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Paper: On prime-order elliptic curves with embedding degrees k=3,4 and 6

Authors:
Koray Karabina
Edlyn Teske
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URL: http://eprint.iacr.org/2007/425
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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
}