Constructing Pairing-Friendly Elliptic Curves under Embedding Degree 1 for Securing Critical Infrastructures

Maocai Wang; Guangming Dai; Kim-Kwang Raymond Choo; Prem Prakash Jayaraman; Rajiv Ranjan

doi:10.1371/journal.pone.0161857

Constructing Pairing-Friendly Elliptic Curves under Embedding Degree 1 for Securing Critical Infrastructures

PLoS One. 2016 Aug 26;11(8):e0161857. doi: 10.1371/journal.pone.0161857. eCollection 2016.

Authors

Maocai Wang^{1

2}, Guangming Dai^{1

2}, Kim-Kwang Raymond Choo^{1

2

3}, Prem Prakash Jayaraman⁴, Rajiv Ranjan⁵

Affiliations

¹ School of Computer, China University of Geosciences, Wuhan, Hubei, China.
² Hubei Key Laboratory of Intelligent Geo-Information Processing, China University of Geosciences, Wuhan, Hubei, China.
³ Department of Information Systems and Cyber Security, University of Texas at San Antonio, San Antonio, Texas, United States of America.
⁴ RMIT University, Melbourne, Australia.
⁵ University of Newcastle, Newcastle, United Kingdom.

Abstract

Information confidentiality is an essential requirement for cyber security in critical infrastructure. Identity-based cryptography, an increasingly popular branch of cryptography, is widely used to protect the information confidentiality in the critical infrastructure sector due to the ability to directly compute the user's public key based on the user's identity. However, computational requirements complicate the practical application of Identity-based cryptography. In order to improve the efficiency of identity-based cryptography, this paper presents an effective method to construct pairing-friendly elliptic curves with low hamming weight 4 under embedding degree 1. Based on the analysis of the Complex Multiplication(CM) method, the soundness of our method to calculate the characteristic of the finite field is proved. And then, three relative algorithms to construct pairing-friendly elliptic curve are put forward. 10 elliptic curves with low hamming weight 4 under 160 bits are presented to demonstrate the utility of our approach. Finally, the evaluation also indicates that it is more efficient to compute Tate pairing with our curves, than that of Bertoni et al.

MeSH terms

Algorithms*
Computer Security*
Monte Carlo Method

Grants and funding

This work was supported by National Natural Science Foundation of China (Grant No. 41571403 and 61472375, http://www.nsfc.gov.cn/) and China Postdoctoral Science Foundation (Grant No. 2012T50681 and 2011M501260, www.chinapostdoctor.org.cn). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.