Paper 2005/342 Original: eprint.iacr.org/2005/342 ↗
Special Polynomial Families for Generating More Suitable Elliptic Curves for Pairing-Based Cryptosystems
Abstract
Constructing non-supersingular elliptic curves for pairing-based cryptosystems have attracted much attention in recent years. The best previous technique builds curves with p = lg(q)/lg(r) = 1 (k = 12) and p = lg(q)/lg(r) = 1.25 (k = 24). When k > 12, most of the previous works address the question by representing r(x) as a cyclotomic polynomial. In this paper, we propose a new method to find more pairing-friendly elliptic curves with arbitrary embedding degree k by certain special polynomial families. The new method generates curves with lg(q)/lg(r) = 1 (k > 48) by random forms of r(x). Different representations of r(x) allow us to obtain many new families of pairing-friendly elliptic curves. In addition, we propose a equation to illustrate how to obtain small values of p by choosing appropriate forms of discriminant D and trace t. Numerous parameters of certain pairing-friendly elliptic curves are presented with support for the theoretical conclusions.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2005-10-03: last updated
- 2005-09-27: published
- Short URL
- https://ia.cr/2005/342
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2005/342,
author = {Pu Duan and Shi Cui and Choong Wah Chan},
title = {Special Polynomial Families for Generating More Suitable Elliptic Curves for Pairing-Based Cryptosystems},
howpublished = {Cryptology {ePrint} Archive, Paper 2005/342},
year = {2005},
url = {https://eprint.iacr.org/2005/342}
}