Analysis Of The Randomicity Of Chaos Mapping

With the development of information technologies and the increasing of infornation exchange,the research on information security is becoming more and more important.The chaos-based encryption system provides an effective way to encrypt. After some treatment the chaotic sequence have very large cycles and excellent randomicity.Through the sensitive dependence on the initial values and parameters,it provides a numerous excellent keys to enhance encryption security.Randomicity of chaos mapping is a premise of applying chaos mapping to sequence encryption.This thesis studies the invariant distribution of chaos mapping,and analyzes the chaos randomicity through the variation of invariant distribution.Main contents and contributions of this thesis are as follows:1.Based on the studing of chaos theory and sequence cryptology theory,it uses the analysis method of randomicity by the variation of invariant distribution to research the randomicity of chaos mapping.The research of the invariant distribution figure of chaos mapping indicates that the method is feasible.2.Formula method,the histogram method and eigenvector method are compared by solving the invariant distribution of the Logistic mapping at the parameterμis 4.The results of the invariant distribution figures getted by three methods are consistent.3.It gets the invariant distribution function of Logistic mapping at the parameter ofμis 4 by formula method,the randomicity of the chaos sequence is proved. The invariant distribution of Logistic mapping(μ≠4) is solved by histogram method and eigenvector method.The experiments indicate that Logistic mapping has no bifurcation and the variation of invariant distribution is very small when the parameterμis between 3.99 and 4.4.The histogram method is used to solve the invariant distribution of hyper-chaos Henon mapping.The experiments indicate that the variation of invariant distribution of Henon map is very small when the parameter a from 1.98 to 2, and the parameter b from -0.005 to 0 or from 0.0084 to 0,so it has good randomness,and it is not overflow in iteration.5.An application project of hyper-chaos sequence cryptology was designed and implemented for a case of image encryption,that was based on image scrambled by Cat mapping and hyper-chaos Henon mapping disturbed by low dimension Logistic mapping.The result of security analysis indicates that the method has good cryptography characteristics. This thesis offers the foundation for application of chaotic sequence cipher by researching for the randomicity of chaos sequence.