A Refined Algorithm for the $\eta_T$ Pairing Calculation in Characteristic Three

Jean-Luc Beuchat; Masaaki Shirase; Tsuyoshi Takagi; Eiji Okamoto

Paper 2007/311

A Refined Algorithm for the $\eta_T$ Pairing Calculation in Characteristic Three

Jean-Luc Beuchat, Masaaki Shirase, Tsuyoshi Takagi, and Eiji Okamoto

Abstract

We describe further improvements of the $\eta_T$ pairing algorithm in characteristic three. Our approach combines the loop unrolling technique introduced by Granger {\em et. al} for the Duursma-Lee algorithm, and a novel algorithm for multiplication over $\mathbb{F}_{3^{6m}}$ proposed by Gorla {\em et al.} at SAC 2007. For $m=97$, the refined algorithm reduces the number of multiplications over $\mathbb{F}_{3^m}$ from $815$ to $692$.

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Published elsewhere. Unknown where it was published
Keywords: $\eta_T$ pairing finite field arithmetic characteristic three
Contact author(s): beuchat @ risk tsukuba ac jp
History: 2007-08-21: revised; 2007-08-16: received; See all versions
Short URL: https://ia.cr/2007/311
License: CC BY

BibTeX

@misc{cryptoeprint:2007/311,
      author = {Jean-Luc Beuchat and Masaaki Shirase and Tsuyoshi Takagi and Eiji Okamoto},
      title = {A Refined Algorithm for the $\e{ta_T}$ Pairing Calculation in Characteristic Three},
      howpublished = {Cryptology {ePrint} Archive, Paper 2007/311},
      year = {2007},
      url = {https://eprint.iacr.org/2007/311}
}