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126 .IX Title "BN_generate_prime 3"
127 .TH BN_generate_prime 3 "2007-10-24" "0.9.8g" "OpenSSL"
128 .\" For nroff, turn off justification. Always turn off hyphenation; it makes
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133 BN_generate_prime, BN_is_prime, BN_is_prime_fasttest \- generate primes and test for primality
135 .IX Header "SYNOPSIS"
137 \& #include <openssl/bn.h>
139 \& BIGNUM *BN_generate_prime(BIGNUM *ret, int num, int safe, BIGNUM *add,
140 \& BIGNUM *rem, void (*callback)(int, int, void *), void *cb_arg);
142 \& int BN_is_prime(const BIGNUM *a, int checks, void (*callback)(int, int,
143 \& void *), BN_CTX *ctx, void *cb_arg);
145 \& int BN_is_prime_fasttest(const BIGNUM *a, int checks,
146 \& void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg,
147 \& int do_trial_division);
150 .IX Header "DESCRIPTION"
151 \&\fIBN_generate_prime()\fR generates a pseudo-random prime number of \fBnum\fR
153 If \fBret\fR is not \fB\s-1NULL\s0\fR, it will be used to store the number.
155 If \fBcallback\fR is not \fB\s-1NULL\s0\fR, it is called as follows:
157 \&\fBcallback(0, i, cb_arg)\fR is called after generating the i\-th
158 potential prime number.
160 While the number is being tested for primality, \fBcallback(1, j,
161 cb_arg)\fR is called as described below.
163 When a prime has been found, \fBcallback(2, i, cb_arg)\fR is called.
165 The prime may have to fulfill additional requirements for use in
166 Diffie-Hellman key exchange:
168 If \fBadd\fR is not \fB\s-1NULL\s0\fR, the prime will fulfill the condition p % \fBadd\fR
169 == \fBrem\fR (p % \fBadd\fR == 1 if \fBrem\fR == \fB\s-1NULL\s0\fR) in order to suit a given
172 If \fBsafe\fR is true, it will be a safe prime (i.e. a prime p so
173 that (p\-1)/2 is also prime).
175 The \s-1PRNG\s0 must be seeded prior to calling \fIBN_generate_prime()\fR.
176 The prime number generation has a negligible error probability.
178 \&\fIBN_is_prime()\fR and \fIBN_is_prime_fasttest()\fR test if the number \fBa\fR is
179 prime. The following tests are performed until one of them shows that
180 \&\fBa\fR is composite; if \fBa\fR passes all these tests, it is considered
183 \&\fIBN_is_prime_fasttest()\fR, when called with \fBdo_trial_division == 1\fR,
184 first attempts trial division by a number of small primes;
185 if no divisors are found by this test and \fBcallback\fR is not \fB\s-1NULL\s0\fR,
186 \&\fBcallback(1, \-1, cb_arg)\fR is called.
187 If \fBdo_trial_division == 0\fR, this test is skipped.
189 Both \fIBN_is_prime()\fR and \fIBN_is_prime_fasttest()\fR perform a Miller-Rabin
190 probabilistic primality test with \fBchecks\fR iterations. If
191 \&\fBchecks == BN_prime_checks\fR, a number of iterations is used that
192 yields a false positive rate of at most 2^\-80 for random input.
194 If \fBcallback\fR is not \fB\s-1NULL\s0\fR, \fBcallback(1, j, cb_arg)\fR is called
195 after the j\-th iteration (j = 0, 1, ...). \fBctx\fR is a
196 pre-allocated \fB\s-1BN_CTX\s0\fR (to save the overhead of allocating and
197 freeing the structure in a loop), or \fB\s-1NULL\s0\fR.
199 .IX Header "RETURN VALUES"
200 \&\fIBN_generate_prime()\fR returns the prime number on success, \fB\s-1NULL\s0\fR otherwise.
202 \&\fIBN_is_prime()\fR returns 0 if the number is composite, 1 if it is
203 prime with an error probability of less than 0.25^\fBchecks\fR, and
206 The error codes can be obtained by \fIERR_get_error\fR\|(3).
208 .IX Header "SEE ALSO"
209 \&\fIbn\fR\|(3), \fIERR_get_error\fR\|(3), \fIrand\fR\|(3)
212 The \fBcb_arg\fR arguments to \fIBN_generate_prime()\fR and to \fIBN_is_prime()\fR
213 were added in SSLeay 0.9.0. The \fBret\fR argument to \fIBN_generate_prime()\fR
214 was added in SSLeay 0.9.1.
215 \&\fIBN_is_prime_fasttest()\fR was added in OpenSSL 0.9.5.