xref: /freebsd/crypto/openssl/doc/man3/BN_generate_prime.pod (revision b9f654b163bce26de79705e77b872427c9f2afa1)
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>.
55If B<ret> is not B<NULL>, it will be used to store the number.
56
57If B<cb> is not B<NULL>, it is used as follows:
58
59=over 2
60
61=item *
62
63B<BN_GENCB_call(cb, 0, i)> is called after generating the i-th
64potential prime number.
65
66=item *
67
68While the number is being tested for primality,
69B<BN_GENCB_call(cb, 1, j)> is called as described below.
70
71=item *
72
73When a prime has been found, B<BN_GENCB_call(cb, 2, i)> is called.
74
75=item *
76
77The callers of BN_generate_prime_ex() may call B<BN_GENCB_call(cb, i, j)> with
78other values as described in their respective man pages; see L</SEE ALSO>.
79
80=back
81
82The prime may have to fulfill additional requirements for use in
83Diffie-Hellman key exchange:
84
85If B<add> is not B<NULL>, the prime will fulfill the condition p % B<add>
86== B<rem> (p % B<add> == 1 if B<rem> == B<NULL>) in order to suit a given
87generator.
88
89If B<safe> is true, it will be a safe prime (i.e. a prime p so
90that (p-1)/2 is also prime).
91
92The PRNG must be seeded prior to calling BN_generate_prime_ex().
93The prime number generation has a negligible error probability.
94
95BN_is_prime_ex() and BN_is_prime_fasttest_ex() test if the number B<p> is
96prime.  The following tests are performed until one of them shows that
97B<p> is composite; if B<p> passes all these tests, it is considered
98prime.
99
100BN_is_prime_fasttest_ex(), when called with B<do_trial_division == 1>,
101first attempts trial division by a number of small primes;
102if no divisors are found by this test and B<cb> is not B<NULL>,
103B<BN_GENCB_call(cb, 1, -1)> is called.
104If B<do_trial_division == 0>, this test is skipped.
105
106Both BN_is_prime_ex() and BN_is_prime_fasttest_ex() perform a Miller-Rabin
107probabilistic primality test with B<nchecks> iterations. If
108B<nchecks == BN_prime_checks>, a number of iterations is used that
109yields a false positive rate of at most 2^-64 for random input.
110The error rate depends on the size of the prime and goes down for bigger primes.
111The rate is 2^-80 starting at 308 bits, 2^-112 at 852 bits, 2^-128 at 1080 bits,
1122^-192 at 3747 bits and 2^-256 at 6394 bits.
113
114When the source of the prime is not random or not trusted, the number
115of checks needs to be much higher to reach the same level of assurance:
116It should equal half of the targeted security level in bits (rounded up to the
117next integer if necessary).
118For instance, to reach the 128 bit security level, B<nchecks> should be set to
11964.
120
121If B<cb> is not B<NULL>, B<BN_GENCB_call(cb, 1, j)> is called
122after the j-th iteration (j = 0, 1, ...). B<ctx> is a
123pre-allocated B<BN_CTX> (to save the overhead of allocating and
124freeing the structure in a loop), or B<NULL>.
125
126BN_GENCB_call() calls the callback function held in the B<BN_GENCB> structure
127and passes the ints B<a> and B<b> as arguments. There are two types of
128B<BN_GENCB> structure that are supported: "new" style and "old" style. New
129programs should prefer the "new" style, whilst the "old" style is provided
130for backwards compatibility purposes.
131
132A B<BN_GENCB> structure should be created through a call to BN_GENCB_new(),
133and freed through a call to BN_GENCB_free().
134
135For "new" style callbacks a BN_GENCB structure should be initialised with a
136call to BN_GENCB_set(), where B<gencb> is a B<BN_GENCB *>, B<callback> is of
137type B<int (*callback)(int, int, BN_GENCB *)> and B<cb_arg> is a B<void *>.
138"Old" style callbacks are the same except they are initialised with a call
139to BN_GENCB_set_old() and B<callback> is of type
140B<void (*callback)(int, int, void *)>.
141
142A callback is invoked through a call to B<BN_GENCB_call>. This will check
143the type of the callback and will invoke B<callback(a, b, gencb)> for new
144style callbacks or B<callback(a, b, cb_arg)> for old style.
145
146It is possible to obtain the argument associated with a BN_GENCB structure
147(set via a call to BN_GENCB_set or BN_GENCB_set_old) using BN_GENCB_get_arg.
148
149BN_generate_prime() (deprecated) works in the same way as
150BN_generate_prime_ex() but expects an old-style callback function
151directly in the B<callback> parameter, and an argument to pass to it in
152the B<cb_arg>. BN_is_prime() and BN_is_prime_fasttest()
153can similarly be compared to BN_is_prime_ex() and
154BN_is_prime_fasttest_ex(), respectively.
155
156=head1 RETURN VALUES
157
158BN_generate_prime_ex() return 1 on success or 0 on error.
159
160BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime() and
161BN_is_prime_fasttest() return 0 if the number is composite, 1 if it is
162prime with an error probability of less than 0.25^B<nchecks>, and
163-1 on error.
164
165BN_generate_prime() returns the prime number on success, B<NULL> otherwise.
166
167BN_GENCB_new returns a pointer to a BN_GENCB structure on success, or B<NULL>
168otherwise.
169
170BN_GENCB_get_arg returns the argument previously associated with a BN_GENCB
171structure.
172
173Callback functions should return 1 on success or 0 on error.
174
175The error codes can be obtained by L<ERR_get_error(3)>.
176
177=head1 REMOVED FUNCTIONALITY
178
179As of OpenSSL 1.1.0 it is no longer possible to create a BN_GENCB structure
180directly, as in:
181
182 BN_GENCB callback;
183
184Instead applications should create a BN_GENCB structure using BN_GENCB_new:
185
186 BN_GENCB *callback;
187 callback = BN_GENCB_new();
188 if (!callback)
189     /* error */
190 ...
191 BN_GENCB_free(callback);
192
193=head1 SEE ALSO
194
195L<DH_generate_parameters(3)>, L<DSA_generate_parameters(3)>,
196L<RSA_generate_key(3)>, L<ERR_get_error(3)>, L<RAND_bytes(3)>
197
198=head1 HISTORY
199
200The BN_GENCB_new(), BN_GENCB_free(),
201and BN_GENCB_get_arg() functions were added in OpenSSL 1.1.0.
202
203=head1 COPYRIGHT
204
205Copyright 2000-2018 The OpenSSL Project Authors. All Rights Reserved.
206
207Licensed under the OpenSSL license (the "License").  You may not use
208this file except in compliance with the License.  You can obtain a copy
209in the file LICENSE in the source distribution or at
210L<https://www.openssl.org/source/license.html>.
211
212=cut
213