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The Eta Pairing Revisited

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3 Author(s)
Hess, F. ; Inst. fur Math., Technische Univ. Berlin ; Smart, N.P. ; Vercauteren, F.

In this paper, we simplify and extend the Eta pairing, originally discovered in the setting of supersingular curves by Barreto , 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 that have large security parameters, complex multiplication by an order of Qopf (radic-3), and when the trace of Frobenius is chosen to be suitably small. Other, more minor savings are obtained for more general curves

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Information Theory, IEEE Transactions on  (Volume:52 ,  Issue: 10 )