Cryptology ePrint Archive: Report 2007/247

A Note on the Ate Pairing

Chang-An Zhao and Fangguo Zhang and Jiwu Huang

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 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 $r^{1/\varphi(k)}$ on more pairing-friendly curves generated by the method of complex multiplications, and hence speed up the pairing computation significantly.

Category / Keywords: Tate pairing, Ate pairing, Elliptic curves, Pairing-based cryptosystems

Date: received 20 Jun 2007, last revised 1 Jan 2008

Contact author: zhcha at mail2 sysu edu cn

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Note: correct some writing errors.

Version: 20080102:031004 (All versions of this report)

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