The Tate-Lichtenbaum Pairing on a Hyperelliptic Curve via Hyperelliptic Nets
The Tate-Lichtenbaum Pairing on a Hyperelliptic Curve via Hyperelliptic Nets
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DOI：
10.1007/978-3-642-36334-4_15
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发表时间：
2012-05
期刊：
影响因子：
--
通讯作者：
Y. Uchida;S. Uchiyama
中科院分区：
文献类型：
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作者：
Y. Uchida;S. Uchiyama
最近，Stange提出了一种计算椭圆曲线上Tate配对的新算法。她的算法是基于椭圆网络的，斯坦格也将其定义为椭圆可除序列的推广。本文将超椭圆网定义为椭圆网到超椭圆曲线的推广。我们还给出了超椭圆曲线上的Tate-Lichtenbaum配对的超椭圆网的表达式。利用这个表达式，我们给出了一个计算亏格为2的超椭圆曲线上的Tate-Lichtenbaum对的算法。
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.