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

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.KeywordsTate-Lichtenbaum pairinghyperelliptic curvehyperelliptic net