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(). 171 172For "new" style callbacks a BN_GENCB structure should be initialised with a 173call to BN_GENCB_set(), where B<gencb> is a B<BN_GENCB *>, B<callback> is of 174type B<int (*callback)(int, int, BN_GENCB *)> and B<cb_arg> is a B<void *>. 175"Old" style callbacks are the same except they are initialised with a call 176to BN_GENCB_set_old() and B<callback> is of type 177B<void (*callback)(int, int, void *)>. 178 179A callback is invoked through a call to B<BN_GENCB_call>. This will check 180the type of the callback and will invoke B<callback(a, b, gencb)> for new 181style callbacks or B<callback(a, b, cb_arg)> for old style. 182 183It is possible to obtain the argument associated with a BN_GENCB structure 184(set via a call to BN_GENCB_set or BN_GENCB_set_old) using BN_GENCB_get_arg. 185 186BN_generate_prime() (deprecated) works in the same way as 187BN_generate_prime_ex() but expects an old-style callback function 188directly in the B<callback> parameter, and an argument to pass to it in 189the B<cb_arg>. BN_is_prime() and BN_is_prime_fasttest() 190can similarly be compared to BN_is_prime_ex() and 191BN_is_prime_fasttest_ex(), respectively. 192 193=head1 RETURN VALUES 194 195BN_generate_prime_ex() return 1 on success or 0 on error. 196 197BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime(), 198BN_is_prime_fasttest() and BN_check_prime return 0 if the number is composite, 1991 if it is prime with an error probability of less than 0.25^B<nchecks>, and 200-1 on error. 201 202BN_generate_prime() returns the prime number on success, B<NULL> otherwise. 203 204BN_GENCB_new returns a pointer to a BN_GENCB structure on success, or B<NULL> 205otherwise. 206 207BN_GENCB_get_arg returns the argument previously associated with a BN_GENCB 208structure. 209 210Callback functions should return 1 on success or 0 on error. 211 212The error codes can be obtained by L<ERR_get_error(3)>. 213 214=head1 REMOVED FUNCTIONALITY 215 216As of OpenSSL 1.1.0 it is no longer possible to create a BN_GENCB structure 217directly, as in: 218 219 BN_GENCB callback; 220 221Instead applications should create a BN_GENCB structure using BN_GENCB_new: 222 223 BN_GENCB *callback; 224 callback = BN_GENCB_new(); 225 if (!callback) 226 /* error */ 227 ... 228 BN_GENCB_free(callback); 229 230=head1 SEE ALSO 231 232L<DH_generate_parameters(3)>, L<DSA_generate_parameters(3)>, 233L<RSA_generate_key(3)>, L<ERR_get_error(3)>, L<RAND_bytes(3)>, 234L<RAND(7)> 235 236=head1 HISTORY 237 238The BN_is_prime_ex() and BN_is_prime_fasttest_ex() functions were 239deprecated in OpenSSL 3.0. 240 241The BN_GENCB_new(), BN_GENCB_free(), 242and BN_GENCB_get_arg() functions were added in OpenSSL 1.1.0. 243 244BN_check_prime() was added in OpenSSL 3.0. 245 246=head1 COPYRIGHT 247 248Copyright 2000-2021 The OpenSSL Project Authors. All Rights Reserved. 249 250Licensed under the Apache License 2.0 (the "License"). You may not use 251this file except in compliance with the License. You can obtain a copy 252in the file LICENSE in the source distribution or at 253L<https://www.openssl.org/source/license.html>. 254 255=cut 256