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BN_GENERATE_PRIME(3) Library Functions Manual BN_GENERATE_PRIME(3)

BN_generate_prime_ex, BN_is_prime_ex, BN_is_prime_fasttest_ex, BN_GENCB_call, BN_GENCB_new, BN_GENCB_free, BN_GENCB_set_old, BN_GENCB_set, BN_GENCB_get_arg, BN_generate_prime, BN_is_prime, BN_is_prime_fasttestgenerate primes and test for primality

#include <openssl/bn.h>

BN_generate_prime_ex(BIGNUM *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, BN_GENCB *cb);

BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, int do_trial_division, BN_GENCB *cb);

BN_GENCB_call(BN_GENCB *cb, int a, int b);


BN_GENCB_free(BN_GENCB *cb);

BN_GENCB_set_old(BN_GENCB *gencb, void (*callback)(int, int, void *), void *cb_arg);

BN_GENCB_set(BN_GENCB *gencb, int (*callback)(int, int, BN_GENCB *), void *cb_arg);

void *
BN_GENCB_get_arg(BN_GENCB *cb);


BN_generate_prime(BIGNUM *ret, int num, int safe, BIGNUM *add, BIGNUM *rem, void (*callback)(int, int, void *), void *cb_arg);

BN_is_prime(const BIGNUM *a, int checks, void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg);

BN_is_prime_fasttest(const BIGNUM *a, int checks, void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg, int do_trial_division);

() 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 NULL, it is used as follows:

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

If 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).

() and 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.

(), 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 NULL, is called. If do_trial_division == 0, this test is skipped.

Both () and BN_is_prime_fasttest_ex() perform a Miller-Rabin probabilistic primality test with nchecks iterations. If nchecks == BN_prime_checks, 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 bits.

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 NULL, 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 NULL.

() 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 () and freed through a call to ().

For "new" style callbacks a BN_GENCB structure should be initialised with a call to (), 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 () and callback is of type void (*callback)(int, int, void *).

A callback is invoked through a call to (). This will check the type of the callback and will invoke (a, b, gencb) for new style callbacks or callback(a, b, cb_arg) for old style.

It is possible to obtain the argument associated with a BN_GENCB structure (set via a call to () or ()) using ().

() (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 () and () are deprecated and can be compared to BN_is_prime_ex() and BN_is_prime_fasttest_ex() respectively.

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

BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime(), and 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, NULL otherwise.

BN_GENCB_new() returns a pointer to a BN_GENCB structure on success, or NULL otherwise.

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_new(3), DH_generate_parameters(3), DSA_generate_parameters(3), RSA_generate_key(3)

BN_generate_prime() and 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 OpenBSD 2.6.

BN_is_prime_fasttest() first appeared in OpenSSL 0.9.5 and has been available since OpenBSD 2.7.

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.

June 24, 2020 OpenBSD-7.1