1BN_GENERATE_PRIME(3ossl) OpenSSL BN_GENERATE_PRIME(3ossl)
2
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
13 #include <openssl/bn.h>
14 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 int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add,
20 const BIGNUM *rem, BN_GENCB *cb);
21 int BN_check_prime(const BIGNUM *p, BN_CTX *ctx, BN_GENCB *cb);
23 int BN_GENCB_call(BN_GENCB *cb, int a, int b);
25 BN_GENCB *BN_GENCB_new(void);
27 void BN_GENCB_free(BN_GENCB *cb);
29 void BN_GENCB_set_old(BN_GENCB *gencb,
31 void (*callback)(int, int, void *), void *cb_arg);
32 void BN_GENCB_set(BN_GENCB *gencb,
34 int (*callback)(int, int, BN_GENCB *), void *cb_arg);
35 void *BN_GENCB_get_arg(BN_GENCB *cb);
37 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 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 int BN_is_prime(const BIGNUM *p, int nchecks,
47 void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg);
48 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 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 int BN_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb);
58 int BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx,
60 int do_trial_division, BN_GENCB *cb);
61
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 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 If add is NULL the returned prime number will have exact bit length
73 bits with the top most two bits set.
74 If ret is not NULL, it will be used to store the number.
76 If cb is not NULL, it is used as follows:
78 • BN_GENCB_call(cb, 0, i) is called after generating the i-th potential
80 prime number.
81 • While the number is being tested for primality, BN_GENCB_call(cb, 1,
83 j) is called as described below.
84 • When a prime has been found, BN_GENCB_call(cb, 2, i) is called.
86 • 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 The prime may have to fulfill additional requirements for use in
92 Diffie-Hellman key exchange:
93 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 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 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 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 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 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 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 If nchecks is larger than the minimum above (64 or 128), nchecks rounds
126 of the Miller-Rabin test will be done.
127 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 BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime() and
132 BN_is_prime_fasttest() are deprecated.
133 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 ctx is a preallocated BN_CTX (to save the overhead of allocating and
139 freeing the structure in a loop), or NULL.
140 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 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 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 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 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 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 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 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
180 BN_generate_prime_ex() return 1 on success or 0 on error.
181 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 BN_generate_prime() returns the prime number on success, NULL
188 otherwise.
189 BN_GENCB_new returns a pointer to a BN_GENCB structure on success, or
191 NULL otherwise.
192 BN_GENCB_get_arg returns the argument previously associated with a
194 BN_GENCB structure.
195 Callback functions should return 1 on success or 0 on error.
197 The error codes can be obtained by ERR_get_error(3).
199
201 As of OpenSSL 1.1.0 it is no longer possible to create a BN_GENCB
202 structure directly, as in:
203 BN_GENCB callback;
205 Instead applications should create a BN_GENCB structure using
207 BN_GENCB_new:
208 BN_GENCB *callback;
210 callback = BN_GENCB_new();
211 if (!callback)
212 /* error */
213 ...
214 BN_GENCB_free(callback);
215
217 DH_generate_parameters(3), DSA_generate_parameters(3),
218 RSA_generate_key(3), ERR_get_error(3), RAND_bytes(3), RAND(7)
219
221 The BN_is_prime_ex() and BN_is_prime_fasttest_ex() functions were
222 deprecated in OpenSSL 3.0.
223 The BN_GENCB_new(), BN_GENCB_free(), and BN_GENCB_get_arg() functions
225 were added in OpenSSL 1.1.0.
226 BN_check_prime() was added in OpenSSL 3.0.
228
230 Copyright 2000-2021 The OpenSSL Project Authors. All Rights Reserved.
231 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>.
2363.0.5 2022-07-05 BN_GENERATE_PRIME(3ossl)