Optimal eta pairing on supersingular genus-2 binary hyperelliptic curves

Abstract

This article presents a novel pairing algorithm over supersingular genus-2 binary hyperelliptic curves. Starting from Vercauteren's work on optimal pairings, we describe how to exploit the action of the 2 3m -th power Verschiebung in order to reduce the loop length of Miller's algorithm even further than the genus-2 η T approach. As a proof of concept, we detail an optimized software implementation and an FPGA accelerator for computing the proposed optimal Eta pairing on a genus-2 hyperelliptic curve over , which satisfies the recommended security level of 128 bits. These designs achieve favourable performance in comparison with the best known implementations of 128-bit-security Type-1 pairings from the literature. © 2012 Springer-Verlag.