Optimised versions of the Ate and Twisted Ate Pairings

Seiichi Matsuda; Naoki Kanayama; Florian Hess; Eiji Okamoto

Paper 2007/013

Optimised versions of the Ate and Twisted Ate Pairings

Seiichi Matsuda, Naoki Kanayama, Florian Hess, and Eiji Okamoto

Abstract

The Ate pairing and the twisted Ate pairing for ordinary elliptic curves which are generalizations of the $η_{T}$ 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.

Note: I have modified the definition of and in section 2 and corrected the abstract.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Published elsewhere. Unknown where it was published
Keywords: Ordinary curve Tate pairing Ate pairing Twisted Ate pairing
Contact author(s): seichi @ cipher risk tsukuba ac jp
History: 2007-01-19: received
Short URL: https://ia.cr/2007/013
License: CC BY

BibTeX

@misc{cryptoeprint:2007/013,
      author = {Seiichi Matsuda and Naoki Kanayama and Florian Hess and Eiji Okamoto},
      title = {Optimised versions of the Ate and Twisted Ate Pairings},
      howpublished = {Cryptology {ePrint} Archive, Paper 2007/013},
      year = {2007},
      url = {https://eprint.iacr.org/2007/013}
}