Math::Prime::Util::ECProjectivePoint - Elliptic curve operations for projective points

Authors

       Dana Jacobsen <dana@acm.org>

Copyright

       Copyright 2012-2013 by Dana Jacobsen <dana@acm.org>

       This program is free software; you can redistribute it and/or modify it under the same terms as Perl
       itself.

perl v5.40.0                                       2024-10-20             Math::Prime::Ut...ProjectivePoint(3pm)

Description

       This really should just be in Math::EllipticCurve.

       To write.

Functions

new
         $point = Math::Prime::Util::ECProjectivePoint->new(c, n, x, z);

       Returns a new point on the curve defined by the Montgomery parameter c.

   cn
       Returns the "c", "d", or "n" values that describe the curve.

   d
       Returns the precalculated value of "int( (c + 2) / 4 )".

   xz
       Returns the "x" or "z" values that define the point on the curve.

   f
       Returns a possible factor found after "normalize".

   add
       Takes another point on the same curve as an argument and adds it this point.

   double
       Double the current point on the curve.

   mul
       Takes an integer and performs scalar multiplication of the point.

   is_infinity
       Returns true if the point is (0,1), which is the point at infinity for the affine coordinates.

   copy
       Returns a copy of the point.

   normalize
       Performs an extended GCD operation to make "z=1".  If a factor of "n" is found it is put in "f".

Name

       Math::Prime::Util::ECProjectivePoint - Elliptic curve operations for projective points

Synopsis

         # 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();