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.IX Title "Math::Prime::Util::ECProjectivePoint 3pm"
.TH Math::Prime::Util::ECProjectivePoint 3pm 2024-03-07 "perl v5.38.2" "User Contributed Perl Documentation"
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.SH NAME
Math::Prime::Util::ECProjectivePoint \- Elliptic curve operations for projective points
.SH VERSION
.IX Header "VERSION"
Version 0.73
.SH SYNOPSIS
.IX Header "SYNOPSIS"
.Vb 2
\&  # Create a point on a curve (a,b,n) with coordinates 0,1
\&  my $ECP = Math::Prime::Util::ECProjectivePoint\->new($c, $n, 0, 1);
\&
\&  # scalar multiplication by $k.
\&  $ECP\->mul($k);
\&
\&  # add two points on the same curve
\&  $ECP\->add($ECP2);
\&
\&  say "P = O" if $ECP\->is_infinity();
.Ve
.SH DESCRIPTION
.IX Header "DESCRIPTION"
This really should just be in Math::EllipticCurve.
.PP
To write.
.SH FUNCTIONS
.IX Header "FUNCTIONS"
.SS new
.IX Subsection "new"
.Vb 1
\&  $point = Math::Prime::Util::ECProjectivePoint\->new(c, n, x, z);
.Ve
.PP
Returns a new point on the curve defined by the Montgomery parameter c.
.SS c
.IX Subsection "c"
.SS n
.IX Subsection "n"
Returns the \f(CW\*(C`c\*(C'\fR, \f(CW\*(C`d\*(C'\fR, or \f(CW\*(C`n\*(C'\fR values that describe the curve.
.SS d
.IX Subsection "d"
Returns the precalculated value of \f(CW\*(C`int( (c + 2) / 4 )\*(C'\fR.
.SS x
.IX Subsection "x"
.SS z
.IX Subsection "z"
Returns the \f(CW\*(C`x\*(C'\fR or \f(CW\*(C`z\*(C'\fR values that define the point on the curve.
.SS f
.IX Subsection "f"
Returns a possible factor found after "normalize".
.SS add
.IX Subsection "add"
Takes another point on the same curve as an argument and adds it this point.
.SS double
.IX Subsection "double"
Double the current point on the curve.
.SS mul
.IX Subsection "mul"
Takes an integer and performs scalar multiplication of the point.
.SS is_infinity
.IX Subsection "is_infinity"
Returns true if the point is (0,1), which is the point at infinity for
the affine coordinates.
.SS copy
.IX Subsection "copy"
Returns a copy of the point.
.SS normalize
.IX Subsection "normalize"
Performs an extended GCD operation to make \f(CW\*(C`z=1\*(C'\fR.  If a factor of \f(CW\*(C`n\*(C'\fR is
found it is put in \f(CW\*(C`f\*(C'\fR.
.SH "SEE ALSO"
.IX Header "SEE ALSO"
Math::EllipticCurve::Prime
.PP
This really should just be in a Math::EllipticCurve module.
.SH AUTHORS
.IX Header "AUTHORS"
Dana Jacobsen <dana@acm.org>
.SH COPYRIGHT
.IX Header "COPYRIGHT"
Copyright 2012\-2013 by Dana Jacobsen <dana@acm.org>
.PP
This program is free software; you can redistribute it and/or modify it under the same terms as Perl itself.