Extension of the ecdsa gem

This library is an extension of the ecdsa gem, which mainly speeds up the computation of points on elliptic curves by using projective rather than affine coordinates.

This gem was not written by a cryptography expert and has not been carefully checked as with the original gem. It is provided "as is" and it is the user's responsibility to make sure it will be suitable for the desired purpose.

Installation

Add this line to your application's Gemfile:

gem 'ecdsa_ext'

And then execute:

$ bundle install

Or install it yourself as:

$ gem install ecdsa_ext

Usage

Convert coordinate from affine to projective

require 'ecdsa_ext'
require 'securerandom'

group = ECDSA::Group::Secp256k1
private_key = 1 + SecureRandom.random_number(group.order - 1)
affine_point = group.generator * private_key
#<ECDSA::Point: secp256k1, 0x22a7d03cd6fec52e13d2713da6921cf8f374631ecea7d575d31c3f338a410ad, 0x530b82285b951582bc330fc0b1d26df56bf93277d1229676ab9c2d4749098a7c>

# convert to projective point
projective_point = affine_point.to_projective
#<ECDSA::Ext::ProjectivePoint:0x00007f45baa7f5b0 @group=#<ECDSA::Group:secp256k1>, @x=979696094695476041658010915065787178569931130816884020506645009594358960301, @y=37562300065191370074864991137132392549749230653372621152572375247509483260540, @z=1>

Create directory

require 'ecdsa_ext'
require 'securerandom'

group = ECDSA::Group::Secp256k1
private_key = 1 + SecureRandom.random_number(group.order - 1)
projective_point = group.generator.to_projective * private_key
#<ECDSA::Ext::ProjectivePoint:0x00007f45baa7f5b0 @group=#<ECDSA::Group:secp256k1>, @x=979696094695476041658010915065787178569931130816884020506645009594358960301, @y=37562300065191370074864991137132392549749230653372621152572375247509483260540, @z=1>

Operation

ECDSA::Ext::ProjectivePoint instance supports point addition, scalar multiplication and negation.

require 'ecdsa_ext'

# addition
projective_point3 = projective_point1 + projective_point2

# multiplication
projective_point4 = projective_point3 * 123

# negation
projective_point4_neg = projective_point4.negate

Convert coordinate from projective to affine

require 'ecdsa_ext'

affine_point = projective_point4.to_affine

Use jacobian coordinates

Jacobian coordinates have been supported since 0.3.0.

When using Jacobian coordinates, use ECDSA::Ext::JacobianPoint instead of ECDSA::Ext::ProjectivePoint. In addition, ECDSA::Point now has a to_jacobian method that convert affine coordinates to jacobian coordinates.

Apply jacobian coordinates to existing ECDSA sign/verify

If you want the existing ECDSA gem to generate and verify signatures in Jacobian coordinates, add the following code. This code is a monkey patch to do the existing process in Jacobian coordinates.

require 'ecdsa/ext/sign_verify'

ecdsa_ext

Runtime