Arithmetic on non supersingular elliptic curves

Abstract

We discuss the different possibilities to choose elliptic curves over different finite fields with respect to application for public key cryptosystems. In 1985 it was proposed to use the multiplication on elliptic curves for the implementation of one way functions. Supersingular curves E with #E(Fq) = q + 1 elements were proposed at that time. New results due to A. Menezes, T. Okamoto and S. Vanstone show, that these curves are not well suited for that purpose. They can be attacked with a new division algorithm recently presented. However, by using non-supersingular elliptic curves this attack can be avoided. We show how to construct suitable curves. Furthermore some aspects of a VLSI-implementation for such a cryptosystem are discussed.