Research On Chaotic Series Complexity Algorithm And Its Application In Image Encryption

The sensitivity to initial values,global boundedness,inherent randomness and high complexity of chaotic systems are closely related to the basic principles of cryptography,which makes chaotic encryption widely used in the field of information security.However,due to the limited computational accuracy and structure of the classical chaotic system,there will be some correlation between the elements of the chaotic sequence and the degradation of the chaotic dynamics characteristics,which will reduce the complexity of the chaotic sequence and bring some potential dangers to the information security.In order to promote the practical application of chaotic sequence in engineering,it is of great significance to analyze the complexity characteristics of chaotic sequence and study the method of increasing entropy value of chaotic sequence.The following four aspects around the above aspects of this work are listed below:Firstly,to test the behavior complexity and structure complexity of three classical chaotic mappings such as Logistic mapping,Tent mapping and Hénon mapping,the sample entropy,spectral entropy and fuzzy entropy of complexity measurement algorithm are fully studied.The effects of system parameters,initial values,time series length and other basic parameters on the complexity of chaotic sequence are analyzed and compared,and the entropy distribution characteristics of the three kinds of chaotic systems are analyzed,which provides a reference for the subsequent application research of chaotic systems.Secondly,according to the law of entropy distribution of classical chaotic maps,the characteristics of entropy distribution of Logistic maps are analyzed and a variance-mean system parameter interval estimation method is also proposed under the multi-scale entropy algorithm.Then,the estimation table of system parameter interval of Logistic and Tent chaotic sequences is obtained by using this method.In view of the chaotic complexity algorithm,the system parameters of some classical low dimensional chaotic sequences are predictable.Thirdly,aiming at the predictability of chaotic system parameters and the increase of sequence correlation caused by limited calculation accuracy of chaotic sequence,an algorithm based on phase space reconstruction technology and PCA algorithm are proposed to improve the complexity of chaotic sequence.The delay time and embedding dimension in the phase space reconstruction technology are obtained by mutual information function method and Cao method,respectively.Through the actual test of logistic sequence and Hénon sequence,the chaotic characteristics of the two chaotic sequences are greatly improved.Finally,in order to retain the advantages of classical chaotic systems and improve the complexity of low-dimensional chaotic time series,a three-dimensional discrete chaotic system,3D-PHM,is proposed,which combines Hénon mapping and piecewise mapping.The test results show that the chaotic properties of the system are better than the original chaotic systems.Then,a color image encryption algorithm with controllable number of rounds is proposed based on the multi-dimensional chaotic mapping.Through the test and statistical analysis of the image encryption algorithm,the performance of the encryption algorithm is validity.