Date of the talk: 20 June 2008
Introduction to Edwards curvesWe present elliptic curves in Edwards form. Using this curve shape we benefit from very fast arithmetic. We will show the affine addition formulas as well as the fast projective formulas. A further speed-up is gained from using inverted coordinates. We will compare these to other coordinate systems which are derived from the Weierstrass normal form. In particular, we will show how Edwards curves relate to elliptic curves in Montgomery form. This leads to the notion of twisted Edwards curves which we will use to explain more about the geometric structure of Edwards curves.