Paper 2004/375

Efficient Pairing Computation on Supersingular Abelian Varieties

Paulo S. L. M. Barreto, Steven Galbraith, Colm O hEigeartaigh, and Michael Scott


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.

Note: Improved presentation of all algorithms to compute the eta_T pairing.

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Tate pairingsupersingular curvespairing-based cryptosystemefficient algorithms
Contact author(s)
pbarreto @ larc usp br
2005-09-05: last of 5 revisions
2005-01-02: received
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Creative Commons Attribution


      author = {Paulo S.  L.  M.  Barreto and Steven Galbraith and Colm O hEigeartaigh and Michael Scott},
      title = {Efficient Pairing Computation on Supersingular Abelian Varieties},
      howpublished = {Cryptology ePrint Archive, Paper 2004/375},
      year = {2004},
      note = {\url{}},
      url = {}
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