An Improved Multi-Chaotic Public Key Algorithm Based on Chebyshev Polynomials

Author:

Zhang Chunfu12ORCID,Bai Jing12,Liang Yanchun3ORCID,Tavares Adriano2,Wang Lidong1,Gomes Tiago2ORCID,Pinto Sandro2ORCID

Affiliation:

1. School of Big Data, Zhuhai College of Science and Technology, Zhuhai 519041, China

2. Department of Industrial Electronics, University of Minho, 4800-058 Guimaraes, Portugal

3. School of Computer Science, Zhuhai College of Science and Technology, Zhuhai 519041, China

Abstract

Due to the similar characteristics of chaotic systems and cryptography, public key encryption algorithms based on chaotic systems are worth in-depth research and have high value for the future. Chebyshev polynomials have good properties and are often used in the design of public key algorithms. This paper improves the Bose Multi-Chaotic Public Key Cryptographic Algorithm (BMPKC) by applying Chebyshev polynomials. The proposed algorithm (CMPKC-ki) introduces the selective coefficient ki based on the properties of Chebyshev polynomials, allowing the special functions that need to be negotiated in the original system to be freely and randomly chosen as Chebyshev polynomials, and can also be expanded to m levels. The improved cryptographic algorithm also utilizes chaotic hash functions and logistic mapping to generate pseudo-random sequences and overcomes shortcomings of the Bose algorithm by iteratively iterating the selected Chebyshev polynomials based on the number of 0s or 1s in the pseudo-random sequence, thus providing better security. Analysis and software testing results indicate that this algorithm has strong robustness against brute force attacks, achieving a higher attack time for breaking the private key compared to the CEPKC, BMPKC, and CMPKC algorithms. Compared to the CMPKC algorithm, our proposal algorithm achieves better performance in the encryption and decryption phases. Furthermore, we combine this Multi-Chaotic System Key Exchange Protocol with the Advanced Encryption Standard (AES) algorithm, while providing a demonstration, offering more possibilities for practical applications of this system.

Funder

National Natural Science Foundation of China

Guangdong Province College Youth Innovative Talent Project

Guangdong Key Disciplines Project

FCT—Foundation for Science and Technology within the R&D Units Project Scope

Publisher

MDPI AG

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