Ate Pairing on Hyperelliptic Curves

  • R. Granger
  • F. Hess
  • R. Oyono
  • N. Thériault
  • F. Vercauteren
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4515)


In this paper we show that the Ate pairing, originally defined for elliptic curves, generalises to hyperelliptic curves and in fact to arbitrary algebraic curves. It has the following surprising properties: The loop length in Miller’s algorithm can be up to g times shorter than for the Tate pairing, with g the genus of the curve, and the pairing is automatically reduced, i.e. no final exponentiation is needed.


Tate pairing Ate pairing hyperelliptic curves finite fields 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • R. Granger
    • 1
  • F. Hess
    • 2
  • R. Oyono
    • 3
  • N. Thériault
    • 4
  • F. Vercauteren
    • 5
  1. 1.Dept. Computer ScienceUniversity of Bristol, MVBBristolUnited Kingdom
  2. 2.Fakultät II, Institut für Mathematik Sekr. MA 8-1Technische Universität BerlinBerlinGermany
  3. 3.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada
  4. 4.Instituto de Matemática y FísicaUniversidad de TalcaTalcaChile
  5. 5.Department of Electrical EngineeringKatholieke Universiteit LeuvenLeuven-HeverleeBelgium

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