Improved Weil and Tate Pairings for Elliptic and Hyperelliptic Curves

  • Kirsten Eisenträger
  • Kristin Lauter
  • Peter L. Montgomery
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3076)


We present algorithms for computing the squared Weil and Tate pairings on elliptic curves and the squared Tate pairing on hyperelliptic curves. The squared pairings introduced in this paper have the advantage that our algorithms for evaluating them are deterministic and do not depend on a random choice of points. Our algorithm to evaluate the squared Weil pairing is about 20% more efficient than the standard Weil pairing. Our algorithm for the squared Tate pairing on elliptic curves matches the efficiency of the algorithm given by Barreto, Lynn, and Scott in the case of arbitrary base points where their denominator cancellation technique does not apply. Our algorithm for the squared Tate pairing for hyperelliptic curves is the first detailed implementation of the pairing for general hyperelliptic curves of genus 2, and saves an estimated 30% over the standard algorithm.


Elliptic Curve Elliptic Curf Hyperelliptic Curve Weil Pairing Tate Pairing 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Kirsten Eisenträger
    • 1
  • Kristin Lauter
    • 2
  • Peter L. Montgomery
    • 2
  1. 1.School of MathematicsInstitute for Advanced StudyPrincetonUSA
  2. 2.Microsoft ResearchRedmondUSA

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