International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Efficient Pairing Computation on Supersingular Abelian Varieties

Paulo S. L. M. Barreto
Steven D. Galbraith
Colm O hEigeartaigh
Michael Scott
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Abstract: We present a general technique for the efficient computation of pairings on supersingular Abelian varieties. This formulation, which we call the eta pairing, generalises results of Duursma and Lee for computing the Tate pairing on supersingular elliptic curves in characteristic three. 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 then used for elliptic and hyperelliptic curves in characteristic 2 with very efficient results. In particular, the hyperelliptic case is faster than all previously known pairing algorithms.
  title={Efficient Pairing Computation on Supersingular Abelian Varieties},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography / Tate pairing, supersingular curves, pairing-based cryptosystem, efficient algorithms},
  note={ 13031 received 1 Jan 2005, last revised 5 Sep 2005},
  author={Paulo S. L. M. Barreto and Steven D. Galbraith and Colm O hEigeartaigh and Michael Scott},