Designs, Codes and Cryptography

, Volume 42, Issue 3, pp 239-271

First online:

Efficient pairing computation on supersingular Abelian varieties

  • Paulo S. L. M. BarretoAffiliated withDepartment of Computing and Digital Systems Engineering, Escola Politécnica, Universidade de São Paulo
  • , Steven D. GalbraithAffiliated withMathematics Department, Royal Holloway University of London
  • , Colm Ó’ hÉigeartaighAffiliated withSchool of Computing, Dublin City University
  • , Michael ScottAffiliated withSchool of Computing, Dublin City University Email author 

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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 pairing Supersingular curves Pairing-based cryptosystems Efficient algorithms

AMS Classification

14G50 14Q05 11G20 94A60 11T71