It is now more than five years since we started working on the book Elliptic Curves in Cryptography and more than four years since it was published. We therefore thought it was time to update the book since a lot has happened in the intervening years. However, it soon became apparent that a simple update would not be sufficient since so much has been developed in this area. We therefore decided to develop a second volume by inviting leading experts to discuss issues which have arisen.

Highlights in the intervening years which we cover in this volume include:

Provable Security. There has been considerable work in the last few years on proving various practical encryption and signature schemes secure. In this new volume we will examine the proofs for the ECDSA signature scheme and the ECIES encryption scheme.

Side-Channel Analysis. The use of power and timing analysis against cryptographic tokens, such as smart cards, is particularly relevant to elliptic curves since elliptic curves are meant to be particularly suited to the constrained environment of smart cards. We shall describe what side-channel analysis is and how one can use properties of elliptic curves to defend against it.

Point Counting. In 1999 the only method for computing the group order of an elliptic curve was the Schoof-Elkies-Atkin algorithm.