Optimal Eta Pairing on Supersingular Genus-2 Binary Hyperelliptic Curves [chapter]

Diego F. Aranha, Jean-Luc Beuchat, Jérémie Detrey, Nicolas Estibals
2012 Lecture Notes in Computer Science  
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 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
more » ... urve 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 128bit-security Type-1 pairings from the literature.
doi:10.1007/978-3-642-27954-6_7 fatcat:bmcheryyl5fgpd3pmjgw476gn4