ECCHacks

A gentle introduction
to elliptic-curve cryptography

Introduction

The clock:

Real clock

Finiteness:

Elliptic curves:

Edwards curves

Edwards addition

Edwards curves

An Edwards curve is a curve in the plane. Specifically, the points on the Edwards curve are the points (x,y) satisfying the equation x²+y²=1+d*x²y². Here are some examples of points on the Edwards curve for d=-300:

(0,1),
(0,-1),
(1,0),
(-1,0).

These are the same as on the real clock. Other points are

(0.8, -0.043188945044921672046),
(-0.4, 0.130930734141595428759).

and there are many more. Plotted over the reals this curve looks like this:

Version: This is version 2014.12.27 of the edwardscurve.html web page.