基于扰动法的抗退化数字混沌系统研究

Design and Research of Anti-Degeneratione of Digital Chaotic System Based on Perturbation Method

研究数字混沌系统的退化问题对混沌密码学的发展有重要意义,扰动法能有效改善数字混沌系统的退化行为。首次提出对一维Chebyshev混沌系统的全部扰动对象进行扰动的方法,使Chebyshev映射表达式的每一个部分都被扰动源所影响,从而达到抗退化的目的。还对改进方案生成混沌序列的性能进行了对比与分析,结果表明,上述方案在低有限精度情况下不仅大大延长了数字Chebyshev混沌系统周期,使系统的动力学性能得到提高,扩展了密钥空间,可用于混沌密码算法的设计中。

The study on the degradation of digital chaotic systems is of great significance to the development of chaotic cryptography.The perturbation method can effectively improve the degradation of digital chaotic systems.The method of perturbing all the perturbed objects of one dimensional Chebyshev chaotic system wais proposed for the first time,so that every part of the Chebyshev mapping expression wais affected by the perturbation source,so as to achieve the purpose of anti-degradation.The performance of the chaotic sequence generated by the improved scheme is was also compared and analyzed.The results show that the scheme not only greatly prolongs the period of the digital Chebyshev chaotic system,but also improves the dynamic performance of the system and expands the space of the secret key.It can be used in the design of chaotic cryptography algorithm.