|BN_GENERATE_PRIME(3)||Library Functions Manual||BN_GENERATE_PRIME(3)|
generate primes and test for primality
*ret, int bits, int safe,
const BIGNUM *add, const BIGNUM
*rem, BN_GENCB *cb);
BN_is_prime_ex(const BIGNUM *p,
int nchecks, BN_CTX *ctx,
*p, int nchecks, BN_CTX
*ctx, int do_trial_division,
int a, int b);
*gencb, void (*callback)(int, int, void *),
int (*callback)(int, int, BN_GENCB *),
int num, int safe,
BIGNUM *add, BIGNUM *rem,
void (*callback)(int, int, void *),
BN_is_prime(const BIGNUM *a,
int checks, void (*callback)(int, int,
void *), BN_CTX *ctx, void
*a, int checks, void
(*callback)(int, int, void *), BN_CTX *ctx,
void *cb_arg, int
BN_generate_prime_ex() generates a
pseudo-random prime number of at least bit length
bits. The returned number is probably prime, but there
is a very small probability of returning a non-prime number. If
ret is not
NULL, it will be
used to store the number.
If cb is not
it is used as follows:
BN_GENCB_call(cb, 0, i) is called after generating the i-th potential prime number.
BN_GENCB_call(cb, 1, j) is called as described below.
BN_GENCB_call(cb, 2, i) is called.
BN_generate_prime_ex() may call
BN_GENCB_call() with other values as described in their respective manual pages; see SEE ALSO.
The prime may have to fulfill additional requirements for use in Diffie-Hellman key exchange:
If add is not
the prime will fulfill the condition p % add ==
rem (p % add == 1 if
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).
BN_is_prime_fasttest_ex() test if the number
p is prime. The following tests are performed until
one of them shows that p is composite; if
p passes all these tests, it is considered prime.
BN_is_prime_fasttest_ex(), 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 cb is not
BN_GENCB_call(cb, 1, -1) is called. If
do_trial_division == 0, this test is skipped.
BN_is_prime_fasttest_ex() perform a Miller-Rabin
probabilistic primality test with nchecks iterations.
If nchecks ==
a number of iterations is used that yields a false positive rate of at most
2^-64 for random input. The error rate depends on the size of the prime and
goes down for bigger primes. The rate is 2^-80 starting at 308 bits, 2^-112
at 852 bits, 2^-128 at 1080 bits, 2^-192 at 3747 bits and 2^-256 at 6394
When the source of the prime is not random or not trusted, the number of checks needs to be much higher to reach the same level of assurance: It should equal half of the targeted security level in bits (rounded up to the next integer if necessary). For instance, to reach the 128 bit security level, nchecks should be set to 64.
If cb is not
BN_GENCB_call cb 1 j 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
BN_GENCB_call() calls the callback
function held in the BN_GENCB structure and passes the
ints a and b as arguments. There
are two types of BN_GENCB structures that are
supported: "new" style and "old" style. New programs
should prefer the "new" style, whilst the "old" style is
provided for backwards compatibility purposes.
A BN_GENCB structure should be created
through a call to
BN_GENCB_new() and freed through a
For "new" style callbacks a
BN_GENCB structure should be initialised with a call
BN_GENCB_set(), where gencb
is a BN_GENCB *, callback is of
type int (*callback)(int, int, BN_GENCB *) and
cb_arg is a void *.
"Old" style callbacks are the same except they are initialised
with a call to
callback is of type void
(*callback)(int, int, void *).
A callback is invoked through a call to
BN_GENCB_call(). This will check the type of the
callback and will invoke
b, gencb) for new style
b, cb_arg) for old style.
It is possible to obtain the argument associated with a
BN_GENCB structure (set via a call to
BN_generate_prime() (deprecated) works in
the same way as
BN_generate_prime_ex() but expects
an old style callback function directly in the
callback parameter, and an argument to pass to it in
the cb_arg. Similarly
BN_is_prime_fasttest() are deprecated and can be
BN_generate_prime_ex() returns 1 on
success or 0 on error.
BN_is_prime_fasttest() return 0 if the number is
composite, 1 if it is prime with an error probability of less than
0.25^nchecks, and -1 on error.
BN_generate_prime() returns the prime
number on success,
BN_GENCB_new() returns a pointer to a
BN_GENCB structure on success, or
BN_GENCB_get_arg() returns the argument
previously associated with a BN_GENCB structure.
Callback functions should return 1 on success or 0 on error.
The error codes can be obtained by ERR_get_error(3).
BN_is_prime() first appeared in SSLeay 0.5.1 and had
their cb_arg argument added in SSLeay 0.9.0. These two
functions have been available since OpenBSD 2.4.
The ret argument to
BN_generate_prime() was added in SSLeay 0.9.1 and
BN_is_prime_fasttest() first appeared in
OpenSSL 0.9.5 and has been available since OpenBSD
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.
|August 25, 2019||OpenBSD-current|