Abstract
A new and improved method based on the number of iterations is proposed to reduce the dynamical degradation of the digital chaotic map in this study. We construct a control function by introducing iteration time instead of external systems, thereby replacing the control parameters in the original chaotic map. Experimental results show that the chaotic map based on the iteration-time combination method is more complicated and effective. The period is extended without completely destroying the phase space, which indicates that our method is effective and can compete with other proposed techniques. A type of pseudorandom bit generator based on the iteration-time combination method is proposed to demonstrate its simple application.
Highlights
Due to the accuracy limitations of devices, most chaotic maps cannot reach their ideal state [1]. us, dynamic degradation occurs where a chaotic system falls into a loop in a limited phase space, which decreases the dynamic performance of the chaotic system and not meet the demand in many cases
We introduce the number of iterations to replace the control parameters in the original chaotic map
We combine this number of iterations with the trigonometric function, such that the control parameter functions satisfy the range requirements of the chaotic map
Summary
Pseudorandom process that appears in nonlinear dynamical systems. e irregularity of the process, sensitivity to the initial state, and good ergodicity of the range make this phenomenon compatible with modern cryptography, which requires the principle of confusion and diffusion. Complexity method [14, 15] can be effectively used to improve the dynamic degradation of chaotic maps by hybrid control of analogy chaotic systems and digital chaotic maps. In this approach, the phase space will be absolutely destroyed. Erefore, in this study, we propose a new approach to improve dynamic degradation by introducing iteration times. Different from many other techniques [9, 16], our proposed method does not destroy the phase space of the original chaotic map while improving the dynamic degradation phenomenon.
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