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Paper 2007/425

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

Koray Karabina and Edlyn Teske

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.

Metadata
Available format(s)
PDF PS
Category
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Keywords
Elliptic curvespairing-based cryptosystemsembedding degreeMNT curves.
Contact author(s)
eteske @ uwaterloo ca
History
2007-11-18: received
Short URL
https://ia.cr/2007/425
License
Creative Commons Attribution
CC BY
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