1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
|
.\" Automatically generated by Pod::Man version 1.15
.\" Thu May 9 13:16:18 2002
.\"
.\" Standard preamble:
.\" ======================================================================
.de Sh \" Subsection heading
.br
.if t .Sp
.ne 5
.PP
\fB\\$1\fR
.PP
..
.de Sp \" Vertical space (when we can't use .PP)
.if t .sp .5v
.if n .sp
..
.de Ip \" List item
.br
.ie \\n(.$>=3 .ne \\$3
.el .ne 3
.IP "\\$1" \\$2
..
.de Vb \" Begin verbatim text
.ft CW
.nf
.ne \\$1
..
.de Ve \" End verbatim text
.ft R
.fi
..
.\" Set up some character translations and predefined strings. \*(-- will
.\" give an unbreakable dash, \*(PI will give pi, \*(L" will give a left
.\" double quote, and \*(R" will give a right double quote. | will give a
.\" real vertical bar. \*(C+ will give a nicer C++. Capital omega is used
.\" to do unbreakable dashes and therefore won't be available. \*(C` and
.\" \*(C' expand to `' in nroff, nothing in troff, for use with C<>
.tr \(*W-|\(bv\*(Tr
.ds C+ C\v'-.1v'\h'-1p'\s-2+\h'-1p'+\s0\v'.1v'\h'-1p'
.ie n \{\
. ds -- \(*W-
. ds PI pi
. if (\n(.H=4u)&(1m=24u) .ds -- \(*W\h'-12u'\(*W\h'-12u'-\" diablo 10 pitch
. if (\n(.H=4u)&(1m=20u) .ds -- \(*W\h'-12u'\(*W\h'-8u'-\" diablo 12 pitch
. ds L" ""
. ds R" ""
. ds C` ""
. ds C' ""
'br\}
.el\{\
. ds -- \|\(em\|
. ds PI \(*p
. ds L" ``
. ds R" ''
'br\}
.\"
.\" If the F register is turned on, we'll generate index entries on stderr
.\" for titles (.TH), headers (.SH), subsections (.Sh), items (.Ip), and
.\" index entries marked with X<> in POD. Of course, you'll have to process
.\" the output yourself in some meaningful fashion.
.if \nF \{\
. de IX
. tm Index:\\$1\t\\n%\t"\\$2"
..
. nr % 0
. rr F
.\}
.\"
.\" For nroff, turn off justification. Always turn off hyphenation; it
.\" makes way too many mistakes in technical documents.
.hy 0
.if n .na
.\"
.\" Accent mark definitions (@(#)ms.acc 1.5 88/02/08 SMI; from UCB 4.2).
.\" Fear. Run. Save yourself. No user-serviceable parts.
.bd B 3
. \" fudge factors for nroff and troff
.if n \{\
. ds #H 0
. ds #V .8m
. ds #F .3m
. ds #[ \f1
. ds #] \fP
.\}
.if t \{\
. ds #H ((1u-(\\\\n(.fu%2u))*.13m)
. ds #V .6m
. ds #F 0
. ds #[ \&
. ds #] \&
.\}
. \" simple accents for nroff and troff
.if n \{\
. ds ' \&
. ds ` \&
. ds ^ \&
. ds , \&
. ds ~ ~
. ds /
.\}
.if t \{\
. ds ' \\k:\h'-(\\n(.wu*8/10-\*(#H)'\'\h"|\\n:u"
. ds ` \\k:\h'-(\\n(.wu*8/10-\*(#H)'\`\h'|\\n:u'
. ds ^ \\k:\h'-(\\n(.wu*10/11-\*(#H)'^\h'|\\n:u'
. ds , \\k:\h'-(\\n(.wu*8/10)',\h'|\\n:u'
. ds ~ \\k:\h'-(\\n(.wu-\*(#H-.1m)'~\h'|\\n:u'
. ds / \\k:\h'-(\\n(.wu*8/10-\*(#H)'\z\(sl\h'|\\n:u'
.\}
. \" troff and (daisy-wheel) nroff accents
.ds : \\k:\h'-(\\n(.wu*8/10-\*(#H+.1m+\*(#F)'\v'-\*(#V'\z.\h'.2m+\*(#F'.\h'|\\n:u'\v'\*(#V'
.ds 8 \h'\*(#H'\(*b\h'-\*(#H'
.ds o \\k:\h'-(\\n(.wu+\w'\(de'u-\*(#H)/2u'\v'-.3n'\*(#[\z\(de\v'.3n'\h'|\\n:u'\*(#]
.ds d- \h'\*(#H'\(pd\h'-\w'~'u'\v'-.25m'\f2\(hy\fP\v'.25m'\h'-\*(#H'
.ds D- D\\k:\h'-\w'D'u'\v'-.11m'\z\(hy\v'.11m'\h'|\\n:u'
.ds th \*(#[\v'.3m'\s+1I\s-1\v'-.3m'\h'-(\w'I'u*2/3)'\s-1o\s+1\*(#]
.ds Th \*(#[\s+2I\s-2\h'-\w'I'u*3/5'\v'-.3m'o\v'.3m'\*(#]
.ds ae a\h'-(\w'a'u*4/10)'e
.ds Ae A\h'-(\w'A'u*4/10)'E
. \" corrections for vroff
.if v .ds ~ \\k:\h'-(\\n(.wu*9/10-\*(#H)'\s-2\u~\d\s+2\h'|\\n:u'
.if v .ds ^ \\k:\h'-(\\n(.wu*10/11-\*(#H)'\v'-.4m'^\v'.4m'\h'|\\n:u'
. \" for low resolution devices (crt and lpr)
.if \n(.H>23 .if \n(.V>19 \
\{\
. ds : e
. ds 8 ss
. ds o a
. ds d- d\h'-1'\(ga
. ds D- D\h'-1'\(hy
. ds th \o'bp'
. ds Th \o'LP'
. ds ae ae
. ds Ae AE
.\}
.rm #[ #] #H #V #F C
.\" ======================================================================
.\"
.IX Title "BN_ADD 1"
.TH BN_ADD 1 "perl v5.6.1" "2000-04-13" "User Contributed Perl Documentation"
.UC
.SH "NAME"
BN_add, BN_sub, BN_mul, BN_div, BN_sqr, BN_mod, BN_mod_mul, BN_exp,
BN_mod_exp, BN_gcd \- arithmetic operations on BIGNUMs
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 1
\& #include <openssl/bn.h>
.Ve
.Vb 1
\& int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
.Ve
.Vb 1
\& int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
.Ve
.Vb 1
\& int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
.Ve
.Vb 2
\& int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *a, const BIGNUM *d,
\& BN_CTX *ctx);
.Ve
.Vb 1
\& int BN_sqr(BIGNUM *r, BIGNUM *a, BN_CTX *ctx);
.Ve
.Vb 1
\& int BN_mod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
.Ve
.Vb 2
\& int BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
\& BN_CTX *ctx);
.Ve
.Vb 1
\& int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx);
.Ve
.Vb 2
\& int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p,
\& const BIGNUM *m, BN_CTX *ctx);
.Ve
.Vb 1
\& int BN_gcd(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
.Ve
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
\&\fIBN_add()\fR adds \fBa\fR and \fBb\fR and places the result in \fBr\fR (\f(CW\*(C`r=a+b\*(C'\fR).
\&\fBr\fR may be the same \fB\s-1BIGNUM\s0\fR as \fBa\fR or \fBb\fR.
.PP
\&\fIBN_sub()\fR subtracts \fBb\fR from \fBa\fR and places the result in \fBr\fR (\f(CW\*(C`r=a\-b\*(C'\fR).
.PP
\&\fIBN_mul()\fR multiplies \fBa\fR and \fBb\fR and places the result in \fBr\fR (\f(CW\*(C`r=a*b\*(C'\fR).
\&\fBr\fR may be the same \fB\s-1BIGNUM\s0\fR as \fBa\fR or \fBb\fR.
For multiplication by powers of 2, use BN_lshift(3).
.PP
\&\fIBN_div()\fR divides \fBa\fR by \fBd\fR and places the result in \fBdv\fR and the
remainder in \fBrem\fR (\f(CW\*(C`dv=a/d, rem=a%d\*(C'\fR). Either of \fBdv\fR and \fBrem\fR may
be \s-1NULL\s0, in which case the respective value is not returned.
For division by powers of 2, use \fIBN_rshift\fR\|(3).
.PP
\&\fIBN_sqr()\fR takes the square of \fBa\fR and places the result in \fBr\fR
(\f(CW\*(C`r=a^2\*(C'\fR). \fBr\fR and \fBa\fR may be the same \fB\s-1BIGNUM\s0\fR.
This function is faster than BN_mul(r,a,a).
.PP
\&\fIBN_mod()\fR find the remainder of \fBa\fR divided by \fBm\fR and places it in
\&\fBrem\fR (\f(CW\*(C`rem=a%m\*(C'\fR).
.PP
\&\fIBN_mod_mul()\fR multiplies \fBa\fR by \fBb\fR and finds the remainder when
divided by \fBm\fR (\f(CW\*(C`r=(a*b)%m\*(C'\fR). \fBr\fR may be the same \fB\s-1BIGNUM\s0\fR as \fBa\fR
or \fBb\fR. For a more efficient algorithm, see
BN_mod_mul_montgomery(3); for repeated
computations using the same modulus, see BN_mod_mul_reciprocal(3).
.PP
\&\fIBN_exp()\fR raises \fBa\fR to the \fBp\fR\-th power and places the result in \fBr\fR
(\f(CW\*(C`r=a^p\*(C'\fR). This function is faster than repeated applications of
\&\fIBN_mul()\fR.
.PP
\&\fIBN_mod_exp()\fR computes \fBa\fR to the \fBp\fR\-th power modulo \fBm\fR (\f(CW\*(C`r=a^p %
m\*(C'\fR). This function uses less time and space than \fIBN_exp()\fR.
.PP
\&\fIBN_gcd()\fR computes the greatest common divisor of \fBa\fR and \fBb\fR and
places the result in \fBr\fR. \fBr\fR may be the same \fB\s-1BIGNUM\s0\fR as \fBa\fR or
\&\fBb\fR.
.PP
For all functions, \fBctx\fR is a previously allocated \fB\s-1BN_CTX\s0\fR used for
temporary variables; see BN_CTX_new(3).
.PP
Unless noted otherwise, the result \fB\s-1BIGNUM\s0\fR must be different from
the arguments.
.SH "RETURN VALUES"
.IX Header "RETURN VALUES"
For all functions, 1 is returned for success, 0 on error. The return
value should always be checked (e.g., \f(CW\*(C`if (!BN_add(r,a,b)) goto err;\*(C'\fR).
The error codes can be obtained by ERR_get_error(3).
.SH "SEE ALSO"
.IX Header "SEE ALSO"
bn(3), err(3), BN_CTX_new(3),
BN_add_word(3), BN_set_bit(3)
.SH "HISTORY"
.IX Header "HISTORY"
\&\fIBN_add()\fR, \fIBN_sub()\fR, \fIBN_div()\fR, \fIBN_sqr()\fR, \fIBN_mod()\fR, \fIBN_mod_mul()\fR,
\&\fIBN_mod_exp()\fR and \fIBN_gcd()\fR are available in all versions of SSLeay and
OpenSSL. The \fBctx\fR argument to \fIBN_mul()\fR was added in SSLeay
0.9.1b. \fIBN_exp()\fR appeared in SSLeay 0.9.0.
|
