Efficient pairing computation on supersingular Abelian varieties

Authors:
Paulo S. Barreto;Steven D. Galbraith;Colm Ó' Héigeartaigh;Michael Scott
Affiliations:
Department of Computing and Digital Systems Engineering, Escola Politécnica, Universidade de São Paulo, São Paulo (SP), Brazil 05508-900;Mathematics Department, Royal Holloway University of London, Egham, Surrey, UK TW20 0EX;School of Computing, Dublin City University, Dublin 9, Ireland;School of Computing, Dublin City University, Dublin 9, Ireland
Venue:
Designs, Codes and Cryptography
Year:
2007

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Abstract

We present a general technique for the efficient computation of pairings on Jacobians of supersingular curves. This formulation, which we call the eta pairing, generalizes results of Duursma and Lee for computing the Tate pairing on supersingular elliptic curves in characteristic 3. We then show how our general technique leads to a new algorithm which is about twice as fast as the Duursma---Lee method. These ideas are applied to elliptic and hyperelliptic curves in characteristic 2 with very efficient results. In particular, the hyperelliptic case is faster than all previously known pairing algorithms.