1=pod 2 3=head1 NAME 4 5BN_generate_prime_ex2, BN_generate_prime_ex, BN_is_prime_ex, BN_check_prime, 6BN_is_prime_fasttest_ex, BN_GENCB_call, BN_GENCB_new, BN_GENCB_free, 7BN_GENCB_set_old, BN_GENCB_set, BN_GENCB_get_arg, BN_generate_prime, 8BN_is_prime, BN_is_prime_fasttest - generate primes and test for primality 9 10=head1 SYNOPSIS 11 12 #include <openssl/bn.h> 13 14 int BN_generate_prime_ex2(BIGNUM *ret, int bits, int safe, 15 const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb, 16 BN_CTX *ctx); 17 18 int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add, 19 const BIGNUM *rem, BN_GENCB *cb); 20 21 int BN_check_prime(const BIGNUM *p, BN_CTX *ctx, BN_GENCB *cb); 22 23 int BN_GENCB_call(BN_GENCB *cb, int a, int b); 24 25 BN_GENCB *BN_GENCB_new(void); 26 27 void BN_GENCB_free(BN_GENCB *cb); 28 29 void BN_GENCB_set_old(BN_GENCB *gencb, 30 void (*callback)(int, int, void *), void *cb_arg); 31 32 void BN_GENCB_set(BN_GENCB *gencb, 33 int (*callback)(int, int, BN_GENCB *), void *cb_arg); 34 35 void *BN_GENCB_get_arg(BN_GENCB *cb); 36 37The following functions have been deprecated since OpenSSL 0.9.8, and can be 38hidden entirely by defining B<OPENSSL_API_COMPAT> with a suitable version value, 39see L<openssl_user_macros(7)>: 40 41 BIGNUM *BN_generate_prime(BIGNUM *ret, int num, int safe, BIGNUM *add, 42 BIGNUM *rem, void (*callback)(int, int, void *), 43 void *cb_arg); 44 45 int BN_is_prime(const BIGNUM *p, int nchecks, 46 void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg); 47 48 int BN_is_prime_fasttest(const BIGNUM *p, int nchecks, 49 void (*callback)(int, int, void *), BN_CTX *ctx, 50 void *cb_arg, int do_trial_division); 51 52The following functions have been deprecated since OpenSSL 3.0, and can be 53hidden entirely by defining B<OPENSSL_API_COMPAT> with a suitable version value, 54see L<openssl_user_macros(7)>: 55 56 int BN_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb); 57 58 int BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, 59 int do_trial_division, BN_GENCB *cb); 60 61=head1 DESCRIPTION 62 63BN_generate_prime_ex2() generates a pseudo-random prime number of 64at least bit length B<bits> using the BN_CTX provided in B<ctx>. The value of 65B<ctx> must not be NULL. 66 67The returned number is probably prime with a negligible error. 68The maximum error rate is 2^-128. 69It's 2^-287 for a 512 bit prime, 2^-435 for a 1024 bit prime, 702^-648 for a 2048 bit prime, and lower than 2^-882 for primes larger 71than 2048 bit. 72 73If B<add> is B<NULL> the returned prime number will have exact bit 74length B<bits> with the top most two bits set. 75 76If B<ret> is not B<NULL>, it will be used to store the number. 77 78If B<cb> is not B<NULL>, it is used as follows: 79 80=over 2 81 82=item * 83 84B<BN_GENCB_call(cb, 0, i)> is called after generating the i-th 85potential prime number. 86 87=item * 88 89While the number is being tested for primality, 90B<BN_GENCB_call(cb, 1, j)> is called as described below. 91 92=item * 93 94When a prime has been found, B<BN_GENCB_call(cb, 2, i)> is called. 95 96=item * 97 98The callers of BN_generate_prime_ex() may call B<BN_GENCB_call(cb, i, j)> with 99other values as described in their respective man pages; see L</SEE ALSO>. 100 101=back 102 103The prime may have to fulfill additional requirements for use in 104Diffie-Hellman key exchange: 105 106If B<add> is not B<NULL>, the prime will fulfill the condition p % B<add> 107== B<rem> (p % B<add> == 1 if B<rem> == B<NULL>) in order to suit a given 108generator. 109 110If B<safe> is true, it will be a safe prime (i.e. a prime p so 111that (p-1)/2 is also prime). If B<safe> is true, and B<rem> == B<NULL> 112the condition will be p % B<add> == 3. 113It is recommended that B<add> is a multiple of 4. 114 115The random generator must be seeded prior to calling BN_generate_prime_ex(). 116If the automatic seeding or reseeding of the OpenSSL CSPRNG fails due to 117external circumstances (see L<RAND(7)>), the operation will fail. 118The random number generator configured for the OSSL_LIB_CTX associated with 119B<ctx> will be used. 120 121BN_generate_prime_ex() is the same as BN_generate_prime_ex2() except that no 122B<ctx> parameter is passed. 123In this case the random number generator associated with the default OSSL_LIB_CTX 124will be used. 125 126BN_check_prime(), BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime() 127and BN_is_prime_fasttest() test if the number B<p> is prime. 128The functions tests until one of the tests shows that B<p> is composite, 129or all the tests passed. 130If B<p> passes all these tests, it is considered a probable prime. 131 132The test performed on B<p> are trial division by a number of small primes 133and rounds of the of the Miller-Rabin probabilistic primality test. 134 135The functions do at least 64 rounds of the Miller-Rabin test giving a maximum 136false positive rate of 2^-128. 137If the size of B<p> is more than 2048 bits, they do at least 128 rounds 138giving a maximum false positive rate of 2^-256. 139 140If B<nchecks> is larger than the minimum above (64 or 128), B<nchecks> 141rounds of the Miller-Rabin test will be done. 142 143If B<do_trial_division> set to B<0>, the trial division will be skipped. 144BN_is_prime_ex() and BN_is_prime() always skip the trial division. 145 146BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime() 147and BN_is_prime_fasttest() are deprecated. 148 149BN_is_prime_fasttest() and BN_is_prime() behave just like 150BN_is_prime_fasttest_ex() and BN_is_prime_ex() respectively, but with the old 151style call back. 152 153B<ctx> is a preallocated B<BN_CTX> (to save the overhead of allocating and 154freeing the structure in a loop), or B<NULL>. 155 156If the trial division is done, and no divisors are found and B<cb> 157is not B<NULL>, B<BN_GENCB_call(cb, 1, -1)> is called. 158 159After each round of the Miller-Rabin probabilistic primality test, 160if B<cb> is not B<NULL>, B<BN_GENCB_call(cb, 1, j)> is called 161with B<j> the iteration (j = 0, 1, ...). 162 163BN_GENCB_call() calls the callback function held in the B<BN_GENCB> structure 164and passes the ints B<a> and B<b> as arguments. There are two types of 165B<BN_GENCB> structure that are supported: "new" style and "old" style. New 166programs should prefer the "new" style, whilst the "old" style is provided 167for backwards compatibility purposes. 168 169A B<BN_GENCB> structure should be created through a call to BN_GENCB_new(), 170and freed through a call to BN_GENCB_free(). If the argument is NULL, 171nothing is done. 172 173For "new" style callbacks a BN_GENCB structure should be initialised with a 174call to BN_GENCB_set(), where B<gencb> is a B<BN_GENCB *>, B<callback> is of 175type B<int (*callback)(int, int, BN_GENCB *)> and B<cb_arg> is a B<void *>. 176"Old" style callbacks are the same except they are initialised with a call 177to BN_GENCB_set_old() and B<callback> is of type 178B<void (*callback)(int, int, void *)>. 179 180A callback is invoked through a call to B<BN_GENCB_call>. This will check 181the type of the callback and will invoke B<callback(a, b, gencb)> for new 182style callbacks or B<callback(a, b, cb_arg)> for old style. 183 184It is possible to obtain the argument associated with a BN_GENCB structure 185(set via a call to BN_GENCB_set or BN_GENCB_set_old) using BN_GENCB_get_arg. 186 187BN_generate_prime() (deprecated) works in the same way as 188BN_generate_prime_ex() but expects an old-style callback function 189directly in the B<callback> parameter, and an argument to pass to it in 190the B<cb_arg>. BN_is_prime() and BN_is_prime_fasttest() 191can similarly be compared to BN_is_prime_ex() and 192BN_is_prime_fasttest_ex(), respectively. 193 194=head1 RETURN VALUES 195 196BN_generate_prime_ex() return 1 on success or 0 on error. 197 198BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime(), 199BN_is_prime_fasttest() and BN_check_prime return 0 if the number is composite, 2001 if it is prime with an error probability of less than 0.25^B<nchecks>, and 201-1 on error. 202 203BN_generate_prime() returns the prime number on success, B<NULL> otherwise. 204 205BN_GENCB_new returns a pointer to a BN_GENCB structure on success, or B<NULL> 206otherwise. 207 208BN_GENCB_get_arg returns the argument previously associated with a BN_GENCB 209structure. 210 211Callback functions should return 1 on success or 0 on error. 212 213The error codes can be obtained by L<ERR_get_error(3)>. 214 215=head1 REMOVED FUNCTIONALITY 216 217As of OpenSSL 1.1.0 it is no longer possible to create a BN_GENCB structure 218directly, as in: 219 220 BN_GENCB callback; 221 222Instead applications should create a BN_GENCB structure using BN_GENCB_new: 223 224 BN_GENCB *callback; 225 callback = BN_GENCB_new(); 226 if (!callback) 227 /* error */ 228 ... 229 BN_GENCB_free(callback); 230 231=head1 SEE ALSO 232 233L<DH_generate_parameters(3)>, L<DSA_generate_parameters(3)>, 234L<RSA_generate_key(3)>, L<ERR_get_error(3)>, L<RAND_bytes(3)>, 235L<RAND(7)> 236 237=head1 HISTORY 238 239The BN_is_prime_ex() and BN_is_prime_fasttest_ex() functions were 240deprecated in OpenSSL 3.0. 241 242The BN_GENCB_new(), BN_GENCB_free(), 243and BN_GENCB_get_arg() functions were added in OpenSSL 1.1.0. 244 245BN_check_prime() was added in OpenSSL 3.0. 246 247=head1 COPYRIGHT 248 249Copyright 2000-2024 The OpenSSL Project Authors. All Rights Reserved. 250 251Licensed under the Apache License 2.0 (the "License"). You may not use 252this file except in compliance with the License. You can obtain a copy 253in the file LICENSE in the source distribution or at 254L<https://www.openssl.org/source/license.html>. 255 256=cut 257