``````package Math::Prime::Util::ECAffinePoint;
use strict;
use warnings;
use Carp qw/carp croak confess/;

BEGIN {
\$Math::Prime::Util::ECAffinePoint::AUTHORITY = 'cpan:DANAJ';
\$Math::Prime::Util::ECAffinePoint::VERSION = '0.73';
}

BEGIN {
do { require Math::BigInt;  Math::BigInt->import(try=>"GMP,Pari"); }
unless defined \$Math::BigInt::VERSION;
}

# Pure perl (with Math::BigInt) manipulation of Elliptic Curves
# in affine coordinates.  Should be split into a point class.

sub new {
my (\$class, \$a, \$b, \$n, \$x, \$y) = @_;
\$a = Math::BigInt->new("\$a") unless ref(\$a) eq 'Math::BigInt';
\$b = Math::BigInt->new("\$b") unless ref(\$b) eq 'Math::BigInt';
\$n = Math::BigInt->new("\$n") unless ref(\$n) eq 'Math::BigInt';
\$x = Math::BigInt->new("\$x") unless ref(\$x) eq 'Math::BigInt';
\$y = Math::BigInt->new("\$y") unless ref(\$y) eq 'Math::BigInt';

croak "n must be >= 2" unless \$n >= 2;
\$a->bmod(\$n);
\$b->bmod(\$n);

my \$self = {
a => \$a,
b => \$b,
n => \$n,
x => \$x,
y => \$y,
f => \$n->copy->bone,
};

bless \$self, \$class;
return \$self;
}

my (\$self, \$P1x, \$P1y, \$P2x, \$P2y) = @_;
my \$n = \$self->{'n'};

if (\$P1x == \$P2x) {
my \$t = (\$P1y + \$P2y) % \$n;
return (Math::BigInt->bzero,Math::BigInt->bone) if \$t == 0;
}
my \$deltax = (\$P2x - \$P1x) % \$n;
\$deltax->bmodinv(\$n);
return (Math::BigInt->bzero,Math::BigInt->bone) if \$deltax eq "NaN";

my \$deltay = (\$P2y - \$P1y) % \$n;
my \$m = (\$deltay * \$deltax) % \$n;   # m = deltay / deltax

my \$x = (\$m*\$m - \$P1x - \$P2x) % \$n;
my \$y = (\$m*(\$P1x - \$x) - \$P1y) % \$n;
return (\$x,\$y);
}

sub _double {
my (\$self, \$P1x, \$P1y) = @_;
my \$n = \$self->{'n'};

my \$m = 2*\$P1y;
\$m->bmodinv(\$n);
return (Math::BigInt->bzero,Math::BigInt->bone) if \$m eq "NaN";

\$m = ((3*\$P1x*\$P1x + \$self->{'a'}) * \$m) % \$n;

my \$x = (\$m*\$m - 2*\$P1x) % \$n;
my \$y = (\$m*(\$P1x - \$x) - \$P1y) % \$n;
return (\$x,\$y);
}

my (\$P1x, \$P1y, \$x, \$y, \$n) = @_;

if (\$P1x == \$x) {
my \$t = (\$P1y + \$y) % \$n;
if (\$t == 0) {
(\$_[2],\$_[3]) = (Math::BigInt->bzero,Math::BigInt->bone);
return;
}
}
my \$deltax = (\$x - \$P1x) % \$n;
\$deltax->bmodinv(\$n);
if (\$deltax eq 'NaN') {
(\$_[2],\$_[3]) = (Math::BigInt->bzero,Math::BigInt->bone);
return;
}
my \$deltay = (\$y - \$P1y) % \$n;
my \$m = (\$deltay * \$deltax) % \$n;   # m = deltay / deltax

\$_[2] = (\$m*\$m - \$P1x - \$x) % \$n;
\$_[3] = (\$m*(\$P1x - \$_[2]) - \$P1y) % \$n;
}
sub _inplace_double {
my(\$x, \$y, \$a, \$n) = @_;
my \$m = \$y+\$y;
\$m->bmodinv(\$n);
if (\$m eq 'NaN') {
(\$_[0],\$_[1]) = (Math::BigInt->bzero,Math::BigInt->bone);
return;
}

my \$xin = \$x->copy;
\$_[0] = (\$m*\$m - \$x - \$x) % \$n;
\$_[1] = (\$m*(\$xin - \$_[0]) - \$y) % \$n;
}

sub mul {
my (\$self, \$k) = @_;
my \$x = \$self->{'x'};
my \$y = \$self->{'y'};
my \$a = \$self->{'a'};
my \$n = \$self->{'n'};
my \$f = \$self->{'f'};
if (ref(\$k) eq 'Math::BigInt' && \$k < ''.~0) {
if (\$] >= 5.008 || ~0 == 4294967295) {
\$k = int(\$k->bstr);
} elsif (\$] < 5.008 && ~0 > 4294967295 && \$k < 562949953421312) {
\$k = unpack('Q',pack('Q',\$k->bstr));
}
}

my \$Bx = \$n->copy->bzero;
my \$By = \$n->copy->bone;
my \$v = 1;

while (\$k > 0) {
if ( (\$k % 2) != 0) {
\$k--;
\$f->bmul(\$Bx-\$x)->bmod(\$n);
if    (\$x->is_zero && \$y->is_one)   { }
elsif (\$Bx->is_zero && \$By->is_one) { (\$Bx,\$By) = (\$x,\$y); }
} else {
\$k >>= 1;
\$f->bmul(2*\$y)->bmod(\$n);
_inplace_double(\$x,\$y,\$a,\$n);
}
}
\$f = Math::BigInt::bgcd(\$f, \$n);
\$self->{'x'} = \$Bx;
\$self->{'y'} = \$By;
\$self->{'f'} = \$f;
return \$self;
}

my (\$self, \$other) = @_;
croak "add takes a EC point"
unless ref(\$other) eq 'Math::Prime::Util::ECAffinePoint';
croak "second point is not on the same curve"
unless \$self->{'a'} == \$other->{'a'} &&
\$self->{'b'} == \$other->{'b'} &&
\$self->{'n'} == \$other->{'n'};

\$other->{'x'}, \$other->{'y'});
return \$self;
}

sub a { return shift->{'a'}; }
sub b { return shift->{'b'}; }
sub n { return shift->{'n'}; }
sub x { return shift->{'x'}; }
sub y { return shift->{'y'}; }
sub f { return shift->{'f'}; }

sub is_infinity {
my \$self = shift;
return (\$self->{'x'}->is_zero() && \$self->{'y'}->is_one());
}

1;

__END__

# ABSTRACT: Elliptic curve operations for affine points

=pod

=encoding utf8

=for stopwords mul

=for test_synopsis use v5.14;  my(\$a,\$b,\$n,\$k,\$ECP2);

Math::Prime::Util::ECAffinePoint - Elliptic curve operations for affine points

Version 0.73

# Create a point on a curve (a,b,n) with coordinates 0,1
my \$ECP = Math::Prime::Util::ECAffinePoint->new(\$a, \$b, \$n, 0, 1);

# scalar multiplication by k.
\$ECP->mul(\$k);

# add two points on the same curve

say "P = O" if \$ECP->is_infinity();

This really should just be in Math::EllipticCurve.

To write.

\$point = Math::Prime::Util::ECAffinePoint->new(a, b, n, x, y);

Returns a new point at C<(x,y,1)> on the curve C<(a,b,n)>.

Returns the C<a>, C<b>, or C<n> values that describe the curve.

Returns the C<x> or C<y> values that define the point on the curve.

Returns a possible factor found during EC multiplication.

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

Takes an integer and performs scalar multiplication of the point.

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

L<Math::EllipticCurve::Prime>

This really should just be in a L<Math::EllipticCurve> module.

Dana Jacobsen E<lt>dana@acm.orgE<gt>

Copyright 2012-2013 by Dana Jacobsen E<lt>dana@acm.orgE<gt>

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

=cut
``````