Optimal Eta Pairing On Supersingular Genus-2 Binary Hyperelliptic Curves

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 eta(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 F(2)367, 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.