Paper 2005/363 Original: eprint.iacr.org/2005/363 ↗
Elliptic Curves with Low Embedding Degree
Abstract
Motivated by the needs of the {\it pairing based cryptography\/}, Miyaji, Nakabayashi and Takano have suggested a construction of so-called MNT elliptic curves with low embedding degree. We give some heuristic arguments which suggest that there are only about $z^{1/2+o(1)}$ of MNT curves with complex multiplication discriminant up to $z$. We also show that there are very few finite fields over which elliptic curves with small embedding degree and small complex multiplication discriminant may exist (regardless of the way they are constructed).
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2005-10-09: last updated
- 2005-10-09: published
- Short URL
- https://ia.cr/2005/363
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2005/363,
author = {Florian Luca and Igor E. Shparlinski},
title = {Elliptic Curves with Low Embedding Degree},
howpublished = {Cryptology {ePrint} Archive, Paper 2005/363},
year = {2005},
url = {https://eprint.iacr.org/2005/363}
}