Paper 2015/835
On near prime-order elliptic curves with small embedding degrees (Full version)
Duc-Phong Le, Nadia El Mrabet, and Chik How Tan
Abstract
In this paper, we extend the method of Scott and Barreto and present an explicit and simple algorithm to generate families of generalized MNT elliptic curves. Our algorithm allows us to obtain all families of generalized MNT curves with any given cofactor. Then, we analyze the complex multiplication equations of these families of curves and transform them into generalized Pell equation. As an example, we describe a way to generate Edwards curves with embedding degree 6, that is, elliptic curves having cofactor h = 4.
Note: Small changes at title and references.
Metadata
- Available format(s)
-
PDF
- Publication info
- Published elsewhere. Minor revision. 6th International Conference on Algebraic Informatics, CAI 2015
- DOI
- 10.1007/978-3-319-23021-4
- Keywords
- Pairing Friendly Elliptic CurveMNT curvesComplex MultiplicationPell's equation.
- Contact author(s)
- tslld @ nus edu sg
- History
- 2016-03-08: revised
- 2015-08-28: received
- See all versions
- Short URL
- https://ia.cr/2015/835
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2015/835,
author = {Duc-Phong Le and Nadia El Mrabet and Chik How Tan},
title = {On near prime-order elliptic curves with small embedding degrees (Full version)},
howpublished = {Cryptology {ePrint} Archive, Paper 2015/835},
year = {2015},
doi = {10.1007/978-3-319-23021-4},
url = {https://eprint.iacr.org/2015/835}
}
