1=pod 2 3=head1 NAME 4 5BN_generate_prime_ex, BN_is_prime_ex, BN_is_prime_fasttest_ex, BN_GENCB_call, 6BN_GENCB_new, BN_GENCB_free, BN_GENCB_set_old, BN_GENCB_set, BN_GENCB_get_arg, 7BN_generate_prime, BN_is_prime, BN_is_prime_fasttest - generate primes and test 8for primality 9 10=head1 SYNOPSIS 11 12 #include <openssl/bn.h> 13 14 int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add, 15 const BIGNUM *rem, BN_GENCB *cb); 16 17 int BN_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb); 18 19 int BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, 20 int do_trial_division, BN_GENCB *cb); 21 22 int BN_GENCB_call(BN_GENCB *cb, int a, int b); 23 24 BN_GENCB *BN_GENCB_new(void); 25 26 void BN_GENCB_free(BN_GENCB *cb); 27 28 void BN_GENCB_set_old(BN_GENCB *gencb, 29 void (*callback)(int, int, void *), void *cb_arg); 30 31 void BN_GENCB_set(BN_GENCB *gencb, 32 int (*callback)(int, int, BN_GENCB *), void *cb_arg); 33 34 void *BN_GENCB_get_arg(BN_GENCB *cb); 35 36Deprecated: 37 38 #if OPENSSL_API_COMPAT < 0x00908000L 39 BIGNUM *BN_generate_prime(BIGNUM *ret, int num, int safe, BIGNUM *add, 40 BIGNUM *rem, void (*callback)(int, int, void *), 41 void *cb_arg); 42 43 int BN_is_prime(const BIGNUM *a, int checks, 44 void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg); 45 46 int BN_is_prime_fasttest(const BIGNUM *a, int checks, 47 void (*callback)(int, int, void *), BN_CTX *ctx, 48 void *cb_arg, int do_trial_division); 49 #endif 50 51=head1 DESCRIPTION 52 53BN_generate_prime_ex() generates a pseudo-random prime number of 54at least bit length B<bits>. The returned number is probably prime 55with a negligible error. If B<add> is B<NULL> the returned prime 56number will have exact bit length B<bits> with the top most two 57bits set. 58 59If B<ret> is not B<NULL>, it will be used to store the number. 60 61If B<cb> is not B<NULL>, it is used as follows: 62 63=over 2 64 65=item * 66 67B<BN_GENCB_call(cb, 0, i)> is called after generating the i-th 68potential prime number. 69 70=item * 71 72While the number is being tested for primality, 73B<BN_GENCB_call(cb, 1, j)> is called as described below. 74 75=item * 76 77When a prime has been found, B<BN_GENCB_call(cb, 2, i)> is called. 78 79=item * 80 81The callers of BN_generate_prime_ex() may call B<BN_GENCB_call(cb, i, j)> with 82other values as described in their respective man pages; see L</SEE ALSO>. 83 84=back 85 86The prime may have to fulfill additional requirements for use in 87Diffie-Hellman key exchange: 88 89If B<add> is not B<NULL>, the prime will fulfill the condition p % B<add> 90== B<rem> (p % B<add> == 1 if B<rem> == B<NULL>) in order to suit a given 91generator. 92 93If B<safe> is true, it will be a safe prime (i.e. a prime p so 94that (p-1)/2 is also prime). If B<safe> is true, and B<rem> == B<NULL> 95the condition will be p % B<add> == 3. 96It is recommended that B<add> is a multiple of 4. 97 98The random generator must be seeded prior to calling BN_generate_prime_ex(). 99If the automatic seeding or reseeding of the OpenSSL CSPRNG fails due to 100external circumstances (see L<RAND(7)>), the operation will fail. 101 102BN_is_prime_ex() and BN_is_prime_fasttest_ex() test if the number B<p> is 103prime. The following tests are performed until one of them shows that 104B<p> is composite; if B<p> passes all these tests, it is considered 105prime. 106 107BN_is_prime_fasttest_ex(), when called with B<do_trial_division == 1>, 108first attempts trial division by a number of small primes; 109if no divisors are found by this test and B<cb> is not B<NULL>, 110B<BN_GENCB_call(cb, 1, -1)> is called. 111If B<do_trial_division == 0>, this test is skipped. 112 113Both BN_is_prime_ex() and BN_is_prime_fasttest_ex() perform a Miller-Rabin 114probabilistic primality test with B<nchecks> iterations. If 115B<nchecks == BN_prime_checks>, a number of iterations is used that 116yields a false positive rate of at most 2^-64 for random input. 117The error rate depends on the size of the prime and goes down for bigger primes. 118The rate is 2^-80 starting at 308 bits, 2^-112 at 852 bits, 2^-128 at 1080 bits, 1192^-192 at 3747 bits and 2^-256 at 6394 bits. 120 121When the source of the prime is not random or not trusted, the number 122of checks needs to be much higher to reach the same level of assurance: 123It should equal half of the targeted security level in bits (rounded up to the 124next integer if necessary). 125For instance, to reach the 128 bit security level, B<nchecks> should be set to 12664. 127 128If B<cb> is not B<NULL>, B<BN_GENCB_call(cb, 1, j)> is called 129after the j-th iteration (j = 0, 1, ...). B<ctx> is a 130preallocated B<BN_CTX> (to save the overhead of allocating and 131freeing the structure in a loop), or B<NULL>. 132 133BN_GENCB_call() calls the callback function held in the B<BN_GENCB> structure 134and passes the ints B<a> and B<b> as arguments. There are two types of 135B<BN_GENCB> structure that are supported: "new" style and "old" style. New 136programs should prefer the "new" style, whilst the "old" style is provided 137for backwards compatibility purposes. 138 139A B<BN_GENCB> structure should be created through a call to BN_GENCB_new(), 140and freed through a call to BN_GENCB_free(). 141 142For "new" style callbacks a BN_GENCB structure should be initialised with a 143call to BN_GENCB_set(), where B<gencb> is a B<BN_GENCB *>, B<callback> is of 144type B<int (*callback)(int, int, BN_GENCB *)> and B<cb_arg> is a B<void *>. 145"Old" style callbacks are the same except they are initialised with a call 146to BN_GENCB_set_old() and B<callback> is of type 147B<void (*callback)(int, int, void *)>. 148 149A callback is invoked through a call to B<BN_GENCB_call>. This will check 150the type of the callback and will invoke B<callback(a, b, gencb)> for new 151style callbacks or B<callback(a, b, cb_arg)> for old style. 152 153It is possible to obtain the argument associated with a BN_GENCB structure 154(set via a call to BN_GENCB_set or BN_GENCB_set_old) using BN_GENCB_get_arg. 155 156BN_generate_prime() (deprecated) works in the same way as 157BN_generate_prime_ex() but expects an old-style callback function 158directly in the B<callback> parameter, and an argument to pass to it in 159the B<cb_arg>. BN_is_prime() and BN_is_prime_fasttest() 160can similarly be compared to BN_is_prime_ex() and 161BN_is_prime_fasttest_ex(), respectively. 162 163=head1 RETURN VALUES 164 165BN_generate_prime_ex() return 1 on success or 0 on error. 166 167BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime() and 168BN_is_prime_fasttest() return 0 if the number is composite, 1 if it is 169prime with an error probability of less than 0.25^B<nchecks>, and 170-1 on error. 171 172BN_generate_prime() returns the prime number on success, B<NULL> otherwise. 173 174BN_GENCB_new returns a pointer to a BN_GENCB structure on success, or B<NULL> 175otherwise. 176 177BN_GENCB_get_arg returns the argument previously associated with a BN_GENCB 178structure. 179 180Callback functions should return 1 on success or 0 on error. 181 182The error codes can be obtained by L<ERR_get_error(3)>. 183 184=head1 REMOVED FUNCTIONALITY 185 186As of OpenSSL 1.1.0 it is no longer possible to create a BN_GENCB structure 187directly, as in: 188 189 BN_GENCB callback; 190 191Instead applications should create a BN_GENCB structure using BN_GENCB_new: 192 193 BN_GENCB *callback; 194 callback = BN_GENCB_new(); 195 if (!callback) 196 /* error */ 197 ... 198 BN_GENCB_free(callback); 199 200=head1 SEE ALSO 201 202L<DH_generate_parameters(3)>, L<DSA_generate_parameters(3)>, 203L<RSA_generate_key(3)>, L<ERR_get_error(3)>, L<RAND_bytes(3)>, 204L<RAND(7)> 205 206=head1 HISTORY 207 208The BN_GENCB_new(), BN_GENCB_free(), 209and BN_GENCB_get_arg() functions were added in OpenSSL 1.1.0. 210 211=head1 COPYRIGHT 212 213Copyright 2000-2020 The OpenSSL Project Authors. All Rights Reserved. 214 215Licensed under the OpenSSL license (the "License"). You may not use 216this file except in compliance with the License. You can obtain a copy 217in the file LICENSE in the source distribution or at 218L<https://www.openssl.org/source/license.html>. 219 220=cut 221