Cryptographic pairings based on elliptic nets

Authors:
Naoki Ogura;Naoki Kanayama;Shigenori Uchiyama;Eiji Okamoto
Affiliations:
Graduate School of Science and Engineering, Tokyo Metropolitan University, Hachioji, Tokyo, Japan;Faculty of Systems and Information Engineering, University of Tsukuba, Tsukuba-Shi, Ibaraki-Ken, Japan;Graduate School of Science and Engineering, Tokyo Metropolitan University, Hachioji, Tokyo, Japan;Faculty of Systems and Information Engineering, University of Tsukuba, Tsukuba-Shi, Ibaraki-Ken, Japan
Venue:
IWSEC'11 Proceedings of the 6th International conference on Advances in information and computer security
Year:
2011

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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.