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A Note on the Ate Pairing
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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 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. |
BibTeX
@misc{eprint-2007-13528, title={A Note on the Ate Pairing}, booktitle={IACR Eprint archive}, keywords={Tate pairing, Ate pairing, Elliptic curves, Pairing-based cryptosystems}, url={http://eprint.iacr.org/2007/247}, note={ zhcha@mail2 sysu edu cn 13843 received 20 Jun 2007, last revised 25 Nov 2007}, author={Chang-An Zhao and Fangguo Zhang and Jiwu Huang}, year=2007 }