An Improvment of the Elliptic Net Algorithm

In this paper we propose a modified Elliptic Net algorithm to compute pairings. By reducing the number of the intermediate variables which should be updated in the iteration loop of the Elliptic Net algorithm, we speed up the computation of pairings. Experimental results show that the proposed method is about $14\%$ faster than the original Elliptic Net algorithm on certain supersingular elliptic curves with embedding degree $two$

Formulae for Computation of Tate Pairing on Hyperelliptic Curve Using Hyperelliptic Nets

Stange has showed how to compute the Tate pairing on an elliptic curve using elliptic nets. After that, Uchida and Uchiyama gave a generalization of elliptic nets to hyperelliptic curves. They also gave an algorithm to compute the Tate pairing on a hyperelliptic curve of genus 2. In this paper, we extend their algorithm for curves of all genus. In a computational point of view, we also study the optimality of these algorithms