Initial Commit
This commit is contained in:
Riley Schneider
285
database/perl/vendor/lib/Math/Prime/Util/ECAffinePoint.pm
vendored
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285
database/perl/vendor/lib/Math/Prime/Util/ECAffinePoint.pm
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package Math::Prime::Util::ECAffinePoint;
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use strict;
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use warnings;
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use Carp qw/carp croak confess/;
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BEGIN {
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$Math::Prime::Util::ECAffinePoint::AUTHORITY = 'cpan:DANAJ';
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$Math::Prime::Util::ECAffinePoint::VERSION = '0.73';
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}
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BEGIN {
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do { require Math::BigInt; Math::BigInt->import(try=>"GMP,Pari"); }
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unless defined $Math::BigInt::VERSION;
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}
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# Pure perl (with Math::BigInt) manipulation of Elliptic Curves
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# in affine coordinates. Should be split into a point class.
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sub new {
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my ($class, $a, $b, $n, $x, $y) = @_;
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$a = Math::BigInt->new("$a") unless ref($a) eq 'Math::BigInt';
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$b = Math::BigInt->new("$b") unless ref($b) eq 'Math::BigInt';
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$n = Math::BigInt->new("$n") unless ref($n) eq 'Math::BigInt';
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$x = Math::BigInt->new("$x") unless ref($x) eq 'Math::BigInt';
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$y = Math::BigInt->new("$y") unless ref($y) eq 'Math::BigInt';
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croak "n must be >= 2" unless $n >= 2;
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$a->bmod($n);
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$b->bmod($n);
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my $self = {
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a => $a,
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b => $b,
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n => $n,
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x => $x,
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y => $y,
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f => $n->copy->bone,
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};
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bless $self, $class;
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return $self;
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}
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sub _add {
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my ($self, $P1x, $P1y, $P2x, $P2y) = @_;
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my $n = $self->{'n'};
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if ($P1x == $P2x) {
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my $t = ($P1y + $P2y) % $n;
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return (Math::BigInt->bzero,Math::BigInt->bone) if $t == 0;
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}
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my $deltax = ($P2x - $P1x) % $n;
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$deltax->bmodinv($n);
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return (Math::BigInt->bzero,Math::BigInt->bone) if $deltax eq "NaN";
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my $deltay = ($P2y - $P1y) % $n;
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my $m = ($deltay * $deltax) % $n; # m = deltay / deltax
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my $x = ($m*$m - $P1x - $P2x) % $n;
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my $y = ($m*($P1x - $x) - $P1y) % $n;
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return ($x,$y);
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}
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sub _double {
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my ($self, $P1x, $P1y) = @_;
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my $n = $self->{'n'};
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my $m = 2*$P1y;
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$m->bmodinv($n);
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return (Math::BigInt->bzero,Math::BigInt->bone) if $m eq "NaN";
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$m = ((3*$P1x*$P1x + $self->{'a'}) * $m) % $n;
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my $x = ($m*$m - 2*$P1x) % $n;
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my $y = ($m*($P1x - $x) - $P1y) % $n;
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return ($x,$y);
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}
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sub _inplace_add {
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my ($P1x, $P1y, $x, $y, $n) = @_;
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if ($P1x == $x) {
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my $t = ($P1y + $y) % $n;
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if ($t == 0) {
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($_[2],$_[3]) = (Math::BigInt->bzero,Math::BigInt->bone);
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return;
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}
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}
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my $deltax = ($x - $P1x) % $n;
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$deltax->bmodinv($n);
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if ($deltax eq 'NaN') {
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($_[2],$_[3]) = (Math::BigInt->bzero,Math::BigInt->bone);
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return;
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}
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my $deltay = ($y - $P1y) % $n;
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my $m = ($deltay * $deltax) % $n; # m = deltay / deltax
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$_[2] = ($m*$m - $P1x - $x) % $n;
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$_[3] = ($m*($P1x - $_[2]) - $P1y) % $n;
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}
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sub _inplace_double {
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my($x, $y, $a, $n) = @_;
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my $m = $y+$y;
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$m->bmodinv($n);
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if ($m eq 'NaN') {
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($_[0],$_[1]) = (Math::BigInt->bzero,Math::BigInt->bone);
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return;
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}
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$m->bmul($x->copy->bmul($x)->bmul(3)->badd($a))->bmod($n);
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my $xin = $x->copy;
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$_[0] = ($m*$m - $x - $x) % $n;
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$_[1] = ($m*($xin - $_[0]) - $y) % $n;
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}
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sub mul {
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my ($self, $k) = @_;
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my $x = $self->{'x'};
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my $y = $self->{'y'};
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my $a = $self->{'a'};
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my $n = $self->{'n'};
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my $f = $self->{'f'};
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if (ref($k) eq 'Math::BigInt' && $k < ''.~0) {
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if ($] >= 5.008 || ~0 == 4294967295) {
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$k = int($k->bstr);
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} elsif ($] < 5.008 && ~0 > 4294967295 && $k < 562949953421312) {
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$k = unpack('Q',pack('Q',$k->bstr));
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}
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}
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my $Bx = $n->copy->bzero;
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my $By = $n->copy->bone;
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my $v = 1;
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while ($k > 0) {
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if ( ($k % 2) != 0) {
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$k--;
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$f->bmul($Bx-$x)->bmod($n);
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if ($x->is_zero && $y->is_one) { }
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elsif ($Bx->is_zero && $By->is_one) { ($Bx,$By) = ($x,$y); }
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else { _inplace_add($x,$y,$Bx,$By,$n); }
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} else {
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$k >>= 1;
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$f->bmul(2*$y)->bmod($n);
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_inplace_double($x,$y,$a,$n);
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}
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}
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$f = Math::BigInt::bgcd($f, $n);
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$self->{'x'} = $Bx;
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$self->{'y'} = $By;
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$self->{'f'} = $f;
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return $self;
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}
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sub add {
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my ($self, $other) = @_;
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croak "add takes a EC point"
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unless ref($other) eq 'Math::Prime::Util::ECAffinePoint';
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croak "second point is not on the same curve"
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unless $self->{'a'} == $other->{'a'} &&
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$self->{'b'} == $other->{'b'} &&
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$self->{'n'} == $other->{'n'};
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($self->{'x'}, $self->{'y'}) = $self->_add($self->{'x'}, $self->{'y'},
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$other->{'x'}, $other->{'y'});
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return $self;
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}
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sub a { return shift->{'a'}; }
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sub b { return shift->{'b'}; }
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sub n { return shift->{'n'}; }
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sub x { return shift->{'x'}; }
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sub y { return shift->{'y'}; }
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sub f { return shift->{'f'}; }
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sub is_infinity {
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my $self = shift;
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return ($self->{'x'}->is_zero() && $self->{'y'}->is_one());
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}
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1;
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__END__
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# ABSTRACT: Elliptic curve operations for affine points
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=pod
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=encoding utf8
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=for stopwords mul
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=for test_synopsis use v5.14; my($a,$b,$n,$k,$ECP2);
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=head1 NAME
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Math::Prime::Util::ECAffinePoint - Elliptic curve operations for affine points
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=head1 VERSION
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Version 0.73
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=head1 SYNOPSIS
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# Create a point on a curve (a,b,n) with coordinates 0,1
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my $ECP = Math::Prime::Util::ECAffinePoint->new($a, $b, $n, 0, 1);
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# scalar multiplication by k.
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$ECP->mul($k);
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# add two points on the same curve
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$ECP->add($ECP2);
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say "P = O" if $ECP->is_infinity();
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=head1 DESCRIPTION
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This really should just be in Math::EllipticCurve.
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To write.
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=head1 FUNCTIONS
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=head2 new
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$point = Math::Prime::Util::ECAffinePoint->new(a, b, n, x, y);
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Returns a new point at C<(x,y,1)> on the curve C<(a,b,n)>.
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=head2 a
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=head2 b
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=head2 n
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Returns the C<a>, C<b>, or C<n> values that describe the curve.
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=head2 x
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=head2 y
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Returns the C<x> or C<y> values that define the point on the curve.
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=head2 f
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Returns a possible factor found during EC multiplication.
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=head2 add
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Takes another point on the same curve as an argument and adds it this point.
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=head2 mul
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Takes an integer and performs scalar multiplication of the point.
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=head2 is_infinity
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Returns true if the point is (0,1), which is the point at infinity for
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the affine coordinates.
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=head1 SEE ALSO
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L<Math::EllipticCurve::Prime>
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This really should just be in a L<Math::EllipticCurve> module.
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=head1 AUTHORS
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Dana Jacobsen E<lt>dana@acm.orgE<gt>
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=head1 COPYRIGHT
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Copyright 2012-2013 by Dana Jacobsen E<lt>dana@acm.orgE<gt>
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This program is free software; you can redistribute it and/or modify it under the same terms as Perl itself.
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=cut
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