改进分段Logistic混沌映射的方法及其性能分析  

Method for improving piecewise Logistic chaotic map and its performance analysis

作　　者：蔡丹[1] 季晓勇[1] 史贺[1] 潘家民[2] 

机构地区：[1]南京大学电子科学与工程学院,南京210023 [2]南京大学网络信息中心,南京210093

出　　处：《南京大学学报（自然科学版）》2016年第5期809-815,共7页Journal of Nanjing University（Natural Science）

摘　　要：Logistic混沌映射和Tent映射是两种广泛应用于通信安全领域的混沌映射,Tent映射具有分段特性,由此联想到将Logistic混沌映射推广为分段映射.提出一种三分段相切的Logistic混沌序列的方法,不仅规避了Tent映射需施加随机扰动的过程,并改善了Logistic混沌映射的随机性能,增加了系统的复杂度和抗攻击能力.实验证明在相同的区间上,三分段相切的Logistic混沌映射更早地进入混沌状态,且在3.57≤μ≤4时运动轨迹愈发地不稳定,Lyapunov指数为逐渐增大的正数,更复杂的非线性方程提高了系统的安全性.在相同的分叉判定阈值下,三分段相切Logistic混沌映射进入混沌状态时需要的迭代次数明显减小.因此,三分段相切的Logistic混沌序列具有更加良好的随机性和不可预测性.经过研究表明,该三分段相切的Logistic混沌映射具有良好的初值敏感性,广泛地适用于信息安全领域.Logistic chaotic maps and Tent chaotic maps are widely applied in the field of the communication security . Tent chaotic maps have piecewise characteristics ;sowe can apply the piecewise features in Logistic chaotic mapsnaturally .The paperproposes a method that Logistic chaotic maps can be divided into three segments which are tangent each other（three‐segment and tangential piecewise Logistic chaotic maps ） .The method can avoid the process that Tent chaotic maps need to apply the stochastic perturbation ,and it also improves the randomness of Logistic chaotic maps ,which increases the complexity and anti‐attack capability of the chaotic system .Onbasis of the experiment ,the paper proves that three‐segment and tangential piecewise Logistic chaotic maps can enter into chaotic state earlier on the same interval ,and their trajectory are increasingly unstable when μis between 3 .57 and 4 .The Lyapunov exponent is positive and it increases gradually ,thus more complicated nonlinear equation improves the security of system .Under the same bifurcate criterion threshold ,the number of iterations is decreased dramatically when three‐segment and tangential piecewise Logistic chaotic maps enter into chaotic state .Therefore ,three‐segment＆amp;nbsp;and tangential piecewise Logistic chaotic sequences have better randomness and unpredictability .The experiment shows that three‐segment and tangential piecewise Logistic chaotic maps are initial‐value sensitivity ,so they will be widely applied in the field of information security .

关 键 词：混沌 分段Logistic混沌映射 TENT映射 随机性 

分 类 号：TN918[电子电信—通信与信息系统]