引用本文:徐辉,佟晓筠,张淼,刘杨,王翥.单峰混沌系统的相空间均匀化及动力学特性[J].控制理论与应用,2019,36(5):759~765.[点击复制]
XU Hui,TONG Xiao-jun,ZHANG Miao,LIU Yang,WANG Zhu.Phase space homogenization and dynamic characteristics of unimodal chaotic system[J].Control Theory and Technology,2019,36(5):759~765.[点击复制]
单峰混沌系统的相空间均匀化及动力学特性
Phase space homogenization and dynamic characteristics of unimodal chaotic system
摘要点击 1954  全文点击 815  投稿时间：2018-03-07  修订日期：2018-09-13
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DOI编号  10.7641/CTA.2018.80157
  2019,36(5):759-765
中文关键词  混沌系统  单峰映射  概率密度  信息熵
英文关键词  chaotic systems  unimodal mapping  probability density  information entropy
基金项目  国家信息保障重点实验室基金(No.KJ-17-004)；2017威海大学共建项目；国家自然科学基金(No.61702139)；黑龙江省普通高等学校青年创新人才培养计划(UNPYSCT-2016036)
作者单位E-mail
徐辉 哈尔滨工业大学 banmianstudent@163.com 
佟晓筠* 哈尔滨工业大学（威海） tong_xiaojun@163.com 
张淼 哈尔滨工业大学（威海）  
刘杨 哈尔滨工业大学（威海）  
王翥 哈尔滨工业大学（威海）  
中文摘要
      由经典一维混沌映射构造密码系统存在短周期轨道、密钥空间小和相空间分布不均匀等安全性缺陷. 为解决经典一维混沌密码的安全性问题, 提出了一种新型的一维单峰混沌系统及其改进的复合形式. 采用普适性均匀化算法来获得等概率分布的混沌序列并给出了概率密度数学证明. 对改进的单峰混沌系统的遍历性、李雅普诺夫指数、相空间和分岔、信息熵和近似熵等动力学和随机特性指标进行了计算和分析. 通过与相关研究的对比可知, 改进的单峰混沌系统具有稳定的李雅普诺夫指数、扩展的相空间、均匀的概率密度和更高的近似熵值. 理论推导和数值计算论证了本方案可以满足密码系统中非线性部件的安全属性要求.
英文摘要
      The cryptosystem constructed by classical one-dimensional chaotic mapping has some shortcomings in terms of security such as short-period orbits, small key space and inhomogeneous distribution of phase space. In order to solve the security problem of classical one-dimensional chaotic ciphers, a novel one-dimensional unimodal chaotic system and its improved composite form were proposed. A universal homogenization algorithm was used to transform the chaotic sequence into an equal probability distribution and a probability density mathematical proof was given. The dynamics and random characteristic indicators such as ergodicity, Lyapunov exponents, phase space, bifurcations, information entropy and approximate entropy were calculated and analyzed for the improved unimodal chaotic system. Through comparison with related researches, it can be seen that the improved unimodal chaotic system has stable Lyapunov exponents, extended phase space, uniform probability density and higher approximate entropy. Theoretical derivation and numerical calculation demonstrate that this scheme can meet the security attributes of nonlinear components in cryptosystem.