Designs, Codes and Cryptography

, Volume 42, Issue 3, pp 239–271

Efficient pairing computation on supersingular Abelian varieties


  • Paulo S. L. M. Barreto
    • Department of Computing and Digital Systems Engineering, Escola PolitécnicaUniversidade de São Paulo
  • Steven D. Galbraith
    • Mathematics DepartmentRoyal Holloway University of London
  • Colm Ó’ hÉigeartaigh
    • School of ComputingDublin City University
    • School of ComputingDublin City University

DOI: 10.1007/s10623-006-9033-6

Cite this article as:
Barreto, P.S.L.M., Galbraith, S.D., hÉigeartaigh, C.Ó. et al. Des Codes Crypt (2007) 42: 239. doi:10.1007/s10623-006-9033-6


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.


Tate pairingSupersingular curvesPairing-based cryptosystemsEfficient algorithms

AMS Classification


Copyright information

© Springer Science+Business Media, LLC 2007