## CryptoDB

### Paper: Some Efficient Algorithms for the Final Exponentiation of $\eta_T$ Pairing

Authors: Masaaki Shirase Tsuyoshi Takagi Eiji Okamoto URL: http://eprint.iacr.org/2006/431 Search ePrint Search Google Recently Tate pairing and its variations are attracted in cryptography. Their operations consist of a main iteration loop and a final exponentiation. The final exponentiation is necessary for generating a unique value of the bilinear pairing in the extension fields. The speed of the main loop has become fast by the recent improvements, e.g., the Duursma-Lee algorithm and $\eta_T$ pairing. In this paper we discuss how to enhance the speed of the final exponentiation of the $\eta_T$ pairing in the extension field ${\mathbb F}_{3^{6n}}$. Indeed, we propose some efficient algorithms using the torus $T_2({\mathbb F}_{3^{3n}})$ that can efficiently compute an inversion and a powering by $3^{n}+1$. Consequently, the total processing cost of computing the $\eta_T$ pairing can be reduced by 17% for n=97.
##### BibTeX
@misc{eprint-2006-21922,
title={Some Efficient Algorithms for the Final Exponentiation of $\eta_T$ Pairing},
booktitle={IACR Eprint archive},
keywords={public-key cryptography / Tate pairing, $\eta_T$ pairing, final exponentiation, torus},
url={http://eprint.iacr.org/2006/431},
note={ shirase@fun.ac.jp 13472 received 20 Nov 2006},
author={Masaaki Shirase and Tsuyoshi Takagi and Eiji Okamoto},
year=2006
}