Article

Designs, Codes and Cryptography

, Volume 58, Issue 1, pp 35-44

First online:

Computing bilinear pairings on elliptic curves with automorphisms

  • Chang-An ZhaoAffiliated withSchool of Computer Science and Educational Software, Guangzhou University Email author 
  • , Dongqing XieAffiliated withSchool of Computer Science and Educational Software, Guangzhou University
  • , Fangguo ZhangAffiliated withSchool of Information Science and Technology, Guangdong Key Laboratory of Information Security Technology, Sun Yat-sen University
  • , Jingwei ZhangAffiliated withSchool of Information Science and Technology, Guangdong Key Laboratory of Information Security Technology, Sun Yat-sen University
  • , Bing-Long ChenAffiliated withDepartment of Mathematics, Sun Yat-Sen University

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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