Counteracting the Dynamical Degradation of Digital Chaos by Applying Stochastic Jump of Chaotic Orbits

Abstract

The performance of digital chaotic systems in secure communications and cryptographic applications is significantly degraded due to the limited precision of digital computational devices that are used to implement digital chaotic systems. However, regardless of the initial value, the digital chaotic map employed in these applications converges to several periodic orbits. Thus, a periodic orbit search algorithm (POSA) can be designed to accurately locate fixed points and limit cycles. In addition, an effective method based on stochastic jumps of chaotic orbits is proposed to counteract the performance degradation of digital chaos. Numerical simulations were performed to assess the effectiveness and feasibility of the proposed method in terms of autocorrelation, phase space inspection, approximate entropy and periodicity analysis. Furthermore, comparison with other existing methods is presented to show the competitiveness of the proposed scheme. Finally, a pseudorandom bit generator (PRBG), with desirable statistical properties, is constructed for chaos cryptography and other applications.