Evolutionary Cryptography Theory-Based Generating Method for Secure ECs

Chao Wang; Feng Hu; Huanguo Zhang; Jie Wu

doi:10.23919/TST.2017.8030539

Tsinghua Science and Technology 2017, 22(5): 499-510 https://doi.org/10.23919/TST.2017.8030539

Open Access | Issue | Published: 11 September 2017

Evolutionary Cryptography Theory-Based Generating Method for Secure ECs

Show Author's Information Hide Author's Information Chao Wang, Feng Hu(

), Huanguo Zhang, Jie Wu

Key Laboratory of Specialty Fiber Optics and Optical Access Networks, School of Communication and Information Engineering, Shanghai University, Shanghai 200072, China.

•Department of Computer and Information Sciences, Temple University, Philadelphia, PA 19122, USA.

Key Lab of Aerospace Information Security and Trusted Computing, Wuhan University, Wuhan 430072, China.

Keywords:

ECs, Weber polynomial, evolutionary algorithm, ant algorithm, complex multiplication

Cite this article:

Wang C, Hu F, Zhang H, et al. Evolutionary Cryptography Theory-Based Generating Method for Secure ECs. Tsinghua Science and Technology, 2017, 22(5): 499-510. https://doi.org/10.23919/TST.2017.8030539

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Abstract

Ant Colony Optimization (ACO) has the character of positive feedback, distributed searching, and greedy searching. It is applicable to optimization grouping problems. Traditional cryptographic research is mainly based on pure mathematical methods which have complicated theories and algorithm. It seems that there is no relationship between cryptography and ACO. Actually, some problems in cryptography are due to optimization grouping problems that could be improved using an evolutionary algorithm. Therefore, this paper presents a new method of solving secure curve selection problems using ACO. We improved Complex Multiplication (CM) by combining Evolutionary Cryptography Theory with Weber polynomial solutions. We found that ACO makes full use of valid information generated from factorization and allocates computing resource reasonably. It greatly increases the performance of Weber polynomial solutions. Compared with traditional CM, which can only search one root once time, our new method searches all roots of the polynomial once, and the average time needed to search for one root reduces rapidly. The more roots are searched, the more ECs are obtained.

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About this article

Evolutionary Cryptography Theory-Based Generating Method for Secure ECs

Show Author's information Hide Author's Information Chao Wang, Feng Hu(

), Huanguo Zhang, Jie Wu

Key Laboratory of Specialty Fiber Optics and Optical Access Networks, School of Communication and Information Engineering, Shanghai University, Shanghai 200072, China.

•Department of Computer and Information Sciences, Temple University, Philadelphia, PA 19122, USA.

Key Lab of Aerospace Information Security and Trusted Computing, Wuhan University, Wuhan 430072, China.

Abstract

Keywords: ECs, Weber polynomial, evolutionary algorithm, ant algorithm, complex multiplication

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Received: 14 November 2016

Accepted: 06 February 2017

Published: 11 September 2017

Issue date: October 2017

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (Nos. 61332019, 61572304, 61272056, and 60970006), the Innovation Grant of Shanghai Municipal Education Commission (No. 14ZZ089), and Shanghai Key Laboratory of Specialty Fiber Optics and Optical Access Networks (No. SKLSFO2014-06).