Designs, Codes and Cryptography

, Volume 58, Issue 1, pp 35–44 | Cite as

Computing bilinear pairings on elliptic curves with automorphisms

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


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.


Elliptic curves Automorphism Pairing based cryptography Weil pairing 

Mathematics Subject Classification (2000)

14H52 11G20 14G15 14Q05 11T71 


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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

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