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