Bit cyclic shift method to reinforce digital chaotic maps and its application in pseudorandom number generator

Abstract

When chaotic systems are realized on finite precision devices, dynamical degradation occurs, which causes many flaws in chaos-based applications. In this paper, a new bit cyclic shift method is introduced to reinforce digital chaotic maps and counteract the problem of dynamical degradation. The state value of digital chaotic map is modified by circularly shifting its bits according to a designed shift strategy. This method is applied to the Logistic map to generate many new improved chaotic maps by changing the shift strategy. Theoretical analysis and numerical experiments demonstrate their chaotic parameter ranges and chaotic behaviors. Furthermore, the simulation results under low computing precision indicate that our method has the ability to counteract the dynamical degradation. This method has high flexibility and can apply to any chaotic system. Finally, a new pseudorandom number generator (PRNG) is designed to show the good performance of the improved digital chaotic maps.