File Manager

Editing File: /opt/alt/openssl/share/man/man3/BN_mod_mul_montgomery.3ssl

.\" Automatically generated by Pod::Man 4.11 (Pod::Simple 3.35)
.\"
.\" Standard preamble:
.\" ========================================================================
.de Sp \" Vertical space (when we can't use .PP)
.if t .sp .5v
.if n .sp
..
.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.  \*(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-
.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" ''
.    ds C`
.    ds C'
'br\}
.\"
.\" Escape single quotes in literal strings from groff's Unicode transform.
.ie \n(.g .ds Aq \(aq
.el       .ds Aq '
.\"
.\" If the F register is >0, we'll generate index entries on stderr for
.\" titles (.TH), headers (.SH), subsections (.SS), items (.Ip), and index
.\" entries marked with X<> in POD.  Of course, you'll have to process the
.\" output yourself in some meaningful fashion.
.\"
.\" Avoid warning from groff about undefined register 'F'.
.de IX
..
.nr rF 0
.if \n(.g .if rF .nr rF 1
.if (\n(rF:(\n(.g==0)) \{\
.    if \nF \{\
.        de IX
.        tm Index:\\$1\t\\n%\t"\\$2"
..
.        if !\nF==2 \{\
.            nr % 0
.            nr F 2
.        \}
.    \}
.\}
.rr rF
.\"
.\" Accent mark definitions (@(#)ms.acc 1.5 88/02/08 SMI; from UCB 4.2).
.\" Fear.  Run.  Save yourself.  No user-serviceable parts.
.    \" 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_mod_mul_montgomery 3"
.TH BN_mod_mul_montgomery 3 "2019-12-20" "1.0.2u" "OpenSSL"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
.\" way too many mistakes in technical documents.
.if n .ad l
.nh
.SH "NAME"
BN_mod_mul_montgomery, BN_MONT_CTX_new, BN_MONT_CTX_init,
BN_MONT_CTX_free, BN_MONT_CTX_set, BN_MONT_CTX_copy,
BN_from_montgomery, BN_to_montgomery \- Montgomery multiplication
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 1
\& #include <openssl/bn.h>
\&
\& BN_MONT_CTX *BN_MONT_CTX_new(void);
\& void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
\& void BN_MONT_CTX_free(BN_MONT_CTX *mont);
\&
\& int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *m, BN_CTX *ctx);
\& BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
\&
\& int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
\&         BN_MONT_CTX *mont, BN_CTX *ctx);
\&
\& int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
\&         BN_CTX *ctx);
\&
\& int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
\&         BN_CTX *ctx);
.Ve
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
These functions implement Montgomery multiplication. They are used
automatically when \fBBN_mod_exp\fR\|(3) is called with suitable input,
but they may be useful when several operations are to be performed
using the same modulus.
.PP
\&\fBBN_MONT_CTX_new()\fR allocates and initializes a \fB\s-1BN_MONT_CTX\s0\fR structure.
\&\fBBN_MONT_CTX_init()\fR initializes an existing uninitialized \fB\s-1BN_MONT_CTX\s0\fR.
.PP
\&\fBBN_MONT_CTX_set()\fR sets up the \fImont\fR structure from the modulus \fIm\fR
by precomputing its inverse and a value R.
.PP
\&\fBBN_MONT_CTX_copy()\fR copies the \fB\s-1BN_MONT_CTX\s0\fR \fIfrom\fR to \fIto\fR.
.PP
\&\fBBN_MONT_CTX_free()\fR frees the components of the \fB\s-1BN_MONT_CTX\s0\fR, and, if
it was created by \fBBN_MONT_CTX_new()\fR, also the structure itself.
.PP
\&\fBBN_mod_mul_montgomery()\fR computes Mont(\fIa\fR,\fIb\fR):=\fIa\fR*\fIb\fR*R^\-1 and places
the result in \fIr\fR.
.PP
\&\fBBN_from_montgomery()\fR performs the Montgomery reduction \fIr\fR = \fIa\fR*R^\-1.
.PP
\&\fBBN_to_montgomery()\fR computes Mont(\fIa\fR,R^2), i.e. \fIa\fR*R.
Note that \fIa\fR must be non-negative and smaller than the modulus.
.PP
For all functions, \fIctx\fR is a previously allocated \fB\s-1BN_CTX\s0\fR used for
temporary variables.
.PP
The \fB\s-1BN_MONT_CTX\s0\fR structure is defined as follows:
.PP
.Vb 10
\& typedef struct bn_mont_ctx_st
\&        {
\&        int ri;         /* number of bits in R */
\&        BIGNUM RR;      /* R^2 (used to convert to Montgomery form) */
\&        BIGNUM N;       /* The modulus */
\&        BIGNUM Ni;      /* R*(1/R mod N) \- N*Ni = 1
\&                         * (Ni is only stored for bignum algorithm) */
\&        BN_ULONG n0;    /* least significant word of Ni */
\&        int flags;
\&        } BN_MONT_CTX;
.Ve
.PP
\&\fBBN_to_montgomery()\fR is a macro.
.SH "RETURN VALUES"
.IX Header "RETURN VALUES"
\&\fBBN_MONT_CTX_new()\fR returns the newly allocated \fB\s-1BN_MONT_CTX\s0\fR, and \s-1NULL\s0
on error.
.PP
\&\fBBN_MONT_CTX_init()\fR and \fBBN_MONT_CTX_free()\fR have no return values.
.PP
For the other functions, 1 is returned for success, 0 on error.
The error codes can be obtained by \fBERR_get_error\fR\|(3).
.SH "WARNING"
.IX Header "WARNING"
The inputs must be reduced modulo \fBm\fR, otherwise the result will be
outside the expected range.
.SH "SEE ALSO"
.IX Header "SEE ALSO"
\&\fBbn\fR\|(3), \fBERR_get_error\fR\|(3), \fBBN_add\fR\|(3),
\&\fBBN_CTX_new\fR\|(3)
.SH "HISTORY"
.IX Header "HISTORY"
\&\fBBN_MONT_CTX_new()\fR, \fBBN_MONT_CTX_free()\fR, \fBBN_MONT_CTX_set()\fR,
\&\fBBN_mod_mul_montgomery()\fR, \fBBN_from_montgomery()\fR and \fBBN_to_montgomery()\fR
are available in all versions of SSLeay and OpenSSL.
.PP
\&\fBBN_MONT_CTX_init()\fR and \fBBN_MONT_CTX_copy()\fR were added in SSLeay 0.9.1b.

Back to Directory File Manager