1BN_GENERATE_PRIME(3) OpenSSL BN_GENERATE_PRIME(3)
2
6 BN_generate_prime_ex, BN_is_prime_ex, BN_is_prime_fasttest_ex,
7 BN_GENCB_call, BN_GENCB_new, BN_GENCB_free, BN_GENCB_set_old,
8 BN_GENCB_set, BN_GENCB_get_arg, BN_generate_prime, BN_is_prime,
9 BN_is_prime_fasttest - generate primes and test for primality
10
12 #include <openssl/bn.h>
13 int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add,
15 const BIGNUM *rem, BN_GENCB *cb);
16 int BN_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb);
18 int BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx,
20 int do_trial_division, BN_GENCB *cb);
21 int BN_GENCB_call(BN_GENCB *cb, int a, int b);
23 BN_GENCB *BN_GENCB_new(void);
25 void BN_GENCB_free(BN_GENCB *cb);
27 void BN_GENCB_set_old(BN_GENCB *gencb,
29 void (*callback)(int, int, void *), void *cb_arg);
30 void BN_GENCB_set(BN_GENCB *gencb,
32 int (*callback)(int, int, BN_GENCB *), void *cb_arg);
33 void *BN_GENCB_get_arg(BN_GENCB *cb);
35 Deprecated:
37 #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 int BN_is_prime(const BIGNUM *a, int checks,
44 void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg);
45 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
52 BN_generate_prime_ex() generates a pseudo-random prime number of at
53 least bit length bits. The returned number is probably prime with a
54 negligible error. If add is NULL the returned prime number will have
55 exact bit length bits with the top most two bits set.
56 If ret is not NULL, it will be used to store the number.
58 If cb is not NULL, it is used as follows:
60 • BN_GENCB_call(cb, 0, i) is called after generating the i-th potential
62 prime number.
63 • While the number is being tested for primality, BN_GENCB_call(cb, 1,
65 j) is called as described below.
66 • When a prime has been found, BN_GENCB_call(cb, 2, i) is called.
68 • The callers of BN_generate_prime_ex() may call BN_GENCB_call(cb, i,
70 j) with other values as described in their respective man pages; see
71 "SEE ALSO".
72 The prime may have to fulfill additional requirements for use in
74 Diffie-Hellman key exchange:
75 If add is not NULL, the prime will fulfill the condition p % add == rem
77 (p % add == 1 if rem == NULL) in order to suit a given generator.
78 If safe is true, it will be a safe prime (i.e. a prime p so that
80 (p-1)/2 is also prime). If safe is true, and rem == NULL the condition
81 will be p % add == 3. It is recommended that add is a multiple of 4.
82 The random generator must be seeded prior to calling
84 BN_generate_prime_ex(). If the automatic seeding or reseeding of the
85 OpenSSL CSPRNG fails due to external circumstances (see RAND(7)), the
86 operation will fail.
87 BN_is_prime_ex() and BN_is_prime_fasttest_ex() test if the number p is
89 prime. The following tests are performed until one of them shows that
90 p is composite; if p passes all these tests, it is considered prime.
91 BN_is_prime_fasttest_ex(), when called with do_trial_division == 1,
93 first attempts trial division by a number of small primes; if no
94 divisors are found by this test and cb is not NULL, BN_GENCB_call(cb,
95 1, -1) is called. If do_trial_division == 0, this test is skipped.
96 Both BN_is_prime_ex() and BN_is_prime_fasttest_ex() perform a Miller-
98 Rabin probabilistic primality test with nchecks iterations. If nchecks
99 == BN_prime_checks, a number of iterations is used that yields a false
100 positive rate of at most 2^-64 for random input. The error rate
101 depends on the size of the prime and goes down for bigger primes. The
102 rate is 2^-80 starting at 308 bits, 2^-112 at 852 bits, 2^-128 at 1080
103 bits, 2^-192 at 3747 bits and 2^-256 at 6394 bits.
104 When the source of the prime is not random or not trusted, the number
106 of checks needs to be much higher to reach the same level of assurance:
107 It should equal half of the targeted security level in bits (rounded up
108 to the next integer if necessary). For instance, to reach the 128 bit
109 security level, nchecks should be set to 64.
110 If cb is not NULL, BN_GENCB_call(cb, 1, j) is called after the j-th
112 iteration (j = 0, 1, ...). ctx is a preallocated BN_CTX (to save the
113 overhead of allocating and freeing the structure in a loop), or NULL.
114 BN_GENCB_call() calls the callback function held in the BN_GENCB
116 structure and passes the ints a and b as arguments. There are two types
117 of BN_GENCB structure that are supported: "new" style and "old" style.
118 New programs should prefer the "new" style, whilst the "old" style is
119 provided for backwards compatibility purposes.
120 A BN_GENCB structure should be created through a call to
122 BN_GENCB_new(), and freed through a call to BN_GENCB_free().
123 For "new" style callbacks a BN_GENCB structure should be initialised
125 with a call to BN_GENCB_set(), where gencb is a BN_GENCB *, callback is
126 of type int (*callback)(int, int, BN_GENCB *) and cb_arg is a void *.
127 "Old" style callbacks are the same except they are initialised with a
128 call to BN_GENCB_set_old() and callback is of type void
129 (*callback)(int, int, void *).
130 A callback is invoked through a call to BN_GENCB_call. This will check
132 the type of the callback and will invoke callback(a, b, gencb) for new
133 style callbacks or callback(a, b, cb_arg) for old style.
134 It is possible to obtain the argument associated with a BN_GENCB
136 structure (set via a call to BN_GENCB_set or BN_GENCB_set_old) using
137 BN_GENCB_get_arg.
138 BN_generate_prime() (deprecated) works in the same way as
140 BN_generate_prime_ex() but expects an old-style callback function
141 directly in the callback parameter, and an argument to pass to it in
142 the cb_arg. BN_is_prime() and BN_is_prime_fasttest() can similarly be
143 compared to BN_is_prime_ex() and BN_is_prime_fasttest_ex(),
144 respectively.
145
147 BN_generate_prime_ex() return 1 on success or 0 on error.
148 BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime() and
150 BN_is_prime_fasttest() return 0 if the number is composite, 1 if it is
151 prime with an error probability of less than 0.25^nchecks, and -1 on
152 error.
153 BN_generate_prime() returns the prime number on success, NULL
155 otherwise.
156 BN_GENCB_new returns a pointer to a BN_GENCB structure on success, or
158 NULL otherwise.
159 BN_GENCB_get_arg returns the argument previously associated with a
161 BN_GENCB structure.
162 Callback functions should return 1 on success or 0 on error.
164 The error codes can be obtained by ERR_get_error(3).
166
168 As of OpenSSL 1.1.0 it is no longer possible to create a BN_GENCB
169 structure directly, as in:
170 BN_GENCB callback;
172 Instead applications should create a BN_GENCB structure using
174 BN_GENCB_new:
175 BN_GENCB *callback;
177 callback = BN_GENCB_new();
178 if (!callback)
179 /* error */
180 ...
181 BN_GENCB_free(callback);
182
184 DH_generate_parameters(3), DSA_generate_parameters(3),
185 RSA_generate_key(3), ERR_get_error(3), RAND_bytes(3), RAND(7)
186
188 The BN_GENCB_new(), BN_GENCB_free(), and BN_GENCB_get_arg() functions
189 were added in OpenSSL 1.1.0.
190
192 Copyright 2000-2020 The OpenSSL Project Authors. All Rights Reserved.
193 Licensed under the OpenSSL license (the "License"). You may not use
195 this file except in compliance with the License. You can obtain a copy
196 in the file LICENSE in the source distribution or at
197 <https://www.openssl.org/source/license.html>.
1981.1.1q 2022-07-07 BN_GENERATE_PRIME(3)