Montgomery ladder for all genus 2 curves in characteristic 2

Abstract

Using the Kummer surface, we generalize Montgomery ladder for scalar multiplication to the Jacobian of genus 2 curves in characteristic 2. Previously this method was known for elliptic curves and for genus 2 curves in odd characteristic. We obtain an algorithm that is competitive compared to usual methods of scalar multiplication and that has additional properties such as resistance to simple side-channel attacks. Moreover it provides a significant speed-up of scalar multiplication in many cases. This new algorithm has very important applications in cryptography using hyperelliptic curves and more particularly for people interested in cryptography on embedded systems (such as smart cards). © 2008 Springer-Verlag Berlin Heidelberg.