Paper 2005/330

A Dedicated Processor for the eta Pairing

Robert Ronan and Colm O hEigeartaigh and Colin Murphy and Michael Scott and Tim Kerins and W.P. Marnane

Abstract

The $\eta$ pairing is an efficient computation technique based on a generalization of the Duursma Lee method for calculating the Tate pairing. The pairing can be computed very efficiently on genus 2 hyperelliptic curves. In this paper it is demonstrated that this pairing operation is well suited to a dedicated parallel hardware implementation. An $\eta$ pairing processor is described in detail and the architectures required for such a system are discussed. Prototype implementation results are presented over a base field of $\mathbb{F}_{2^{103}}$ and the advantages of implementing the pairing on the dedicated processor are discussed.