# NAME

Math::EllipticCurve::Prime::Point - points for elliptic curve operations over prime fields

# VERSION

version 0.001

# SYNOPSIS

use Math::EllipticCurve::Prime::Point;

my $p = Math::EllipticCurve::Prime::Point->new(curve => 'secp256r1', x => Math::BigInt->new('0x01ff'), y => Math::BigInt->new('0x03bc')); # not real points on the curve my $p2 = $p->double; print "(" . $p2->x . ", " . $p2->y . ")\n";

# Creates a point at infinity. my $p3 = Math::EllipticCurve::Prime::Point->new(curve => 'secp256r1');

# Creates a point from a hexadecimal SEC representation. my $p4 = Math::EllipticCurve::Prime::Point->from_hex("0401ff03bc"); $p4->curve(Math::EllipticCurve::Prime->new(name => 'secp256r1'));

# DESCRIPTION

This class represents a point on a given elliptic curve. Using the methods provided, arithmetic operations can be performed, including point addition and scalar multiplication. Currently the operations are limited to these, as these are the operations most commonly used in cryptography.

# METHODS

## new

Create a new point. This constructor takes a hash as its sole argument. If the arguments x and y are both provided, assumes that these are instances of Math::BigInt. If x and y are not both provided, creates a new point at infinity.

## from_hex

This method takes a hexadecimal-encoded representation of a point in the SEC format and creates a new Math::EllipticCurve::Prime::Point object. Currently this only understands uncompressed points (first byte 0x04) and the point at infinity.

## from_bytes

This method takes a representation of a point in the SEC format and creates a new Math::EllipticCurve::Prime::Point object. Calls from_hex under the hood.

## to_hex

This method produces a hexadecimal string representing a point in the uncompressed SEC format.

## to_bytes

This method produces a byte string representing a point in the uncompressed SEC format.

## copy

Makes a copy of the current point.

## clone

A synonym for copy.

## bmul

Multiplies this point by a scalar. The scalar should be a Math::BigInt. Like Math::BigInt, this modifies the present point. If you want to preserve this point, use the copy method to create a clone of the current point.

Requires that a curve has been set.

## badd

Adds this point to another point. Like Math::BigInt, this modifies the present point. If you want to preserve this point, use the copy method to create a clone of the current point.

Requires that a curve has been set.

## bdbl

Doubles the current point. Like Math::BigInt, this modifies the present point. If you want to preserve this point, use the copy method to create a clone of the current point.

Requires that a curve has been set.

## multiply

Multiplies this point by a scalar. Returns a new point object.

Requires that a curve has been set.

## add

Adds this point to another point. Returns a new point object.

Requires that a curve has been set.

## double

Doubles this point. Returns a new point object.

Requires that a curve has been set.

## infinity

Returns true if this point is the point at infinity, false otherwise.

## x

Returns a Math::BigInt representing the x-coordinate of the point. Returns undef if this is the point at infinity. You should make a copy of the returned object; otherwise, you will modify the point.

## y

Returns a Math::BigInt representing the y-coordinate of the point. Returns undef if this is the point at infinity. You should make a copy of the returned object; otherwise, you will modify the point.

## curve

Returns the Math::EllipticCurve::Prime curve associated with this point, if any. Optionally takes an argument to set the curve.

# AUTHOR

brian m. carlson <sandals@crustytoothpaste.net>

# COPYRIGHT AND LICENSE

This software is copyright (c) 2012 by brian m. carlson.

This is free software; you can redistribute it and/or modify it under the same terms as the Perl 5 programming language system itself.