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131 .IX Title "BN_generate_prime 3"
132 .TH BN_generate_prime 3 "2017-05-25" "1.0.2l" "OpenSSL"
133 .\" For nroff, turn off justification. Always turn off hyphenation; it makes
134 .\" way too many mistakes in technical documents.
138 BN_generate_prime_ex, BN_is_prime_ex, BN_is_prime_fasttest_ex, BN_GENCB_call,
139 BN_GENCB_set_old, BN_GENCB_set, BN_generate_prime, BN_is_prime,
140 BN_is_prime_fasttest \- generate primes and test for primality
142 .IX Header "SYNOPSIS"
144 \& #include <openssl/bn.h>
146 \& int BN_generate_prime_ex(BIGNUM *ret,int bits,int safe, const BIGNUM *add,
147 \& const BIGNUM *rem, BN_GENCB *cb);
149 \& int BN_is_prime_ex(const BIGNUM *p,int nchecks, BN_CTX *ctx, BN_GENCB *cb);
151 \& int BN_is_prime_fasttest_ex(const BIGNUM *p,int nchecks, BN_CTX *ctx,
152 \& int do_trial_division, BN_GENCB *cb);
154 \& int BN_GENCB_call(BN_GENCB *cb, int a, int b);
156 \& #define BN_GENCB_set_old(gencb, callback, cb_arg) ...
158 \& #define BN_GENCB_set(gencb, callback, cb_arg) ...
164 \& BIGNUM *BN_generate_prime(BIGNUM *ret, int num, int safe, BIGNUM *add,
165 \& BIGNUM *rem, void (*callback)(int, int, void *), void *cb_arg);
167 \& int BN_is_prime(const BIGNUM *a, int checks, void (*callback)(int, int,
168 \& void *), BN_CTX *ctx, void *cb_arg);
170 \& int BN_is_prime_fasttest(const BIGNUM *a, int checks,
171 \& void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg,
172 \& int do_trial_division);
175 .IX Header "DESCRIPTION"
176 \&\fIBN_generate_prime_ex()\fR generates a pseudo-random prime number of
177 bit length \fBbits\fR.
178 If \fBret\fR is not \fB\s-1NULL\s0\fR, it will be used to store the number.
180 If \fBcb\fR is not \fB\s-1NULL\s0\fR, it is used as follows:
182 \&\fBBN_GENCB_call(cb, 0, i)\fR is called after generating the i\-th
183 potential prime number.
185 While the number is being tested for primality,
186 \&\fBBN_GENCB_call(cb, 1, j)\fR is called as described below.
188 When a prime has been found, \fBBN_GENCB_call(cb, 2, i)\fR is called.
190 The prime may have to fulfill additional requirements for use in
191 Diffie-Hellman key exchange:
193 If \fBadd\fR is not \fB\s-1NULL\s0\fR, the prime will fulfill the condition p % \fBadd\fR
194 == \fBrem\fR (p % \fBadd\fR == 1 if \fBrem\fR == \fB\s-1NULL\s0\fR) in order to suit a given
197 If \fBsafe\fR is true, it will be a safe prime (i.e. a prime p so
198 that (p\-1)/2 is also prime).
200 The \s-1PRNG\s0 must be seeded prior to calling \fIBN_generate_prime_ex()\fR.
201 The prime number generation has a negligible error probability.
203 \&\fIBN_is_prime_ex()\fR and \fIBN_is_prime_fasttest_ex()\fR test if the number \fBp\fR is
204 prime. The following tests are performed until one of them shows that
205 \&\fBp\fR is composite; if \fBp\fR passes all these tests, it is considered
208 \&\fIBN_is_prime_fasttest_ex()\fR, when called with \fBdo_trial_division == 1\fR,
209 first attempts trial division by a number of small primes;
210 if no divisors are found by this test and \fBcb\fR is not \fB\s-1NULL\s0\fR,
211 \&\fBBN_GENCB_call(cb, 1, \-1)\fR is called.
212 If \fBdo_trial_division == 0\fR, this test is skipped.
214 Both \fIBN_is_prime_ex()\fR and \fIBN_is_prime_fasttest_ex()\fR perform a Miller-Rabin
215 probabilistic primality test with \fBnchecks\fR iterations. If
216 \&\fBnchecks == BN_prime_checks\fR, a number of iterations is used that
217 yields a false positive rate of at most 2^\-80 for random input.
219 If \fBcb\fR is not \fB\s-1NULL\s0\fR, \fBBN_GENCB_call(cb, 1, j)\fR is called
220 after the j\-th iteration (j = 0, 1, ...). \fBctx\fR is a
221 pre-allocated \fB\s-1BN_CTX\s0\fR (to save the overhead of allocating and
222 freeing the structure in a loop), or \fB\s-1NULL\s0\fR.
224 BN_GENCB_call calls the callback function held in the \fB\s-1BN_GENCB\s0\fR structure
225 and passes the ints \fBa\fR and \fBb\fR as arguments. There are two types of
226 \&\fB\s-1BN_GENCB\s0\fR structure that are supported: \*(L"new\*(R" style and \*(L"old\*(R" style. New
227 programs should prefer the \*(L"new\*(R" style, whilst the \*(L"old\*(R" style is provided
228 for backwards compatibility purposes.
230 For \*(L"new\*(R" style callbacks a \s-1BN_GENCB\s0 structure should be initialised with a
231 call to BN_GENCB_set, where \fBgencb\fR is a \fB\s-1BN_GENCB\s0 *\fR, \fBcallback\fR is of
232 type \fBint (*callback)(int, int, \s-1BN_GENCB\s0 *)\fR and \fBcb_arg\fR is a \fBvoid *\fR.
233 \&\*(L"Old\*(R" style callbacks are the same except they are initialised with a call
234 to BN_GENCB_set_old and \fBcallback\fR is of type
235 \&\fBvoid (*callback)(int, int, void *)\fR.
237 A callback is invoked through a call to \fBBN_GENCB_call\fR. This will check
238 the type of the callback and will invoke \fBcallback(a, b, gencb)\fR for new
239 style callbacks or \fBcallback(a, b, cb_arg)\fR for old style.
241 BN_generate_prime (deprecated) works in the same way as
242 BN_generate_prime_ex but expects an old style callback function
243 directly in the \fBcallback\fR parameter, and an argument to pass to it in
244 the \fBcb_arg\fR. Similarly BN_is_prime and BN_is_prime_fasttest are
245 deprecated and can be compared to BN_is_prime_ex and
246 BN_is_prime_fasttest_ex respectively.
248 .IX Header "RETURN VALUES"
249 \&\fIBN_generate_prime_ex()\fR return 1 on success or 0 on error.
251 \&\fIBN_is_prime_ex()\fR, \fIBN_is_prime_fasttest_ex()\fR, \fIBN_is_prime()\fR and
252 \&\fIBN_is_prime_fasttest()\fR return 0 if the number is composite, 1 if it is
253 prime with an error probability of less than 0.25^\fBnchecks\fR, and
256 \&\fIBN_generate_prime()\fR returns the prime number on success, \fB\s-1NULL\s0\fR otherwise.
258 Callback functions should return 1 on success or 0 on error.
260 The error codes can be obtained by \fIERR_get_error\fR\|(3).
262 .IX Header "SEE ALSO"
263 \&\fIbn\fR\|(3), \fIERR_get_error\fR\|(3), \fIrand\fR\|(3)
266 The \fBcb_arg\fR arguments to \fIBN_generate_prime()\fR and to \fIBN_is_prime()\fR
267 were added in SSLeay 0.9.0. The \fBret\fR argument to \fIBN_generate_prime()\fR
268 was added in SSLeay 0.9.1.
269 \&\fIBN_is_prime_fasttest()\fR was added in OpenSSL 0.9.5.