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_add 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_add, BN_sub, BN_mul, BN_sqr, BN_div, BN_mod, BN_nnmod, BN_mod_add,
192 BN_mod_sub, BN_mod_mul, BN_mod_sqr, BN_exp, BN_mod_exp, BN_gcd \-
193 arithmetic operations on BIGNUMs
197 \& #include <openssl/bn.h>
200 \& int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
203 \& int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
206 \& int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
209 \& int BN_sqr(BIGNUM *r, BIGNUM *a, BN_CTX *ctx);
212 \& int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *a, const BIGNUM *d,
216 \& int BN_mod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
219 \& int BN_nnmod(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
222 \& int BN_mod_add(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
226 \& int BN_mod_sub(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
230 \& int BN_mod_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
234 \& int BN_mod_sqr(BIGNUM *r, BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
237 \& int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx);
240 \& int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p,
241 \& const BIGNUM *m, BN_CTX *ctx);
244 \& int BN_gcd(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
247 \fIBN_add()\fR adds \fIa\fR and \fIb\fR and places the result in \fIr\fR (\f(CWr=a+b\fR).
248 \fIr\fR may be the same \fBBIGNUM\fR as \fIa\fR or \fIb\fR.
250 \fIBN_sub()\fR subtracts \fIb\fR from \fIa\fR and places the result in \fIr\fR (\f(CWr=a-b\fR).
252 \fIBN_mul()\fR multiplies \fIa\fR and \fIb\fR and places the result in \fIr\fR (\f(CWr=a*b\fR).
253 \fIr\fR may be the same \fBBIGNUM\fR as \fIa\fR or \fIb\fR.
254 For multiplication by powers of 2, use BN_lshift(3).
256 \fIBN_sqr()\fR takes the square of \fIa\fR and places the result in \fIr\fR
257 (\f(CWr=a^2\fR). \fIr\fR and \fIa\fR may be the same \fBBIGNUM\fR.
258 This function is faster than \fIBN_mul\fR\|(r,a,a).
260 \fIBN_div()\fR divides \fIa\fR by \fId\fR and places the result in \fIdv\fR and the
261 remainder in \fIrem\fR (\f(CWdv=a/d, rem=a%d\fR). Either of \fIdv\fR and \fIrem\fR may
262 be \fBNULL\fR, in which case the respective value is not returned.
263 The result is rounded towards zero; thus if \fIa\fR is negative, the
264 remainder will be zero or negative.
265 For division by powers of 2, use \fIBN_rshift\fR\|(3).
267 \fIBN_mod()\fR corresponds to \fIBN_div()\fR with \fIdv\fR set to \fBNULL\fR.
269 \fIBN_nnmod()\fR reduces \fIa\fR modulo \fIm\fR and places the non-negative
270 remainder in \fIr\fR.
272 \fIBN_mod_add()\fR adds \fIa\fR to \fIb\fR modulo \fIm\fR and places the non-negative
275 \fIBN_mod_sub()\fR subtracts \fIb\fR from \fIa\fR modulo \fIm\fR and places the
276 non-negative result in \fIr\fR.
278 \fIBN_mod_mul()\fR multiplies \fIa\fR by \fIb\fR and finds the non-negative
279 remainder respective to modulus \fIm\fR (\f(CWr=(a*b) mod m\fR). \fIr\fR may be
280 the same \fBBIGNUM\fR as \fIa\fR or \fIb\fR. For more efficient algorithms for
281 repeated computations using the same modulus, see
282 BN_mod_mul_montgomery(3) and
283 BN_mod_mul_reciprocal(3).
285 \fIBN_mod_sqr()\fR takes the square of \fIa\fR modulo \fBm\fR and places the
288 \fIBN_exp()\fR raises \fIa\fR to the \fIp\fR\-th power and places the result in \fIr\fR
289 (\f(CWr=a^p\fR). This function is faster than repeated applications of
292 \fIBN_mod_exp()\fR computes \fIa\fR to the \fIp\fR\-th power modulo \fIm\fR (\f(CWr=a^p %
293 m\fR). This function uses less time and space than \fIBN_exp()\fR.
295 \fIBN_gcd()\fR computes the greatest common divisor of \fIa\fR and \fIb\fR and
296 places the result in \fIr\fR. \fIr\fR may be the same \fBBIGNUM\fR as \fIa\fR or
299 For all functions, \fIctx\fR is a previously allocated \fBBN_CTX\fR used for
300 temporary variables; see BN_CTX_new(3).
302 Unless noted otherwise, the result \fBBIGNUM\fR must be different from
305 For all functions, 1 is returned for success, 0 on error. The return
306 value should always be checked (e.g., \f(CWif (!BN_add(r,a,b)) goto err;\fR).
307 The error codes can be obtained by ERR_get_error(3).
309 bn(3), ERR_get_error(3), BN_CTX_new(3),
310 BN_add_word(3), BN_set_bit(3)
312 \fIBN_add()\fR, \fIBN_sub()\fR, \fIBN_sqr()\fR, \fIBN_div()\fR, \fIBN_mod()\fR, \fIBN_mod_mul()\fR,
313 \fIBN_mod_exp()\fR and \fIBN_gcd()\fR are available in all versions of SSLeay and
314 OpenSSL. The \fIctx\fR argument to \fIBN_mul()\fR was added in SSLeay
315 0.9.1b. \fIBN_exp()\fR appeared in SSLeay 0.9.0.
316 \fIBN_nnmod()\fR, \fIBN_mod_add()\fR, \fIBN_mod_sub()\fR, and \fIBN_mod_sqr()\fR were added in
321 .IX Name "BN_add, BN_sub, BN_mul, BN_sqr, BN_div, BN_mod, BN_nnmod, BN_mod_add,
322 BN_mod_sub, BN_mod_mul, BN_mod_sqr, BN_exp, BN_mod_exp, BN_gcd - arithmetic operations on BIGNUMs"
326 .IX Header "SYNOPSIS"
328 .IX Header "DESCRIPTION"
330 .IX Header "RETURN VALUES"
332 .IX Header "SEE ALSO"