The tate-lichtenbaum pairing on a hyperelliptic curve via hyperelliptic nets

Authors:
Yukihiro Uchida;Shigenori Uchiyama
Affiliations:
Department of Mathematics and Information Sciences, Tokyo Metropolitan University, Hachioji, Tokyo, Japan;Department of Mathematics and Information Sciences, Tokyo Metropolitan University, Hachioji, Tokyo, Japan
Venue:
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
Year:
2012

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Abstract

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.