The Characteristic Analysis Of The Complicated Chaotic System And Its Application In Image Encryption

The hot topic for developing new information security protection technologies is to integrate various non-traditional approaches into those fields of information security,it is increasingly drawing more and more attention.Chaos is the natural phenomenon of nonlinear dynamic,and it poses those special features of great sensitivity to initial values,high randomness and unpredictability of chaotic orbit,which are closely related to confusion and diffusion in cryptography.Combining chaos theory to cryptography becomes chaotic cryptography.The chaotic cryptography has popularly grown in the interdisciplinary research of nonlinear science and information science due to strong privacy guarantee,better randomness and larger key space.Chaos system commonly contains two categories: the simple chaotic system and the complicated chaotic system.Compared with a simple one,the complicated model owns multiple positive Lyapunov exponents,the longer orbit period and more complicated dynamic behaviors.With aim to enhance the security,the complicated model is used in the chaos-based cryptography.Especially,the coupled map lattice(CML)model is a classical complicated one,due to the parallel structure,it has the advantage of high efficiency.Meanwhile,its chaotic sequences are strong randomness.Therefore,CML has been widely used in those sub-fields,such as pseudo-random number generator(PRNG)and the image encryption.Moreover,the digital image is an important carrier of multimedia information in the era of big data,and it is closely related to the privacy protection of personal sensitive information,country’s economic and military interests.So,it is fairly essential to discuss the privacy of digital images.This thesis analyzes the current states of chaotic cryptography,CML model,PRNG,the chaos-based image encryption algorithm and the chaos-based compression image encryption algorithm at home and abroad to outline the main challenges in the current research.From the view of application in information security,theoretical analysis of those security characteristics in a complicated chaotic system is relatively lacking,probability density distribution(PDD)of chaotic sequences generated by complicated chaotic system is not uniform,there is also lack of theoretical basis in secure of PRNG,both security and efficiency of the chaos-based image encryption algorithm should be further improved,there exists few research in image encryption algorithm of combing the complicated chaotic system and compressive sensing.To overcome those above-mentioned problems,the following core issues are depicted from theory to practice,including characteristics analyses of the complicated chaotic model,the designing of PRNG via the theoretical results,the chaos-based image encryption algorithm and the chaos-based compressive image encryption algorithm.To sum up,the main works and contributions in this thesis are summarized as(1)Lyapunov exponent and synchronization stability of two-dimensional(2D)CML model and three-dimensional(3D)CML model are theoretically analyzed.Lyapunov exponent is the critical issue for measuring whether the dynamical system is in a chaotic state or not.In this thesis,mathematical expressions of Lyapunov exponent in the 2D CML model and 3D CML model are given theoretically.Consequently,Lyapunov exponent values are calculated accurately to judge the CML’s chaotic state,as well as providing some theoretical outstanding for CML’s engineering application.Synchronization stability is used to measure the degree of chaotic state in the models,mathematical expressions in the 2D CML model and the 3D CML model are derived in this thesis,according to those mathematical expressions,the CML’s parameters are set reasonably to avoid the synchronization phenomenon of models in cryptographic applications.(2)This thesis performs the uniform processing in PDD of the 2D CML model and the 3D CML model.Those experimental analyses show that the 2D CML and 3D CML’s PDDs are not uniform,from the standpoint of security application in cryptography,the non-uniform PDD leads to security risks of easily being attacked and predicted in those chaos-based schemes 2D CML and 3D CML’s PDDs become uniform via the offset method and the uniform algorithm,respectively.The uniform PDD enhances the security and offers security guarantees for CML being applied to the cryptography fields.(3)Theoretical research and quantitative verification are carried out from chaos theory to pseudo-random number.PRNG,as a well-known component in cryptography application,is designed based upon the complicated chaotic system(i.e.2D CML and3 D CML).The 2D CML’s theoretical characteristics of decimal and the uniform bounded deviation are theoretically demonstrated at first.Under the above-analyzed theory guidance,PRNG is designed via the 2D CML model,and also the extraction algorithm E is proposed through simple operations such as XOR.The algorithm E with theoretical guarantees has been discussed from the qualitative and quantitative analysis.At the same time,it also takes into account efficiency.Finally,the fast and safe PRNG algorithm is proposed according to the 3D CML model,the truncation algorithm T is designed through simple operations such as interception.Those quantitative analyses show that algorithm T has high security and high efficiency.Therefore,PRNGs designed via the 2D CML model and the 3D CML model can meet the needs of security application in cryptography.(4)The chaos-based image encryption algorithm is proposed via the 2D CML model and 3D CML model.To begin with,the storage space of original color image is decreased using the singular value decomposition(SVD)method.Then,the red,green and blue(RGB)channels of image are combined and scrambled in blocks according to the Arnold transform.Finally,the chaotic sequences generated by the 2D CML and 3D CML model are used to diffuse the scrambled image.The experimental analyses,such as statistics,information entropy,differential attack,security and so on,show that the proposed chaos-based image encryption algorithm has good encryption performance,high efficiency and important application prospects.(5)The chaos-based image encryption algorithm is designed combining the improved 2D CML model(or the 3D CML model)and compressive sensing.To further improve the computational efficiency of the 2D CML model,the model with coupling four nodes has been improved the model with two nodes firstly,and also mathematical expression of Lyapunov exponent in the improved 2D CML model is theoretically showed in this thesis.It is verified that the improved 2D CML model follows independent and identical distribution with the independent testing,it satisfies the Restricted Isometry Property(RIP)protocol.Then,the improved model is utilized to construct the chaotic measurement matrix and perform the compressed sampling of the image.And also the image diffusion is realized through the chaotic sequences generated by the improved 2D CML model.The simulation analyses,such as statistics,information entropy,differential attack,security and so on,show the proposed chaos-based compression image encryption algorithm has outstanding performance and huge application potential.To sum up,the research of this thesis is carried out for the theoretical and application problems that need to be solved urgently in the complicated chaotic systems,and also the theory research and practice research are closely combined,which has both important theoretical value and practical application value.