1BN_GENERATE_PRIME(3ossl)            OpenSSL           BN_GENERATE_PRIME(3ossl)
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NAME

6       BN_generate_prime_ex2, BN_generate_prime_ex, BN_is_prime_ex,
7       BN_check_prime, BN_is_prime_fasttest_ex, BN_GENCB_call, BN_GENCB_new,
8       BN_GENCB_free, BN_GENCB_set_old, BN_GENCB_set, BN_GENCB_get_arg,
9       BN_generate_prime, BN_is_prime, BN_is_prime_fasttest - generate primes
10       and test for primality
11

SYNOPSIS

13        #include <openssl/bn.h>
14
15        int BN_generate_prime_ex2(BIGNUM *ret, int bits, int safe,
16                                  const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb,
17                                  BN_CTX *ctx);
18
19        int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add,
20                                 const BIGNUM *rem, BN_GENCB *cb);
21
22        int BN_check_prime(const BIGNUM *p, BN_CTX *ctx, BN_GENCB *cb);
23
24        int BN_GENCB_call(BN_GENCB *cb, int a, int b);
25
26        BN_GENCB *BN_GENCB_new(void);
27
28        void BN_GENCB_free(BN_GENCB *cb);
29
30        void BN_GENCB_set_old(BN_GENCB *gencb,
31                              void (*callback)(int, int, void *), void *cb_arg);
32
33        void BN_GENCB_set(BN_GENCB *gencb,
34                          int (*callback)(int, int, BN_GENCB *), void *cb_arg);
35
36        void *BN_GENCB_get_arg(BN_GENCB *cb);
37
38       The following functions have been deprecated since OpenSSL 0.9.8, and
39       can be hidden entirely by defining OPENSSL_API_COMPAT with a suitable
40       version value, see openssl_user_macros(7):
41
42        BIGNUM *BN_generate_prime(BIGNUM *ret, int num, int safe, BIGNUM *add,
43                                  BIGNUM *rem, void (*callback)(int, int, void *),
44                                  void *cb_arg);
45
46        int BN_is_prime(const BIGNUM *p, int nchecks,
47                        void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg);
48
49        int BN_is_prime_fasttest(const BIGNUM *p, int nchecks,
50                                 void (*callback)(int, int, void *), BN_CTX *ctx,
51                                 void *cb_arg, int do_trial_division);
52
53       The following functions have been deprecated since OpenSSL 3.0, and can
54       be hidden entirely by defining OPENSSL_API_COMPAT with a suitable
55       version value, see openssl_user_macros(7):
56
57        int BN_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb);
58
59        int BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx,
60                                    int do_trial_division, BN_GENCB *cb);
61

DESCRIPTION

63       BN_generate_prime_ex2() generates a pseudo-random prime number of at
64       least bit length bits using the BN_CTX provided in ctx. The value of
65       ctx must not be NULL.
66
67       The returned number is probably prime with a negligible error.  The
68       maximum error rate is 2^-128.  It's 2^-287 for a 512 bit prime, 2^-435
69       for a 1024 bit prime, 2^-648 for a 2048 bit prime, and lower than
70       2^-882 for primes larger than 2048 bit.
71
72       If add is NULL the returned prime number will have exact bit length
73       bits with the top most two bits set.
74
75       If ret is not NULL, it will be used to store the number.
76
77       If cb is not NULL, it is used as follows:
78
79BN_GENCB_call(cb, 0, i) is called after generating the i-th potential
80         prime number.
81
82       • While the number is being tested for primality, BN_GENCB_call(cb, 1,
83         j) is called as described below.
84
85       • When a prime has been found, BN_GENCB_call(cb, 2, i) is called.
86
87       • The callers of BN_generate_prime_ex() may call BN_GENCB_call(cb, i,
88         j) with other values as described in their respective man pages; see
89         "SEE ALSO".
90
91       The prime may have to fulfill additional requirements for use in
92       Diffie-Hellman key exchange:
93
94       If add is not NULL, the prime will fulfill the condition p % add == rem
95       (p % add == 1 if rem == NULL) in order to suit a given generator.
96
97       If safe is true, it will be a safe prime (i.e. a prime p so that
98       (p-1)/2 is also prime). If safe is true, and rem == NULL the condition
99       will be p % add == 3.  It is recommended that add is a multiple of 4.
100
101       The random generator must be seeded prior to calling
102       BN_generate_prime_ex().  If the automatic seeding or reseeding of the
103       OpenSSL CSPRNG fails due to external circumstances (see RAND(7)), the
104       operation will fail.  The random number generator configured for the
105       OSSL_LIB_CTX associated with ctx will be used.
106
107       BN_generate_prime_ex() is the same as BN_generate_prime_ex2() except
108       that no ctx parameter is passed.  In this case the random number
109       generator associated with the default OSSL_LIB_CTX will be used.
110
111       BN_check_prime(), BN_is_prime_ex(), BN_is_prime_fasttest_ex(),
112       BN_is_prime() and BN_is_prime_fasttest() test if the number p is prime.
113       The functions tests until one of the tests shows that p is composite,
114       or all the tests passed.  If p passes all these tests, it is considered
115       a probable prime.
116
117       The test performed on p are trial division by a number of small primes
118       and rounds of the of the Miller-Rabin probabilistic primality test.
119
120       The functions do at least 64 rounds of the Miller-Rabin test giving a
121       maximum false positive rate of 2^-128.  If the size of p is more than
122       2048 bits, they do at least 128 rounds giving a maximum false positive
123       rate of 2^-256.
124
125       If nchecks is larger than the minimum above (64 or 128), nchecks rounds
126       of the Miller-Rabin test will be done.
127
128       If do_trial_division set to 0, the trial division will be skipped.
129       BN_is_prime_ex() and BN_is_prime() always skip the trial division.
130
131       BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime() and
132       BN_is_prime_fasttest() are deprecated.
133
134       BN_is_prime_fasttest() and BN_is_prime() behave just like
135       BN_is_prime_fasttest_ex() and BN_is_prime_ex() respectively, but with
136       the old style call back.
137
138       ctx is a preallocated BN_CTX (to save the overhead of allocating and
139       freeing the structure in a loop), or NULL.
140
141       If the trial division is done, and no divisors are found and cb is not
142       NULL, BN_GENCB_call(cb, 1, -1) is called.
143
144       After each round of the Miller-Rabin probabilistic primality test, if
145       cb is not NULL, BN_GENCB_call(cb, 1, j) is called with j the iteration
146       (j = 0, 1, ...).
147
148       BN_GENCB_call() calls the callback function held in the BN_GENCB
149       structure and passes the ints a and b as arguments. There are two types
150       of BN_GENCB structure that are supported: "new" style and "old" style.
151       New programs should prefer the "new" style, whilst the "old" style is
152       provided for backwards compatibility purposes.
153
154       A BN_GENCB structure should be created through a call to
155       BN_GENCB_new(), and freed through a call to BN_GENCB_free().
156
157       For "new" style callbacks a BN_GENCB structure should be initialised
158       with a call to BN_GENCB_set(), where gencb is a BN_GENCB *, callback is
159       of type int (*callback)(int, int, BN_GENCB *) and cb_arg is a void *.
160       "Old" style callbacks are the same except they are initialised with a
161       call to BN_GENCB_set_old() and callback is of type void
162       (*callback)(int, int, void *).
163
164       A callback is invoked through a call to BN_GENCB_call. This will check
165       the type of the callback and will invoke callback(a, b, gencb) for new
166       style callbacks or callback(a, b, cb_arg) for old style.
167
168       It is possible to obtain the argument associated with a BN_GENCB
169       structure (set via a call to BN_GENCB_set or BN_GENCB_set_old) using
170       BN_GENCB_get_arg.
171
172       BN_generate_prime() (deprecated) works in the same way as
173       BN_generate_prime_ex() but expects an old-style callback function
174       directly in the callback parameter, and an argument to pass to it in
175       the cb_arg. BN_is_prime() and BN_is_prime_fasttest() can similarly be
176       compared to BN_is_prime_ex() and BN_is_prime_fasttest_ex(),
177       respectively.
178

RETURN VALUES

180       BN_generate_prime_ex() return 1 on success or 0 on error.
181
182       BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime(),
183       BN_is_prime_fasttest() and BN_check_prime return 0 if the number is
184       composite, 1 if it is prime with an error probability of less than
185       0.25^nchecks, and -1 on error.
186
187       BN_generate_prime() returns the prime number on success, NULL
188       otherwise.
189
190       BN_GENCB_new returns a pointer to a BN_GENCB structure on success, or
191       NULL otherwise.
192
193       BN_GENCB_get_arg returns the argument previously associated with a
194       BN_GENCB structure.
195
196       Callback functions should return 1 on success or 0 on error.
197
198       The error codes can be obtained by ERR_get_error(3).
199

REMOVED FUNCTIONALITY

201       As of OpenSSL 1.1.0 it is no longer possible to create a BN_GENCB
202       structure directly, as in:
203
204        BN_GENCB callback;
205
206       Instead applications should create a BN_GENCB structure using
207       BN_GENCB_new:
208
209        BN_GENCB *callback;
210        callback = BN_GENCB_new();
211        if (!callback)
212            /* error */
213        ...
214        BN_GENCB_free(callback);
215

SEE ALSO

217       DH_generate_parameters(3), DSA_generate_parameters(3),
218       RSA_generate_key(3), ERR_get_error(3), RAND_bytes(3), RAND(7)
219

HISTORY

221       The BN_is_prime_ex() and BN_is_prime_fasttest_ex() functions were
222       deprecated in OpenSSL 3.0.
223
224       The BN_GENCB_new(), BN_GENCB_free(), and BN_GENCB_get_arg() functions
225       were added in OpenSSL 1.1.0.
226
227       BN_check_prime() was added in OpenSSL 3.0.
228
230       Copyright 2000-2021 The OpenSSL Project Authors. All Rights Reserved.
231
232       Licensed under the Apache License 2.0 (the "License").  You may not use
233       this file except in compliance with the License.  You can obtain a copy
234       in the file LICENSE in the source distribution or at
235       <https://www.openssl.org/source/license.html>.
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2393.0.9                             2023-07-27          BN_GENERATE_PRIME(3ossl)
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