New and Efficient Method for Extending Cycle Length of Digital Chaotic Systems

Implementing chaotic systems using digital computers with finite arithmetic precision leads to significant degradations on their quality of chaotic dynamics, and the important shortcoming found on digital chaotic systems is their limited cycle length. Notable efforts have been exerted recently to overcome this problem and enhance the quality of digital chaotic generators, and the aim is to generate chaotic sequences with long cycle lengths. Perturbation of chaotic systems orbits is the most efficient technique that has been adopted in this context. In this paper, we propose a new method for perturbing the orbits of chaotic systems. Compared to many proposals, our method does not need an external generator to perturb the chaotic orbit, and it has a self-perturbation mechanism. Evaluation results showed that the proposed method can extremely extend the cycle length of a given chaotic system in which no repeated patterns have been detected even using low arithmetic precision. The results also showed that the perturbed chaotic system has good statistical proprieties in terms of randomness; it passed successfully a set of statistical tests (NIST and Diehard). The whole system has been implemented in FPGA-based hardware, and real-time results are given. Compared with some proposals, the proposed method has provided better results in terms of randomness and hardware performance.