Computing Bilinear Pairings on Elliptic Curves with Automorphisms

Chang-An Zhao; Dongqing Xie; Fangguo Zhang; Jingwei Zhang; Bing-Long Chen

Paper 2008/209

Computing Bilinear Pairings on Elliptic Curves with Automorphisms

Chang-An Zhao, Dongqing Xie, Fangguo Zhang, Jingwei Zhang, and Bing-Long Chen

Abstract

In this paper, we present a novel method for constructing a super-optimal pairing with great efficiency, which we call the omega pairing. The computation of the omega pairing requires the simple final exponentiation and short loop length in Miller's algorithm which leads to a significant improvement over the previously known techniques on certain pairing-friendly curves. Experimental results show that the omega pairing is about 22% faster and 19% faster than the super-optimal pairing proposed by Scott at security level of AES 80 bits on certain pairing-friendly curves in affine coordinate systems and projective coordinate systems, respectively.

Note: Minor typing corrections to publication version.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Published by Designs, Codes and Cryptography.
Keywords: Elliptic curves Automorphism Pairing based cryptography Weil pairing
Contact author(s): zhaochan3 @ mail sysu edu cn
changanzhao @ gmail com
History: 2013-11-24: last of 6 revisions; 2008-05-21: received; See all versions
Short URL: https://ia.cr/2008/209
License: CC BY

BibTeX

@misc{cryptoeprint:2008/209,
      author = {Chang-An Zhao and Dongqing Xie and Fangguo Zhang and Jingwei Zhang and Bing-Long Chen},
      title = {Computing Bilinear Pairings on Elliptic Curves with Automorphisms},
      howpublished = {Cryptology {ePrint} Archive, Paper 2008/209},
      year = {2008},
      url = {https://eprint.iacr.org/2008/209}
}