A note on the Ate pairing

Authors:
Chang-An Zhao;Fangguo Zhang;Jiwu Huang
Affiliations:
Guangzhou Univ., School of Comp. Sci. and Educational Software, 510006, Guangzhou and and SunYat-Sen Univ., School of Information Science and Technology, 510275, Guangzhou, People’s Republi ...;SunYat-Sen Univ., School of Information Science and Technology, 510275, Guangzhou and and SunYat-Sen Univ., Guangdong Key Lab. of Information Security Technology, 510275, Guangzhou, People’ ...;SunYat-Sen Univ., School of Information Science and Technology, 510275, Guangzhou and and SunYat-Sen Univ., Guangdong Key Lab. of Information Security Technology, 510275, Guangzhou, People’ ...
Venue:
International Journal of Information Security
Year:
2008

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Abstract

The Ate pairing has been suggested since it can be computed efficiently on ordinary elliptic curves with small values of the traces of Frobenius t. However, not all pairing-friendly elliptic curves have this property. In this paper, we generalize the Ate pairing and find a series of the variations of the Ate pairing. We show that the shortest Miller loop of the variations of the Ate pairing can possibly be as small as r 1/φ(k) on some special pairing-friendly curves with large values of Frobenius trace, and hence speed up the pairing computation significantly.