Paper 2010/353

Cryptographic Pairings Based on Elliptic Nets

Naoki Ogura, Naoki Kanayama, Shigenori Uchiyama, and Eiji Okamoto


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.

Available format(s)
Publication info
Published elsewhere. Unknown where it was published
Tate pairingAte pairingR-Ate pairingOptimal pairingelliptic netnormalization
Contact author(s)
ogura-naoki @ ed tmu ac jp
2011-05-11: last of 4 revisions
2010-06-18: received
See all versions
Short URL
Creative Commons Attribution


      author = {Naoki Ogura and Naoki Kanayama and Shigenori Uchiyama and Eiji Okamoto},
      title = {Cryptographic Pairings Based on Elliptic Nets},
      howpublished = {Cryptology ePrint Archive, Paper 2010/353},
      year = {2010},
      note = {\url{}},
      url = {}
Note: In order to protect the privacy of readers, does not use cookies or embedded third party content.