[Resource Topic] 2010/559: Optimal Eta Pairing on Supersingular Genus-2 Binary Hyperelliptic Curves

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Optimal Eta Pairing on Supersingular Genus-2 Binary Hyperelliptic Curves

Authors: Diego F. Aranha, Jean-Luc Beuchat, Jérémie Detrey, Nicolas Estibals


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 \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.

ePrint: https://eprint.iacr.org/2010/559

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