The Tate-Lichtenbaum Pairing on a Hyperelliptic Curve via Hyperelliptic Nets

  • Yukihiro Uchida
  • Shigenori Uchiyama
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7708)


Recently, Stange proposed a new algorithm to compute the Tate pairing on an elliptic curve. Her algorithm is based on elliptic nets, which are also defined by Stange as a generalization of elliptic divisibility sequences. In this paper, we define hyperelliptic nets as a generalization of elliptic nets to hyperelliptic curves. We also give an expression for the Tate-Lichtenbaum pairing on a hyperelliptic curve in terms of hyperelliptic nets. Using this expression, we give an algorithm to compute the Tate-Lichtenbaum pairing on a hyperelliptic curve of genus 2.


Tate-Lichtenbaum pairing hyperelliptic curve hyperelliptic net 


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Yukihiro Uchida
    • 1
  • Shigenori Uchiyama
    • 1
  1. 1.Department of Mathematics and Information SciencesTokyo Metropolitan UniversityHachiojiJapan

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