有限精度下Skew Tent映射的抗退化研究  

Research on Anti-degradation of Skew Tent Mapping with Finite Accuracy

作　　者：高世蕊 赵耿[1] 马英杰[1] GAO Shirui;ZHAo Geng;MA Yingjie(Beijing Electronic Science and Technology Institute,Beijing 100070,P.R.China)

机构地区：[1]北京电子科技学院,北京市100070

出　　处：《北京电子科技学院学报》2023年第1期19-29,共11页Journal of Beijing Electronic Science And Technology Institute

基　　金：北京高校“高精尖”学科建设项目(项目编号:3201017);国家自然科学基金资助项目(项目编号:61772047)。

摘　　要：混沌是指确定性动力学系统在初值变化细微的情况下,经过足够多的迭代后表现出来的不可预测性、类随机性的非周期性运动。随着混沌系统在通信工程、密码学、图像加密等方向的应用,有限精度下混沌系统动力学性能退化的问题就随之出现。提高混沌系统有限精度下的动力学性能有多种方法,其中,直接提升应用环境计算精度的代价太大、实际操作性不强。文中从提高混沌系统的抗退化性能方向入手,提出一种利用Lorenz系统对Skew Tent进行参数、输出扰动,从而提高Skew Tent系统的抗退化性能的方法,同时也克服了Skew Tent系统会进入不动点的情况。随后通过对改进后的系统进行初值敏感性、回归映射、自相关性、近似熵测试以及对量化后混沌序列进行NIST测试,结果表明使用该方案改进后的Skew Tent系统具有良好的混沌性,在通信工程、混沌密码算法设计、图像加密等方面有良好的应用前景。Chaos refers to an unpredictable and randomness-like aperiodic motion of deterministic dy-namic system after sufficient iterations in the case of slight initial value change.With the wide applica-tion of chaotic system in communication engineering,cryptography,image encryption and other fields,dynamic performance degradation problem of chaotic system under finite accuracy appears.Dynamic performance of chaotic system under finite accuracy could be improved by many ways,among which,the way of directly improving the application environment calculation accuracy has problems of high cost and weak practical operability.In this paper,improving the anti-degradation performance of chaotic sys-tem is first discussed and a method utilizing the Lorenz system to perturb the parameters and output of the Skew Tent is proposed,to improve the anti-degradation performance of Skew Tent system as well as avoid the condition that the Skew Tent system gets into the fixed point.Then,the improved system is tested in many respects including the initial value sensitivity,the chaotic return mapping,the autocor-relation and the approximate entropy.In addition,the NIST test of the quantized chaotic sequence is performed.Test results show that the improved Skew Tent system has great chaos and a promising appli-cation prospect in communication engineering,chaotic cipher algorithm design,image encryption,etc.

关 键 词：洛伦兹映射 斜帐篷映射 抗退化 扰动 有限精度 

分 类 号：O415.5[理学—理论物理]