Cryptology ePrint Archive: Report 2010/353

Cryptographic Pairings Based on Elliptic Nets

Naoki Ogura and Naoki Kanayama and Shigenori Uchiyama and Eiji Okamoto

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.

Category / Keywords: Tate pairing, Ate pairing, R-Ate pairing, Optimal pairing, elliptic net, normalization

Date: received 17 Jun 2010, last revised 11 May 2011

Contact author: ogura-naoki at ed tmu ac jp

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Version: 20110511:104702 (All versions of this report)

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