Efficient pairing computation on Elliptic curves in Hessian form

Authors:
Haihua Gu;Dawu Gu;WenLu Xie
Affiliations:
Computer Science and Engineering Department, Shanghai Jiao Tong University, Shanghai, P.R. China and Shanghai Huahong Integrated Circuit Co., Ltd., Shanghai,P.R. China;Shanghai Huahong Integrated Circuit Co., Ltd., Shanghai,P.R. China;Computer Science and Engineering Department, Shanghai Jiao Tong University, Shanghai, P.R. China
Venue:
ICISC'10 Proceedings of the 13th international conference on Information security and cryptology
Year:
2010

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Abstract

Pairings in elliptic curve cryptography are functions which map a pair of elliptic curve points to a non-zero element of a finite field. In recent years, many useful cryptographic protocols based on pairings have been proposed. The fast implementations of pairings have become a subject of active research areas in cryptology. In this paper, we give the geometric interpretation of the group law on Hessian curves. Furthermore, we propose the first algorithm for computing the Tate pairing on elliptic curves in Hessian form. Analysis indicates that it is faster than all algorithms of Tate pairing computation known so far for Weierstrass and Edwards curves excepted for the very special elliptic curves with a4 = 0, a6 = b2.