On the Final Exponentiation for Calculating Pairings on Ordinary Elliptic Curves

  • Michael Scott
  • Naomi Benger
  • Manuel Charlemagne
  • Luis J. Dominguez Perez
  • Ezekiel J. Kachisa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5671)

Abstract

When performing a Tate pairing (or a derivative thereof) on an ordinary pairing-friendly elliptic curve, the computation can be looked at as having two stages, the Miller loop and the so-called final exponentiation. As a result of good progress being made to reduce the Miller loop component of the algorithm (particularly with the discovery of “truncated loop” pairings like the R-ate pairing [18]), the final exponentiation has become a more significant component of the overall calculation. Here we exploit the structure of pairing-friendly elliptic curves to reduce to a minimum the computation required for the final exponentiation.

Keywords

Tate pairing addition sequences addition chains 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Michael Scott
    • 1
  • Naomi Benger
    • 1
  • Manuel Charlemagne
    • 1
  • Luis J. Dominguez Perez
    • 1
  • Ezekiel J. Kachisa
    • 1
  1. 1.School of ComputingDublin City University, BallymunDublin 9Ireland

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