22

✏️ Editing: EC_POINTs_mul.3

.\" 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 "EC_POINT_ADD 3"
.TH EC_POINT_ADD 3 "2023-09-11" "1.1.1w" "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"
EC_POINT_add, EC_POINT_dbl, EC_POINT_invert, EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp, EC_POINT_make_affine, EC_POINTs_make_affine, EC_POINTs_mul, EC_POINT_mul, EC_GROUP_precompute_mult, EC_GROUP_have_precompute_mult \- Functions for performing mathematical operations and tests on EC_POINT objects
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 1
\& #include <openssl/ec.h>
\&
\& int EC_POINT_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
\&                  const EC_POINT *b, BN_CTX *ctx);
\& int EC_POINT_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx);
\& int EC_POINT_invert(const EC_GROUP *group, EC_POINT *a, BN_CTX *ctx);
\& int EC_POINT_is_at_infinity(const EC_GROUP *group, const EC_POINT *p);
\& int EC_POINT_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx);
\& int EC_POINT_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx);
\& int EC_POINT_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx);
\& int EC_POINTs_make_affine(const EC_GROUP *group, size_t num,
\&                           EC_POINT *points[], BN_CTX *ctx);
\& int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *n, size_t num,
\&                   const EC_POINT *p[], const BIGNUM *m[], BN_CTX *ctx);
\& int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *n,
\&                  const EC_POINT *q, const BIGNUM *m, BN_CTX *ctx);
\& int EC_GROUP_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
\& int EC_GROUP_have_precompute_mult(const EC_GROUP *group);
.Ve
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
EC_POINT_add adds the two points \fBa\fR and \fBb\fR and places the result in \fBr\fR. Similarly EC_POINT_dbl doubles the point \fBa\fR and places the
result in \fBr\fR. In both cases it is valid for \fBr\fR to be one of \fBa\fR or \fBb\fR.
.PP
EC_POINT_invert calculates the inverse of the supplied point \fBa\fR. The result is placed back in \fBa\fR.
.PP
The function EC_POINT_is_at_infinity tests whether the supplied point is at infinity or not.
.PP
EC_POINT_is_on_curve tests whether the supplied point is on the curve or not.
.PP
EC_POINT_cmp compares the two supplied points and tests whether or not they are equal.
.PP
The functions EC_POINT_make_affine and EC_POINTs_make_affine force the internal representation of the \s-1EC_POINT\s0(s) into the affine
co-ordinate system. In the case of EC_POINTs_make_affine the value \fBnum\fR provides the number of points in the array \fBpoints\fR to be
forced.
.PP
EC_POINT_mul is a convenient interface to EC_POINTs_mul: it calculates the value generator * \fBn\fR + \fBq\fR * \fBm\fR and stores the result in \fBr\fR.
The value \fBn\fR may be \s-1NULL\s0 in which case the result is just \fBq\fR * \fBm\fR (variable point multiplication). Alternatively, both \fBq\fR and \fBm\fR may be \s-1NULL,\s0 and \fBn\fR non-NULL, in which case the result is just generator * \fBn\fR (fixed point multiplication).
When performing a single fixed or variable point multiplication, the underlying implementation uses a constant time algorithm, when the input scalar (either \fBn\fR or \fBm\fR) is in the range [0, ec_group_order).
.PP
EC_POINTs_mul calculates the value generator * \fBn\fR + \fBq[0]\fR * \fBm[0]\fR + ... + \fBq[num\-1]\fR * \fBm[num\-1]\fR. As for EC_POINT_mul the value \fBn\fR may be \s-1NULL\s0 or \fBnum\fR may be zero.
When performing a fixed point multiplication (\fBn\fR is non-NULL and \fBnum\fR is 0) or a variable point multiplication (\fBn\fR is \s-1NULL\s0 and \fBnum\fR is 1), the underlying implementation uses a constant time algorithm, when the input scalar (either \fBn\fR or \fBm[0]\fR) is in the range [0, ec_group_order).
.PP
The function EC_GROUP_precompute_mult stores multiples of the generator for faster point multiplication, whilst
EC_GROUP_have_precompute_mult tests whether precomputation has already been done. See \fBEC_GROUP_copy\fR\|(3) for information
about the generator.
.SH "RETURN VALUES"
.IX Header "RETURN VALUES"
The following functions return 1 on success or 0 on error: EC_POINT_add, EC_POINT_dbl, EC_POINT_invert, EC_POINT_make_affine,
EC_POINTs_make_affine, EC_POINTs_make_affine, EC_POINT_mul, EC_POINTs_mul and EC_GROUP_precompute_mult.
.PP
EC_POINT_is_at_infinity returns 1 if the point is at infinity, or 0 otherwise.
.PP
EC_POINT_is_on_curve returns 1 if the point is on the curve, 0 if not, or \-1 on error.
.PP
EC_POINT_cmp returns 1 if the points are not equal, 0 if they are, or \-1 on error.
.PP
EC_GROUP_have_precompute_mult return 1 if a precomputation has been done, or 0 if not.
.SH "SEE ALSO"
.IX Header "SEE ALSO"
\&\fBcrypto\fR\|(7), \fBEC_GROUP_new\fR\|(3), \fBEC_GROUP_copy\fR\|(3),
\&\fBEC_POINT_new\fR\|(3), \fBEC_KEY_new\fR\|(3),
\&\fBEC_GFp_simple_method\fR\|(3), \fBd2i_ECPKParameters\fR\|(3)
.SH "COPYRIGHT"
.IX Header "COPYRIGHT"
Copyright 2013\-2018 The OpenSSL Project Authors. All Rights Reserved.
.PP
Licensed under the OpenSSL license (the \*(L"License\*(R").  You may not use
this file except in compliance with the License.  You can obtain a copy
in the file \s-1LICENSE\s0 in the source distribution or at
<https://www.openssl.org/source/license.html>.

MR SKB