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
Available format(s): Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation
Note: correct some writing errors.
Version: 20080102:031004 (All versions of this report)
Short URL: ia.cr/2007/247
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