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 23m-th power Verschiebung in order to reduce the loop length of Miller's algorithm even further than the genus-2 ηT 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 $\mathbb{F}_{2^{367}}$ , 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.