CryptoDB
Special Polynomial Families for Generating More Suitable Elliptic Curves for Pairing-Based Cryptosystems
| Authors: | |
|---|---|
| Download: | |
| 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. |
BibTeX
@misc{eprint-2005-12676,
title={Special Polynomial Families for Generating More Suitable Elliptic Curves for Pairing-Based Cryptosystems},
booktitle={IACR Eprint archive},
keywords={public-key cryptography / elliptic curves, pairing-based cryptosystems},
url={http://eprint.iacr.org/2005/342},
note={ pg03460751@ntu.edu.sg, dp@pmail.ntu.edu.sg 13059 received 21 Sep 2005, last revised 3 Oct 2005},
author={Pu Duan and Shi Cui and Choong Wah Chan},
year=2005
}