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 37Deprecated since OpenSSL 0.9.8, can be hidden entirely by defining 38B<OPENSSL_API_COMPAT> with a suitable version value, see 39L<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 52Deprecated since OpenSSL 3.0: 53 54 int BN_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb); 55 56 int BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, 57 int do_trial_division, BN_GENCB *cb); 58 59=head1 DESCRIPTION 60 61BN_generate_prime_ex2() generates a pseudo-random prime number of 62at least bit length B<bits> using the BN_CTX provided in B<ctx>. The value of 63B<ctx> must not be NULL. 64 65The returned number is probably prime with a negligible error. 66The maximum error rate is 2^-128. 67It's 2^-287 for a 512 bit prime, 2^-435 for a 1024 bit prime, 682^-648 for a 2048 bit prime, and lower than 2^-882 for primes larger 69than 2048 bit. 70 71If B<add> is B<NULL> the returned prime number will have exact bit 72length B<bits> with the top most two bits set. 73 74If B<ret> is not B<NULL>, it will be used to store the number. 75 76If B<cb> is not B<NULL>, it is used as follows: 77 78=over 2 79 80=item * 81 82B<BN_GENCB_call(cb, 0, i)> is called after generating the i-th 83potential prime number. 84 85=item * 86 87While the number is being tested for primality, 88B<BN_GENCB_call(cb, 1, j)> is called as described below. 89 90=item * 91 92When a prime has been found, B<BN_GENCB_call(cb, 2, i)> is called. 93 94=item * 95 96The callers of BN_generate_prime_ex() may call B<BN_GENCB_call(cb, i, j)> with 97other values as described in their respective man pages; see L</SEE ALSO>. 98 99=back 100 101The prime may have to fulfill additional requirements for use in 102Diffie-Hellman key exchange: 103 104If B<add> is not B<NULL>, the prime will fulfill the condition p % B<add> 105== B<rem> (p % B<add> == 1 if B<rem> == B<NULL>) in order to suit a given 106generator. 107 108If B<safe> is true, it will be a safe prime (i.e. a prime p so 109that (p-1)/2 is also prime). If B<safe> is true, and B<rem> == B<NULL> 110the condition will be p % B<add> == 3. 111It is recommended that B<add> is a multiple of 4. 112 113The random generator must be seeded prior to calling BN_generate_prime_ex(). 114If the automatic seeding or reseeding of the OpenSSL CSPRNG fails due to 115external circumstances (see L<RAND(7)>), the operation will fail. 116The random number generator configured for the OSSL_LIB_CTX associated with 117B<ctx> will be used. 118 119BN_generate_prime_ex() is the same as BN_generate_prime_ex2() except that no 120B<ctx> parameter is passed. 121In this case the random number generator associated with the default OSSL_LIB_CTX 122will be used. 123 124BN_check_prime(), BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime() 125and BN_is_prime_fasttest() test if the number B<p> is prime. 126The functions tests until one of the tests shows that B<p> is composite, 127or all the tests passed. 128If B<p> passes all these tests, it is considered a probable prime. 129 130The test performed on B<p> are trial division by a number of small primes 131and rounds of the of the Miller-Rabin probabilistic primality test. 132 133The functions do at least 64 rounds of the Miller-Rabin test giving a maximum 134false positive rate of 2^-128. 135If the size of B<p> is more than 2048 bits, they do at least 128 rounds 136giving a maximum false positive rate of 2^-256. 137 138If B<nchecks> is larger than the minimum above (64 or 128), B<nchecks> 139rounds of the Miller-Rabin test will be done. 140 141If B<do_trial_division> set to B<0>, the trial division will be skipped. 142BN_is_prime_ex() and BN_is_prime() always skip the trial division. 143 144BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime() 145and BN_is_prime_fasttest() are deprecated. 146 147BN_is_prime_fasttest() and BN_is_prime() behave just like 148BN_is_prime_fasttest_ex() and BN_is_prime_ex() respectively, but with the old 149style call back. 150 151B<ctx> is a preallocated B<BN_CTX> (to save the overhead of allocating and 152freeing the structure in a loop), or B<NULL>. 153 154If the trial division is done, and no divisors are found and B<cb> 155is not B<NULL>, B<BN_GENCB_call(cb, 1, -1)> is called. 156 157After each round of the Miller-Rabin probabilistic primality test, 158if B<cb> is not B<NULL>, B<BN_GENCB_call(cb, 1, j)> is called 159with B<j> the iteration (j = 0, 1, ...). 160 161BN_GENCB_call() calls the callback function held in the B<BN_GENCB> structure 162and passes the ints B<a> and B<b> as arguments. There are two types of 163B<BN_GENCB> structure that are supported: "new" style and "old" style. New 164programs should prefer the "new" style, whilst the "old" style is provided 165for backwards compatibility purposes. 166 167A B<BN_GENCB> structure should be created through a call to BN_GENCB_new(), 168and freed through a call to BN_GENCB_free(). 169 170For "new" style callbacks a BN_GENCB structure should be initialised with a 171call to BN_GENCB_set(), where B<gencb> is a B<BN_GENCB *>, B<callback> is of 172type B<int (*callback)(int, int, BN_GENCB *)> and B<cb_arg> is a B<void *>. 173"Old" style callbacks are the same except they are initialised with a call 174to BN_GENCB_set_old() and B<callback> is of type 175B<void (*callback)(int, int, void *)>. 176 177A callback is invoked through a call to B<BN_GENCB_call>. This will check 178the type of the callback and will invoke B<callback(a, b, gencb)> for new 179style callbacks or B<callback(a, b, cb_arg)> for old style. 180 181It is possible to obtain the argument associated with a BN_GENCB structure 182(set via a call to BN_GENCB_set or BN_GENCB_set_old) using BN_GENCB_get_arg. 183 184BN_generate_prime() (deprecated) works in the same way as 185BN_generate_prime_ex() but expects an old-style callback function 186directly in the B<callback> parameter, and an argument to pass to it in 187the B<cb_arg>. BN_is_prime() and BN_is_prime_fasttest() 188can similarly be compared to BN_is_prime_ex() and 189BN_is_prime_fasttest_ex(), respectively. 190 191=head1 RETURN VALUES 192 193BN_generate_prime_ex() return 1 on success or 0 on error. 194 195BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime(), 196BN_is_prime_fasttest() and BN_check_prime return 0 if the number is composite, 1971 if it is prime with an error probability of less than 0.25^B<nchecks>, and 198-1 on error. 199 200BN_generate_prime() returns the prime number on success, B<NULL> otherwise. 201 202BN_GENCB_new returns a pointer to a BN_GENCB structure on success, or B<NULL> 203otherwise. 204 205BN_GENCB_get_arg returns the argument previously associated with a BN_GENCB 206structure. 207 208Callback functions should return 1 on success or 0 on error. 209 210The error codes can be obtained by L<ERR_get_error(3)>. 211 212=head1 REMOVED FUNCTIONALITY 213 214As of OpenSSL 1.1.0 it is no longer possible to create a BN_GENCB structure 215directly, as in: 216 217 BN_GENCB callback; 218 219Instead applications should create a BN_GENCB structure using BN_GENCB_new: 220 221 BN_GENCB *callback; 222 callback = BN_GENCB_new(); 223 if (!callback) 224 /* error */ 225 ... 226 BN_GENCB_free(callback); 227 228=head1 SEE ALSO 229 230L<DH_generate_parameters(3)>, L<DSA_generate_parameters(3)>, 231L<RSA_generate_key(3)>, L<ERR_get_error(3)>, L<RAND_bytes(3)>, 232L<RAND(7)> 233 234=head1 HISTORY 235 236The BN_is_prime_ex() and BN_is_prime_fasttest_ex() functions were 237deprecated in OpenSSL 3.0. 238 239The BN_GENCB_new(), BN_GENCB_free(), 240and BN_GENCB_get_arg() functions were added in OpenSSL 1.1.0. 241 242BN_check_prime() was added in OpenSSL 3.0. 243 244=head1 COPYRIGHT 245 246Copyright 2000-2021 The OpenSSL Project Authors. All Rights Reserved. 247 248Licensed under the Apache License 2.0 (the "License"). You may not use 249this file except in compliance with the License. You can obtain a copy 250in the file LICENSE in the source distribution or at 251L<https://www.openssl.org/source/license.html>. 252 253=cut 254