Cryptology ePrint Archive: Report 2006/110

The Eta Pairing Revisited

F. Hess and N.P. Smart and F. Vercauteren

Abstract: In this paper we simplify and extend the Eta pairing, originally discovered in the setting of supersingular curves by Baretto et al., to ordinary curves. Furthermore, we show that by swapping the arguments of the Eta pairing, one obtains a very efficient algorithm resulting in a speed-up of a factor of around six over the usual Tate pairing, in the case of curves which have large security parameters, complex multiplication by $D=-3$, and when the trace of Frobenius is chosen to be suitably small. Other, more minor savings are obtained for more general curves.

Category / Keywords: implementation /

Date: received 22 Mar 2006, last revised 16 Jun 2006

Contact author: nigel at cs bris ac uk

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Note: Minor corrections and extra explanation included

Version: 20060616:101118 (All versions of this report)

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