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On prime-order elliptic curves with embedding degrees k=3,4 and 6
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Abstract: | We further analyze the solutions to the Diophantine equations from which prime-order elliptic curves of embedding degrees $k=3,4$ or $6$ (MNT curves) may be obtained. We give an explicit algorithm to generate such curves. We derive a heuristic lower bound for the number $E(z)$ of MNT curves with $k=6$ and discriminant $D\le z$, and compare this lower bound with experimental data. |
BibTeX
@misc{eprint-2007-13705, title={On prime-order elliptic curves with embedding degrees k=3,4 and 6}, booktitle={IACR Eprint archive}, keywords={public-key cryptography / Elliptic curves, pairing-based cryptosystems, embedding degree, MNT curves.}, url={http://eprint.iacr.org/2007/425}, note={ eteske@uwaterloo.ca 13830 received 12 Nov 2007, last revised 13 Nov 2007}, author={Koray Karabina and Edlyn Teske}, year=2007 }