305 lines
8.2 KiB
Groff
305 lines
8.2 KiB
Groff
.rn '' }`
|
|
'''
|
|
'''
|
|
.de Sh
|
|
.br
|
|
.if t .Sp
|
|
.ne 5
|
|
.PP
|
|
\fB\\$1\fR
|
|
.PP
|
|
..
|
|
.de Sp
|
|
.if t .sp .5v
|
|
.if n .sp
|
|
..
|
|
.de Ip
|
|
.br
|
|
.ie \\n(.$>=3 .ne \\$3
|
|
.el .ne 3
|
|
.IP "\\$1" \\$2
|
|
..
|
|
.de Vb
|
|
.ft CW
|
|
.nf
|
|
.ne \\$1
|
|
..
|
|
.de Ve
|
|
.ft R
|
|
|
|
.fi
|
|
..
|
|
'''
|
|
'''
|
|
''' Set up \*(-- to give an unbreakable dash;
|
|
''' string Tr holds user defined translation string.
|
|
''' Bell System Logo is used as a dummy character.
|
|
'''
|
|
.tr \(*W-|\(bv\*(Tr
|
|
.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" ""
|
|
''' \*(M", \*(S", \*(N" and \*(T" are the equivalent of
|
|
''' \*(L" and \*(R", except that they are used on ".xx" lines,
|
|
''' such as .IP and .SH, which do another additional levels of
|
|
''' double-quote interpretation
|
|
.ds M" """
|
|
.ds S" """
|
|
.ds N" """""
|
|
.ds T" """""
|
|
.ds L' '
|
|
.ds R' '
|
|
.ds M' '
|
|
.ds S' '
|
|
.ds N' '
|
|
.ds T' '
|
|
'br\}
|
|
.el\{\
|
|
.ds -- \(em\|
|
|
.tr \*(Tr
|
|
.ds L" ``
|
|
.ds R" ''
|
|
.ds M" ``
|
|
.ds S" ''
|
|
.ds N" ``
|
|
.ds T" ''
|
|
.ds L' `
|
|
.ds R' '
|
|
.ds M' `
|
|
.ds S' '
|
|
.ds N' `
|
|
.ds T' '
|
|
.ds PI \(*p
|
|
'br\}
|
|
.\" If the F register is turned on, we'll generate
|
|
.\" index entries out stderr for the following things:
|
|
.\" TH Title
|
|
.\" SH Header
|
|
.\" Sh Subsection
|
|
.\" Ip Item
|
|
.\" X<> Xref (embedded
|
|
.\" Of course, you have to process the output yourself
|
|
.\" in some meaninful fashion.
|
|
.if \nF \{
|
|
.de IX
|
|
.tm Index:\\$1\t\\n%\t"\\$2"
|
|
..
|
|
.nr % 0
|
|
.rr F
|
|
.\}
|
|
.TH BN_add 3 "0.9.5a" "22/Jul/2000" "OpenSSL"
|
|
.UC
|
|
.if n .hy 0
|
|
.if n .na
|
|
.ds C+ C\v'-.1v'\h'-1p'\s-2+\h'-1p'+\s0\v'.1v'\h'-1p'
|
|
.de CQ \" put $1 in typewriter font
|
|
.ft CW
|
|
'if n "\c
|
|
'if t \\&\\$1\c
|
|
'if n \\&\\$1\c
|
|
'if n \&"
|
|
\\&\\$2 \\$3 \\$4 \\$5 \\$6 \\$7
|
|
'.ft R
|
|
..
|
|
.\" @(#)ms.acc 1.5 88/02/08 SMI; from UCB 4.2
|
|
. \" AM - accent mark definitions
|
|
.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 ? ?
|
|
. ds ! !
|
|
. ds /
|
|
. ds q
|
|
.\}
|
|
.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 ? \s-2c\h'-\w'c'u*7/10'\u\h'\*(#H'\zi\d\s+2\h'\w'c'u*8/10'
|
|
. ds ! \s-2\(or\s+2\h'-\w'\(or'u'\v'-.8m'.\v'.8m'
|
|
. ds / \\k:\h'-(\\n(.wu*8/10-\*(#H)'\z\(sl\h'|\\n:u'
|
|
. 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'
|
|
.\}
|
|
. \" 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 v \\k:\h'-(\\n(.wu*9/10-\*(#H)'\v'-\*(#V'\*(#[\s-4v\s0\v'\*(#V'\h'|\\n:u'\*(#]
|
|
.ds _ \\k:\h'-(\\n(.wu*9/10-\*(#H+(\*(#F*2/3))'\v'-.4m'\z\(hy\v'.4m'\h'|\\n:u'
|
|
.ds . \\k:\h'-(\\n(.wu*8/10)'\v'\*(#V*4/10'\z.\v'-\*(#V*4/10'\h'|\\n:u'
|
|
.ds 3 \*(#[\v'.2m'\s-2\&3\s0\v'-.2m'\*(#]
|
|
.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
|
|
.ds oe o\h'-(\w'o'u*4/10)'e
|
|
.ds Oe O\h'-(\w'O'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 v \h'-1'\o'\(aa\(ga'
|
|
. ds _ \h'-1'^
|
|
. ds . \h'-1'.
|
|
. ds 3 3
|
|
. 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
|
|
. ds oe oe
|
|
. ds Oe OE
|
|
.\}
|
|
.rm #[ #] #H #V #F C
|
|
.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 "LIBRARY"
|
|
libcrypto, -lcrypto
|
|
.SH "SYNOPSIS"
|
|
.PP
|
|
.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"
|
|
\fIBN_add()\fR adds \fBa\fR and \fBb\fR and places the result in \fBr\fR (\f(CWr=a+b\fR).
|
|
\fBr\fR may be the same \fBBIGNUM\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(CWr=a-b\fR).
|
|
.PP
|
|
\fIBN_mul()\fR multiplies \fBa\fR and \fBb\fR and places the result in \fBr\fR (\f(CWr=a*b\fR).
|
|
\fBr\fR may be the same \fBBIGNUM\fR as \fBa\fR or \fBb\fR.
|
|
For multiplication by powers of 2, use the \fIBN_lshift(3)|BN_lshift(3)\fR manpage.
|
|
.PP
|
|
\fIBN_div()\fR divides \fBa\fR by \fBd\fR and places the result in \fBdv\fR and the
|
|
remainder in \fBrem\fR (\f(CWdv=a/d, rem=a%d\fR). Either of \fBdv\fR and \fBrem\fR may
|
|
be NULL, 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(CWr=a^2\fR). \fBr\fR and \fBa\fR may be the same \fBBIGNUM\fR.
|
|
This function is faster than \fIBN_mul\fR\|(r,a,a).
|
|
.PP
|
|
\fIBN_mod()\fR find the remainder of \fBa\fR divided by \fBm\fR and places it in
|
|
\fBrem\fR (\f(CWrem=a%m\fR).
|
|
.PP
|
|
\fIBN_mod_mul()\fR multiplies \fBa\fR by \fBb\fR and finds the remainder when
|
|
divided by \fBm\fR (\f(CWr=(a*b)%m\fR). \fBr\fR may be the same \fBBIGNUM\fR as \fBa\fR
|
|
or \fBb\fR. For a more efficient algorithm, see
|
|
the \fIBN_mod_mul_montgomery(3)|BN_mod_mul_montgomery(3)\fR manpage; for repeated
|
|
computations using the same modulus, see the \fIBN_mod_mul_reciprocal(3)|BN_mod_mul_reciprocal(3)\fR manpage.
|
|
.PP
|
|
\fIBN_exp()\fR raises \fBa\fR to the \fBp\fR\-th power and places the result in \fBr\fR
|
|
(\f(CWr=a^p\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(CWr=a^p %
|
|
m\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 \fBBIGNUM\fR as \fBa\fR or
|
|
\fBb\fR.
|
|
.PP
|
|
For all functions, \fBctx\fR is a previously allocated \fBBN_CTX\fR used for
|
|
temporary variables; see the \fIBN_CTX_new(3)|BN_CTX_new(3)\fR manpage.
|
|
.PP
|
|
Unless noted otherwise, the result \fBBIGNUM\fR must be different from
|
|
the arguments.
|
|
.SH "RETURN VALUES"
|
|
For all functions, 1 is returned for success, 0 on error. The return
|
|
value should always be checked (e.g., \f(CWif (!BN_add(r,a,b)) goto err;\fR).
|
|
The error codes can be obtained by the \fIERR_get_error(3)|ERR_get_error(3)\fR manpage.
|
|
.SH "SEE ALSO"
|
|
the \fIbn(3)|bn(3)\fR manpage, the \fIerr(3)|err(3)\fR manpage, the \fIBN_CTX_new(3)|BN_CTX_new(3)\fR manpage,
|
|
the \fIBN_add_word(3)|BN_add_word(3)\fR manpage, the \fIBN_set_bit(3)|BN_set_bit(3)\fR manpage
|
|
.SH "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.
|
|
|
|
.rn }` ''
|
|
.IX Title "BN_add 3"
|
|
.IX 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"
|
|
|
|
.IX Header "NAME"
|
|
|
|
.IX Header "SYNOPSIS"
|
|
|
|
.IX Header "DESCRIPTION"
|
|
|
|
.IX Header "RETURN VALUES"
|
|
|
|
.IX Header "SEE ALSO"
|
|
|
|
.IX Header "HISTORY"
|
|
|