generate primes and test for
BN_is_prime_ex(const BIGNUM *a,
int nchecks, BN_CTX *ctx,
*a, int nchecks, BN_CTX
*ctx, int do_trial_division,
*ret, int bits, int safe,
const BIGNUM *modulus, const BIGNUM
*remainder, BN_GENCB *cb);
int state_code, int
int (*cb_fp)(int, int, BN_GENCB *),
void (*cb_fp)(int, int, void *), void
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_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.
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
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
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
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.
calls the callback function held in cb and passes the
state_code and the serial_number
as arguments. If cb is
does not contain a callback function, no action occurs.
allocates a new BN_GENCB object.
frees cb. If cb is
NULL, no action occurs.
initialises cb to use the callback function pointer
cb_fp and the additional callback argument
The deprecated function
initialises cb to use the old-style callback function
pointer cb_fp and the additional callback argument
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
BN_generate_prime_ex() returns 1 on
success or 0 on error.
BN_GENCB_call() returns 1 on success,
including when cb is
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
In some cases, error codes can be obtained by ERR_get_error(3).
BN_new(3), DH_generate_parameters(3), DSA_generate_parameters(3), RSA_generate_key(3)
BN_GENCB_set() first appeared in OpenSSL 0.9.8 and
have been available since OpenBSD 4.5.
BN_GENCB_get_arg() first appeared in OpenSSL 1.1.0
and have been available since OpenBSD 6.3.