Cryptographic Pairings Based on Elliptic Nets

Abstract

In 2007, Stange proposed a novel method of computing the Tate pairing on an elliptic curve over a finite field. This method is based on elliptic nets, which are maps from $\mathbb{Z}^n$ to a ring that satisfy a certain recurrence relation. In this paper, we explicitly give formulae for computing some variants of the Tate pairing: Ate, Ate$_i$, R-Ate and Optimal pairings, based on elliptic nets. We also discuss their efficiency by using some experimental results