2 ''' $RCSfile$$Revision$$Date$
20 .ie \\n(.$>=3 .ne \\$3
36 ''' Set up \*(-- to give an unbreakable dash;
37 ''' string Tr holds user defined translation string.
38 ''' Bell System Logo is used as a dummy character.
44 .if (\n(.H=4u)&(1m=24u) .ds -- \(*W\h'-12u'\(*W\h'-12u'-\" diablo 10 pitch
45 .if (\n(.H=4u)&(1m=20u) .ds -- \(*W\h'-12u'\(*W\h'-8u'-\" diablo 12 pitch
48 ''' \*(M", \*(S", \*(N" and \*(T" are the equivalent of
49 ''' \*(L" and \*(R", except that they are used on ".xx" lines,
50 ''' such as .IP and .SH, which do another additional levels of
51 ''' double-quote interpretation
80 .\" If the F register is turned on, we'll generate
81 .\" index entries out stderr for the following things:
86 .\" X<> Xref (embedded
87 .\" Of course, you have to process the output yourself
88 .\" in some meaninful fashion.
91 .tm Index:\\$1\t\\n%\t"\\$2"
96 .TH BN_generate_prime 3 "0.9.7d" "2/Sep/2004" "OpenSSL"
100 .ds C+ C\v'-.1v'\h'-1p'\s-2+\h'-1p'+\s0\v'.1v'\h'-1p'
101 .de CQ \" put $1 in typewriter font
107 \\&\\$2 \\$3 \\$4 \\$5 \\$6 \\$7
110 .\" @(#)ms.acc 1.5 88/02/08 SMI; from UCB 4.2
111 . \" AM - accent mark definitions
113 . \" fudge factors for nroff and troff
122 . ds #H ((1u-(\\\\n(.fu%2u))*.13m)
128 . \" simple accents for nroff and troff
141 . ds ' \\k:\h'-(\\n(.wu*8/10-\*(#H)'\'\h"|\\n:u"
142 . ds ` \\k:\h'-(\\n(.wu*8/10-\*(#H)'\`\h'|\\n:u'
143 . ds ^ \\k:\h'-(\\n(.wu*10/11-\*(#H)'^\h'|\\n:u'
144 . ds , \\k:\h'-(\\n(.wu*8/10)',\h'|\\n:u'
145 . ds ~ \\k:\h'-(\\n(.wu-\*(#H-.1m)'~\h'|\\n:u'
146 . ds ? \s-2c\h'-\w'c'u*7/10'\u\h'\*(#H'\zi\d\s+2\h'\w'c'u*8/10'
147 . ds ! \s-2\(or\s+2\h'-\w'\(or'u'\v'-.8m'.\v'.8m'
148 . ds / \\k:\h'-(\\n(.wu*8/10-\*(#H)'\z\(sl\h'|\\n:u'
149 . ds q o\h'-\w'o'u*8/10'\s-4\v'.4m'\z\(*i\v'-.4m'\s+4\h'\w'o'u*8/10'
151 . \" troff and (daisy-wheel) nroff accents
152 .ds : \\k:\h'-(\\n(.wu*8/10-\*(#H+.1m+\*(#F)'\v'-\*(#V'\z.\h'.2m+\*(#F'.\h'|\\n:u'\v'\*(#V'
153 .ds 8 \h'\*(#H'\(*b\h'-\*(#H'
154 .ds v \\k:\h'-(\\n(.wu*9/10-\*(#H)'\v'-\*(#V'\*(#[\s-4v\s0\v'\*(#V'\h'|\\n:u'\*(#]
155 .ds _ \\k:\h'-(\\n(.wu*9/10-\*(#H+(\*(#F*2/3))'\v'-.4m'\z\(hy\v'.4m'\h'|\\n:u'
156 .ds . \\k:\h'-(\\n(.wu*8/10)'\v'\*(#V*4/10'\z.\v'-\*(#V*4/10'\h'|\\n:u'
157 .ds 3 \*(#[\v'.2m'\s-2\&3\s0\v'-.2m'\*(#]
158 .ds o \\k:\h'-(\\n(.wu+\w'\(de'u-\*(#H)/2u'\v'-.3n'\*(#[\z\(de\v'.3n'\h'|\\n:u'\*(#]
159 .ds d- \h'\*(#H'\(pd\h'-\w'~'u'\v'-.25m'\f2\(hy\fP\v'.25m'\h'-\*(#H'
160 .ds D- D\\k:\h'-\w'D'u'\v'-.11m'\z\(hy\v'.11m'\h'|\\n:u'
161 .ds th \*(#[\v'.3m'\s+1I\s-1\v'-.3m'\h'-(\w'I'u*2/3)'\s-1o\s+1\*(#]
162 .ds Th \*(#[\s+2I\s-2\h'-\w'I'u*3/5'\v'-.3m'o\v'.3m'\*(#]
163 .ds ae a\h'-(\w'a'u*4/10)'e
164 .ds Ae A\h'-(\w'A'u*4/10)'E
165 .ds oe o\h'-(\w'o'u*4/10)'e
166 .ds Oe O\h'-(\w'O'u*4/10)'E
167 . \" corrections for vroff
168 .if v .ds ~ \\k:\h'-(\\n(.wu*9/10-\*(#H)'\s-2\u~\d\s+2\h'|\\n:u'
169 .if v .ds ^ \\k:\h'-(\\n(.wu*10/11-\*(#H)'\v'-.4m'^\v'.4m'\h'|\\n:u'
170 . \" for low resolution devices (crt and lpr)
171 .if \n(.H>23 .if \n(.V>19 \
175 . ds v \h'-1'\o'\(aa\(ga'
191 BN_generate_prime, BN_is_prime, BN_is_prime_fasttest \- generate primes and test for primality
195 \& #include <openssl/bn.h>
198 \& BIGNUM *BN_generate_prime(BIGNUM *ret, int num, int safe, BIGNUM *add,
199 \& BIGNUM *rem, void (*callback)(int, int, void *), void *cb_arg);
202 \& int BN_is_prime(const BIGNUM *a, int checks, void (*callback)(int, int,
203 \& void *), BN_CTX *ctx, void *cb_arg);
206 \& int BN_is_prime_fasttest(const BIGNUM *a, int checks,
207 \& void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg,
208 \& int do_trial_division);
211 \fIBN_generate_prime()\fR generates a pseudo-random prime number of \fBnum\fR
213 If \fBret\fR is not \fBNULL\fR, it will be used to store the number.
215 If \fBcallback\fR is not \fBNULL\fR, it is called as follows:
217 \fBcallback(0, i, cb_arg)\fR is called after generating the i-th
218 potential prime number.
220 While the number is being tested for primality, \fBcallback(1, j,
221 cb_arg)\fR is called as described below.
223 When a prime has been found, \fBcallback(2, i, cb_arg)\fR is called.
225 The prime may have to fulfill additional requirements for use in
226 Diffie-Hellman key exchange:
228 If \fBadd\fR is not \fB\s-1NULL\s0\fR, the prime will fulfill the condition p % \fBadd\fR
229 == \fBrem\fR (p % \fBadd\fR == 1 if \fBrem\fR == \fB\s-1NULL\s0\fR) in order to suit a given
232 If \fBsafe\fR is true, it will be a safe prime (i.e. a prime p so
233 that (p-1)/2 is also prime).
235 The \s-1PRNG\s0 must be seeded prior to calling \fIBN_generate_prime()\fR.
236 The prime number generation has a negligible error probability.
238 \fIBN_is_prime()\fR and \fIBN_is_prime_fasttest()\fR test if the number \fBa\fR is
239 prime. The following tests are performed until one of them shows that
240 \fBa\fR is composite; if \fBa\fR passes all these tests, it is considered
243 \fIBN_is_prime_fasttest()\fR, when called with \fBdo_trial_division == 1\fR,
244 first attempts trial division by a number of small primes;
245 if no divisors are found by this test and \fBcallback\fR is not \fB\s-1NULL\s0\fR,
246 \fBcallback(1, \-1, cb_arg)\fR is called.
247 If \fBdo_trial_division == 0\fR, this test is skipped.
249 Both \fIBN_is_prime()\fR and \fIBN_is_prime_fasttest()\fR perform a Miller-Rabin
250 probabilistic primality test with \fBchecks\fR iterations. If
251 \fBchecks == BN_prime_checks\fR, a number of iterations is used that
252 yields a false positive rate of at most 2^\-80 for random input.
254 If \fBcallback\fR is not \fB\s-1NULL\s0\fR, \fBcallback(1, j, cb_arg)\fR is called
255 after the j-th iteration (j = 0, 1, ...). \fBctx\fR is a
256 pre-allocated \fB\s-1BN_CTX\s0\fR (to save the overhead of allocating and
257 freeing the structure in a loop), or \fB\s-1NULL\s0\fR.
259 \fIBN_generate_prime()\fR returns the prime number on success, \fBNULL\fR otherwise.
261 \fIBN_is_prime()\fR returns 0 if the number is composite, 1 if it is
262 prime with an error probability of less than 0.25^\fBchecks\fR, and
265 The error codes can be obtained by ERR_get_error(3).
267 bn(3), ERR_get_error(3), rand(3)
269 The \fBcb_arg\fR arguments to \fIBN_generate_prime()\fR and to \fIBN_is_prime()\fR
270 were added in SSLeay 0.9.0. The \fBret\fR argument to \fIBN_generate_prime()\fR
271 was added in SSLeay 0.9.1.
272 \fIBN_is_prime_fasttest()\fR was added in OpenSSL 0.9.5.
275 .IX Title "BN_generate_prime 3"
276 .IX Name "BN_generate_prime, BN_is_prime, BN_is_prime_fasttest - generate primes and test for primality"
280 .IX Header "SYNOPSIS"
282 .IX Header "DESCRIPTION"
290 .IX Header "RETURN VALUES"
292 .IX Header "SEE ALSO"