Efficient Pairing Computation with Theta Functions

  • David Lubicz
  • Damien Robert
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6197)


In this paper, we present a new approach based on theta functions to compute Weil and Tate pairings. A benefit of our method, which does not rely on the classical Miller’s algorithm, is its generality since it extends to all abelian varieties the classical Weil and Tate pairing formulas. In the case of dimension 1 and 2 abelian varieties our algorithms lead to implementations which are efficient and naturally deterministic. We also introduce symmetric Weil and Tate pairings on Kummer varieties and explain how to compute them efficiently. We exhibit a nice algorithmic compatibility between some algebraic groups quotiented by the action of the automorphism − 1, where the ℤ-action can be computed efficiently with a Montgomery ladder type algorithm.


Theta Function Abelian Variety Natural Projection Hyperelliptic Curve Symmetric Pairing 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • David Lubicz
    • 1
    • 2
  • Damien Robert
    • 3
  1. 1.DGA-MI, BP 7419Bruz
  2. 2.IRMAR, Universté de Rennes 1Rennes
  3. 3.LORIA, CARAMEL ProjectVandoeuvre-lès-Nancy Cedex

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