## CryptoDB

### Paper: Optimised versions of the Ate and Twisted Ate Pairings

Authors: Seiichi Matsuda Naoki Kanayama Florian Hess Eiji Okamoto URL: http://eprint.iacr.org/2007/013 Search ePrint Search Google The Ate pairing and the twisted Ate pairing for ordinary elliptic curves which are generalizations of the $\eta_T$ pairing for supersingular curves have previously been proposed. It is not necessarily the case that both pairings are faster than the Tate pairing. In this paper we propose optimized versions of the Ate and twisted Ate pairings with the loop reduction method and show that both pairings are always at least as fast as the Tate pairing. We also provide suitable families of elliptic curves that our optimized Ate and optimized twisted Ate pairings can be computed with half the loop length compared to the Tate pairing.
##### BibTeX
@misc{eprint-2007-13295,
title={Optimised versions of the Ate and Twisted Ate Pairings},
booktitle={IACR Eprint archive},
keywords={foundations / Ordinary curve, Tate pairing, Ate pairing, Twisted Ate pairing},
url={http://eprint.iacr.org/2007/013},
note={ seichi@cipher.risk.tsukuba.ac.jp 13525 received 11 Jan 2007, last revised 12 Jan 2007},
author={Seiichi Matsuda and Naoki Kanayama and Florian Hess and Eiji Okamoto},
year=2007
}