Counteracting dynamical degradation of a class of digital chaotic systems via Unscented Kalman Filter and perturbation

Abstract

Theoretically, any chaotic system or chaotic map has ideal complex dynamics. However, because of the finite precision of simulation software and digital devices during implementation, chaotic systems often undergo dynamical degradation, which hinders the further application of digital chaotic systems in many fields. Therefore in this paper, the method based on the perturbation and Unscented Kalman Filter (UKF) theory is designed to counteract the dynamical degradation of digital chaotic systems. Specifically, the UKF algorithm is employed to reinstate the original dynamic performance of the chaotic system, and then perturbation feedback technology is used to cause the chaotic system to obtain strong dynamic performance to resist attacks. The experimental and simulation results demonstrate that this method has good effect on improving the dynamic degradation of digital chaotic map. In addition, the corresponding pseudorandom number generator (PRNG) is constructed via this method, and its randomness is evaluated using the National Institute of Standards and Technology (NIST) SP800-22 and TestU01 test suites. By comparing with other schemes, it can be seen that this PRNG has better performance which illustrates the proposed scheme can be applied in the chaos-based cryptography and utilized in other potential applications.</p