Designs, Codes and Cryptography

, Volume 58, Issue 1, pp 35–44

Computing bilinear pairings on elliptic curves with automorphisms

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

DOI: 10.1007/s10623-010-9383-y

Cite this article as:
Zhao, CA., Xie, D., Zhang, F. et al. Des. Codes Cryptogr. (2011) 58: 35. doi:10.1007/s10623-010-9383-y

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.

Keywords

Elliptic curvesAutomorphismPairing based cryptographyWeil pairing

Mathematics Subject Classification (2000)

14H5211G2014G1514Q0511T71

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Chang-An Zhao
    • 1
  • Dongqing Xie
    • 1
  • Fangguo Zhang
    • 2
  • Jingwei Zhang
    • 2
  • Bing-Long Chen
    • 3
  1. 1.School of Computer Science and Educational SoftwareGuangzhou UniversityGuangzhouPeople’s Republic of China
  2. 2.School of Information Science and Technology, Guangdong Key Laboratory of Information Security TechnologySun Yat-sen UniversityGuangzhouPeople’s Republic of China
  3. 3.Department of MathematicsSun Yat-Sen UniversityGuangzhouPeople’s Republic of China