Abstract
In 2007, Stange proposed a novel method for computing the Tate pairing on an elliptic curve over a finite field. This method is based on elliptic nets, which are maps from Zn to a ring and satisfy a certain recurrence relation. In the present paper, we explicitly give formulae based on elliptic nets for computing the following variants of the Tate pairing: the Ate, Atei, R-Ate, and optimal pairings. We also discuss their efficiency by using some experimental results.
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