279 lines
8.8 KiB
Groff
279 lines
8.8 KiB
Groff
.\" $NetBSD: BN_add.3,v 1.12 2003/07/24 14:16:37 itojun Exp $
|
|
.\"
|
|
.\" Automatically generated by Pod::Man version 1.02
|
|
.\" Thu Jul 24 13:07:51 2003
|
|
.\"
|
|
.\" 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 3"
|
|
.TH BN_add 3 "0.9.7b" "2002-09-25" "OpenSSL"
|
|
.UC
|
|
.SH "NAME"
|
|
BN_add, BN_sub, BN_mul, BN_sqr, BN_div, BN_mod, BN_nnmod, BN_mod_add,
|
|
BN_mod_sub, BN_mod_mul, BN_mod_sqr, BN_exp, BN_mod_exp, BN_gcd \-
|
|
arithmetic operations on BIGNUMs
|
|
.SH "LIBRARY"
|
|
libcrypto, -lcrypto
|
|
.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 1
|
|
\& int BN_sqr(BIGNUM *r, BIGNUM *a, 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_mod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
|
|
.Ve
|
|
.Vb 1
|
|
\& int BN_nnmod(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
|
|
.Ve
|
|
.Vb 2
|
|
\& int BN_mod_add(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
|
|
\& BN_CTX *ctx);
|
|
.Ve
|
|
.Vb 2
|
|
\& int BN_mod_sub(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
|
|
\& BN_CTX *ctx);
|
|
.Ve
|
|
.Vb 2
|
|
\& int BN_mod_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
|
|
\& BN_CTX *ctx);
|
|
.Ve
|
|
.Vb 1
|
|
\& int BN_mod_sqr(BIGNUM *r, BIGNUM *a, 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 \fIa\fR and \fIb\fR and places the result in \fIr\fR (\f(CW\*(C`r=a+b\*(C'\fR).
|
|
\&\fIr\fR may be the same \fB\s-1BIGNUM\s0\fR as \fIa\fR or \fIb\fR.
|
|
.PP
|
|
\&\fIBN_sub()\fR subtracts \fIb\fR from \fIa\fR and places the result in \fIr\fR (\f(CW\*(C`r=a\-b\*(C'\fR).
|
|
.PP
|
|
\&\fIBN_mul()\fR multiplies \fIa\fR and \fIb\fR and places the result in \fIr\fR (\f(CW\*(C`r=a*b\*(C'\fR).
|
|
\&\fIr\fR may be the same \fB\s-1BIGNUM\s0\fR as \fIa\fR or \fIb\fR.
|
|
For multiplication by powers of 2, use BN_lshift(3).
|
|
.PP
|
|
\&\fIBN_sqr()\fR takes the square of \fIa\fR and places the result in \fIr\fR
|
|
(\f(CW\*(C`r=a^2\*(C'\fR). \fIr\fR and \fIa\fR may be the same \fB\s-1BIGNUM\s0\fR.
|
|
This function is faster than BN_mul(r,a,a).
|
|
.PP
|
|
\&\fIBN_div()\fR divides \fIa\fR by \fId\fR and places the result in \fIdv\fR and the
|
|
remainder in \fIrem\fR (\f(CW\*(C`dv=a/d, rem=a%d\*(C'\fR). Either of \fIdv\fR and \fIrem\fR may
|
|
be \fB\s-1NULL\s0\fR, in which case the respective value is not returned.
|
|
The result is rounded towards zero; thus if \fIa\fR is negative, the
|
|
remainder will be zero or negative.
|
|
For division by powers of 2, use \fIBN_rshift\fR\|(3).
|
|
.PP
|
|
\&\fIBN_mod()\fR corresponds to \fIBN_div()\fR with \fIdv\fR set to \fB\s-1NULL\s0\fR.
|
|
.PP
|
|
\&\fIBN_nnmod()\fR reduces \fIa\fR modulo \fIm\fR and places the non-negative
|
|
remainder in \fIr\fR.
|
|
.PP
|
|
\&\fIBN_mod_add()\fR adds \fIa\fR to \fIb\fR modulo \fIm\fR and places the non-negative
|
|
result in \fIr\fR.
|
|
.PP
|
|
\&\fIBN_mod_sub()\fR subtracts \fIb\fR from \fIa\fR modulo \fIm\fR and places the
|
|
non-negative result in \fIr\fR.
|
|
.PP
|
|
\&\fIBN_mod_mul()\fR multiplies \fIa\fR by \fIb\fR and finds the non-negative
|
|
remainder respective to modulus \fIm\fR (\f(CW\*(C`r=(a*b) mod m\*(C'\fR). \fIr\fR may be
|
|
the same \fB\s-1BIGNUM\s0\fR as \fIa\fR or \fIb\fR. For more efficient algorithms for
|
|
repeated computations using the same modulus, see
|
|
BN_mod_mul_montgomery(3) and
|
|
BN_mod_mul_reciprocal(3).
|
|
.PP
|
|
\&\fIBN_mod_sqr()\fR takes the square of \fIa\fR modulo \fBm\fR and places the
|
|
result in \fIr\fR.
|
|
.PP
|
|
\&\fIBN_exp()\fR raises \fIa\fR to the \fIp\fR\-th power and places the result in \fIr\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 \fIa\fR to the \fIp\fR\-th power modulo \fIm\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 \fIa\fR and \fIb\fR and
|
|
places the result in \fIr\fR. \fIr\fR may be the same \fB\s-1BIGNUM\s0\fR as \fIa\fR or
|
|
\&\fIb\fR.
|
|
.PP
|
|
For all functions, \fIctx\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"
|
|
openssl_bn(3), ERR_get_error(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_sqr()\fR, \fIBN_div()\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 \fIctx\fR argument to \fIBN_mul()\fR was added in SSLeay
|
|
0.9.1b. \fIBN_exp()\fR appeared in SSLeay 0.9.0.
|
|
\&\fIBN_nnmod()\fR, \fIBN_mod_add()\fR, \fIBN_mod_sub()\fR, and \fIBN_mod_sqr()\fR were added in
|
|
OpenSSL 0.9.7.
|