Computing bilinear pairings on elliptic curves with automorphisms

Authors:
Chang-An Zhao;Dongqing Xie;Fangguo Zhang;Jingwei Zhang;Bing-Long Chen
Affiliations:
School of Computer Science and Educational Software, Guangzhou University, Guangzhou, People's Republic of China 510006;School of Computer Science and Educational Software, Guangzhou University, Guangzhou, People's Republic of China 510006;School of Information Science and Technology, Guangdong Key Laboratory of Information Security Technology, Sun Yat-sen University, Guangzhou, People's Republic of China 510275;School of Information Science and Technology, Guangdong Key Laboratory of Information Security Technology, Sun Yat-sen University, Guangzhou, People's Republic of China 510275;Department of Mathematics, Sun Yat-Sen University, Guangzhou, People's Republic of China 510275
Venue:
Designs, Codes and Cryptography
Year:
2011

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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.