when cb is NULL or does not contain a callback function, or 0 on error.

BN_GENCB_new() returns a pointer to the newly allocated BN_GENCB object or NULL if memory allocation fails.

The callback functions pointed to by the cb_fp arguments are supposed to return 1 on success or 0 on error.

BN_GENCB_get_arg() returns the cb_arg pointer that was previously stored in cb using BN_GENCB_set() or BN_GENCB_set_old().

In some cases, error codes can be obtained by ERR_get_error(3).

SEE ALSO
BN_new(3), DH_generate_parameters(3), DSA_generate_parameters(3), RSA_generate_key(3)

HISTORY
BN_generate_prime_ex(), BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_GENCB_call(), BN_GENCB_set_old(), and BN_GENCB_set() first appeared in OpenSSL 0.9.8 and have been available since OpenBSD 4.5.

BN_GENCB_new(), BN_GENCB_free(), and BN_GENCB_get_arg() first appeared in OpenSSL 1.1.0 and have been available since OpenBSD 6.3.