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