Construction and application of new high-order polynomial chaotic maps

Springer Science and Business Media LLC - Tập 107 - Trang 1247-1261 - 2021
Hongyan Zang1, Xinxin Zhao1, Xinyuan Wei1
1Mathematics and Physics School, University of Science and Technology Beijing, Beijing, China

Tóm tắt

Generating pseudorandom numbers with good statistical performance based on chaotic maps has become a topic of interest in chaotic cryptography. Several high-order polynomial chaotic maps with special forms are proposed by the Li–Yorke theorem in this paper, and chaotic conditions and intervals are given. The dynamical behaviors of chaotic maps satisfying the chaotic conditions are numerically analyzed, such as the bifurcation and Lyapunov exponent, the analysis results show the correctness of the related chaos criterion theorems. Chaotic maps are essential for the design of pseudorandom number generator and are widely used in many applications. Based on the superposition of chaotic maps, a pseudorandom number generator is designed, and the available chaotic parameters of the pseudorandom number generator are increased through the superposition of chaotic maps. This paper tests and analyses the performance of pseudorandom sequences produced by the pseudorandom number generator, and the analysis results show that pseudorandom sequences produced by pseudorandom number generator have good randomness, uniformity, complexity, and sensitivity to the initial parameters. Performance analyses show that the pseudorandom number generator in this paper can generate sequences with high quality. Several high-order polynomial chaotic maps we constructed based on the Li–Yorke theorem enrich the chaotic map and provide the possibility for its application in the field of cryptography.

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