A fast diffie-hellman protocol in genus 2

Abstract

In this paper it is shown how the multiplication by M map on the Kummer surface of a curve of genus 2 defined over q can be used to construct a Diffie-Hellman protocol. We show that this map can be computed using only additions and multiplications in q. In particular we do not use any divisions, polynomial arithmetic, or square root functions in q, hence this may be easier to implement than multiplication by M on the Jacobian. In addition we show that using the Kummer surface does not lead to any loss in security. © 1999 International Association for Cryptologic Research.