A gentle introduction
to elliptic-curve cryptography

The clock:
Real clock
Clock addition
Finite fields
Finite clocks
Clock crypto
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.