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
-
CC BY
BibTeX
@misc{cryptoeprint:2007/425,
author = {Koray Karabina and Edlyn Teske},
title = {On prime-order elliptic curves with embedding degrees k=3,4 and 6},
howpublished = {Cryptology {ePrint} Archive, Paper 2007/425},
year = {2007},
url = {https://eprint.iacr.org/2007/425}
}
