Designs, Codes and Cryptography

, Volume 58, Issue 1, pp 35–44

Computing bilinear pairings on elliptic curves with automorphisms

Authors

    • School of Computer Science and Educational SoftwareGuangzhou University
  • Dongqing Xie
    • School of Computer Science and Educational SoftwareGuangzhou University
  • Fangguo Zhang
    • School of Information Science and Technology, Guangdong Key Laboratory of Information Security TechnologySun Yat-sen University
  • Jingwei Zhang
    • School of Information Science and Technology, Guangdong Key Laboratory of Information Security TechnologySun Yat-sen University
  • Bing-Long Chen
    • Department of MathematicsSun Yat-Sen University
Article

DOI: 10.1007/s10623-010-9383-y

Cite this article as:
Zhao, C., 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 curves Automorphism Pairing based cryptography Weil pairing

Mathematics Subject Classification (2000)

14H52 11G20 14G15 14Q05 11T71

Copyright information

© Springer Science+Business Media, LLC 2010