Construction of a novel nth-order polynomial chaotic map and its application in the pseudorandom number generator

• Published in: Nonlinear dynamics 2022-09, Vol.110 (1), p.821-839
• Main Authors: Zhao, Xinxin, Zang, Hongyan, Wei, Xinyuan
• Format: Article
• Language: English
• Subjects: Automotive Engineering; Chaos theory; Chebyshev approximation; Classical Mechanics; Conjugation; Control; Cryptography; Dynamic characteristics; Dynamical Systems; Engineering; Liapunov exponents; Mechanical Engineering; Original Paper; Polynomials; Pseudorandom sequences; Vibration
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-022-07641-x

Chaotic maps with good chaotic performance have been extensively designed in cryptography recently. This paper gives an n th-order polynomial chaotic map by using topological conjugation with piecewise linear chaos map. The range of chaotic parameters of this n th-order polynomial chaotic map is large and continuous. And the larger n is, the greater the Lyapunov exponent is and the more complex the dynamic characteristic of the n th-order polynomial chaotic map. The above characteristics of the n th-order polynomial chaotic map avoid the disadvantages of one-dimensional chaotic systems in secure application to some extent. Furthermore, the n th-order polynomial chaotic map is proved to be an extension of the Chebyshev polynomial map, which enriches chaotic map. The numerical simulation of dynamic behaviors for an 8th-order polynomial map satisfying the chaotic condition is carried out, and the numerical simulation results show the correctness of the related conclusion. This paper proposed the pseudorandom number generator according to the 8th-order polynomial chaotic map constructed in this paper. Using the performance analysis of the proposed pseudorandom number generator, the analysis result shows that the pseudorandom number generator according to the 8th-order polynomial chaotic map can efficiently generate pseudorandom sequences with higher performance through the randomness analysis with NIST SP800-22 and TestU01, security analysis and efficiency analysis. Compared with the other pseudorandom number generators based on chaotic systems in recent references, this paper performs a comprehensive performance analysis of the pseudorandom number generator according to the 8th-order polynomial chaotic map, which indicates the potential of its application in cryptography.