Using the Bit Interleaving Shift Method to Counteract the Dynamic Degradation of Digital Chaotic Systems

The operation of digital chaotic systems on devices with finite precision can lead to dynamical degradation, thereby posing a potential treat to system security. This study proposes a method called Bit Interleaving Shift (BIS) to counteract the dynamical degradation issue arising in the iterative process of digital chaotic maps. This method performs BIS on chaotic maps represented in fixed-point numbers using the generated interleaving block matrix. Simulation analysis shows that chaotic maps improved by this method have longer periods compared to traditional methods, making them more effective in combating dynamical degradation. Moreover, a novel pseudo-random number generator (PRNG) has been designed, and its exceptional randomness has been confirmed. Therefore, this method can be applied to fields such as cryptography and spread spectrum communication.