BN_GENERATE_PRIME(3ssl) OpenSSL BN_GENERATE_PRIME(3ssl) BN_generate_prime_ex2, BN_generate_prime_ex, BN_is_prime_ex, BN_check_prime, 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_fasttest - #include int BN_generate_prime_ex2(BIGNUM *ret, int bits, int safe, const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb, BN_CTX *ctx); int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb); int BN_check_prime(const BIGNUM *p, BN_CTX *ctx, BN_GENCB *cb); int BN_GENCB_call(BN_GENCB *cb, int a, int b); BN_GENCB *BN_GENCB_new(void); void BN_GENCB_free(BN_GENCB *cb); void BN_GENCB_set_old(BN_GENCB *gencb, void (*callback)(int, int, void *), void *cb_arg); void BN_GENCB_set(BN_GENCB *gencb, int (*callback)(int, int, BN_GENCB *), void *cb_arg); void *BN_GENCB_get_arg(BN_GENCB *cb); OpenSSL 0.9.8 OPENSSL_API_COMPAT openssl_user_macros(7): 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 *p, int nchecks, void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg); int BN_is_prime_fasttest(const BIGNUM *p, int nchecks, void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg, int do_trial_division); OpenSSL 3.0 OPENSSL_API_COMPAT openssl_user_macros(7): int BN_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb); int BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, int do_trial_division, BN_GENCB *cb); BN_generate_prime_ex2() bits BN_CTX ctx. ctx NULL. . 2^-128. 2^-287 512 2^-435 1024 2^-648 2048 2^-882 2048 . add NULL bits . ret NULL . cb NULL : o BN_GENCB_call(cb, 0, i) i. o BN_GENCB_call(cb, 1, j) . o BN_GENCB_call(cb, 2, i) . o BN_generate_prime_ex() BN_GENCB_call(cb, i, j) " ". Diffie-Hellman: add NULL p % add == rem (p % add == 1 rem == NULL) . safe ( p (p-1)/2 ). safe rem == NULL p % add == 3. add 4. BN_generate_prime_ex(). CSPRNG OpenSSL ( RAND(7)) . OSSL_LIB_CTX ctx. BN_generate_prime_ex() BN_generate_prime_ex2() ctx. OSSL_LIB_CTX . BN_check_prime() BN_is_prime_ex() BN_is_prime_fasttest_ex() BN_is_prime() BN_is_prime_fasttest() p . p . p . p - . 64 - 2^-128. p 2048 128 2^-256. nchecks (64 128) nchecks -. do_trial_division 0 . BN_is_prime_ex() BN_is_prime() . BN_is_prime_ex() BN_is_prime_fasttest_ex() BN_is_prime() BN_is_prime_fasttest() . BN_is_prime_fasttest() BN_is_prime() BN_is_prime_fasttest_ex() BN_is_prime_ex() . ctx BN_CTX ( ) NULL. cb NULL BN_GENCB_call(cb, 1, -1). - cb NULL BN_GENCB_call(cb, 1, j) j (j = 0, 1, ...). BN_GENCB_call() BN_GENCB a b . BN_GENCB : "" "". "" "" . BN_GENCB BN_GENCB_new() BN_GENCB_free(). NULL . "" BN_GENCB BN_GENCB_set() gencb BN_GENCB * callback int (*callback)(int, int, BN_GENCB *) cb_arg void *. "" BN_GENCB_set_old() callback void (*callback)(int, int, void *). BN_GENCB_call. callback(a, b, gencb) callback(a, b, cb_arg) . BN_GENCB ( BN_GENCB_set BN_GENCB_set_old) BN_GENCB_get_arg. BN_generate_prime() () BN_generate_prime_ex() callback cb_arg. BN_is_prime() BN_is_prime_fasttest() BN_is_prime_ex() BN_is_prime_fasttest_ex() . BN_generate_prime_ex() 1 0 . BN_is_prime_ex() BN_is_prime_fasttest_ex() BN_is_prime() BN_is_prime_fasttest() BN_check_prime 0 1 0.25^nchecks -1 . BN_generate_prime() NULL . BN_GENCB_new BN_GENCB NULL . BN_GENCB_get_arg BN_GENCB. 1 0 . ERR_get_error(3). OpenSSL 1.1.0 BN_GENCB : BN_GENCB callback; BN_GENCB BN_GENCB_new: BN_GENCB *callback; callback = BN_GENCB_new(); if (!callback) /* error */ ... BN_GENCB_free(callback); DH_generate_parameters(3), DSA_generate_parameters(3), RSA_generate_key(3), ERR_get_error(3), RAND_bytes(3), RAND(7) BN_is_prime_ex() BN_is_prime_fasttest_ex() OpenSSL 3.0. BN_GENCB_new() BN_GENCB_free() BN_GENCB_get_arg() OpenSSL 1.1.0. BN_check_prime() OpenSSL 3.0. 2000-2025 OpenSSL. . Apache 2.0 ( ""). . LICENSE . 3 . . : . 3.6.2 7 2026 BN_GENERATE_PRIME(3ssl)