Special polynomial families for generating more suitable pairing-friendly elliptic curves

Authors:
Pu Duan;Shi Cui;Choong Wah Chan
Affiliations:
School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore;School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore;School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore
Venue:
EHAC'06 Proceedings of the 5th WSEAS International Conference on Electronics, Hardware, Wireless and Optical Communications
Year:
2006

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Abstract

Constructing non-supersingular elliptic curves for pairing-based cryptosystems have attracted much attention in recent years. The best previous technique builds curves with ρ = lg(q) / lg(r) ≈ 1 (k = 12) and ρ = 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 method to find more pairing-friendly elliptic curves by various forms of irreducible polynomial r(x). In addition, we propose a equation to illustrate how to obtain small values of ρ 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.