Optimal Eta pairing on supersingular genus-2 binary hyperelliptic curves

Diego Aranha 1 Jean-Luc Beuchat 2 Jérémie Detrey 3, * Nicolas Estibals 3
* Corresponding author
3 CARAMEL - Cryptology, Arithmetic: Hardware and Software
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : This article presents a novel optimal pairing 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 further reduce the loop length of Miller's algorithm compared to 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.
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Diego Aranha, Jean-Luc Beuchat, Jérémie Detrey, Nicolas Estibals. Optimal Eta pairing on supersingular genus-2 binary hyperelliptic curves. Cryptographer's Track at the RSA Conference 2012 (CT-RSA 2012), Feb 2012, San Francisco, United States. pp.19. ⟨inria-00540002⟩

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