Pairing calculation on supersingular genus 2 curves

Abstract

In this paper we describe how to efficiently implement pairing calculation on supersingular genus 2 curves over prime fields. We find that, contrary to the results reported in [8], pairing calculation on supersingular genus 2 curves over prime fields is efficient and a viable candidate for the practical implementation of pairing-based cryptosystems. We also show how to eliminate divisions in an efficient manner when computing the Tate pairing, assuming an even embedding degree, and how this algorithm is useful for curves of genus greater than one. © Springer-Verlag Berlin Heidelberg 2007.