Research On Application Of Chaos In Information Security

Chaos theory deals with nonlinear dynamical systems with special properties. It is widely existed in natural world. It can be found in some science and technology, such as physical, chemical, biological phenomenon and also can be found in social sciences. Such chaotic properties as ergodicity, sensitive dependence on initial conditions, positive Lyapunov exponent, counterfeit stochastic, etc. are quite advantageous to construct information security scheme such as image encryption, secure communication, disposing of digital graph, disposing of signal, controlling and optimization. Chaotic system and its useful application in information have been widely studied in recent years and many kinds of chaos application scheme have been proposed so far. The dissertation focuses on the principles, theory, and applications of chaotic information security, such as in-deep and systemic study on how to improve image encryption algorithm and chaotic system, design digital image data hiding and digital watermarking algorithm, solve the chaotic synchronization problems and apply chaos to security communication. The main achievements of this dissertation include: 1,An digital image encryption and decryption algorithm based on chaos sequence has been proposed. This algorithm improved general digital image encryption algorithm. Based on sensitive dependence on initial conditions of chaotic sequence, image is directly encrypted. This algorithm provides low computational complexity, high security and no distortion. Experimental results are satisfactory. 2,A new kind of method to design chaotic system which can be applied to generate chaotic sequence ciphers. Firstly, one kind of simply and easily realized chaotic system is designed and mathematic properties of this chaotic system is also given; Secondly, several statistics properties of chaotic system are studied based on simulation experiment. The results show that the chaotic sequence generated by this chaotic system has excellent statistical properties. Finally, this chaotic system is applied to generate chaotic sequence ciphers; the experiment results show that ciphers have excellent correlation. 3,A digital image hiding technology based on chaos map and image blending is proposed. Firstly, with chaos map, a hiding image is randomly scrambled. Secondly, the carrier image is divided into subblocks according to the size of the hiding image, each subblock correspond to each pixel of scrambled image. Then with the digital image blending technology, the pixel of hiding image is blended into the subblock of carrier image. Chaos map and image blending technology are introduced to improve the imperceptibility, security and robustness of hiding image. A watermarking system based on digital signature and chaos map is proposed. Based on original image, chaos map, it can generate a new a black and white image, this image is a security image. Chaos map and digital Signature technology are introduced to improve the watermarking security. A digital watermarking algorithm of image based on chaos mod is proposed. The embedded positions are determined by chaos sequence generated by chaos map, so position for embedding is random. Retrieval of the embedded watermark does not need the original image. 4,The synchronization of the generalized Lorenz systems via observer approach is further investigated. A corollary for the synchronization of the unified chaotic system is deduced. Numerical simulation shows its feasibility. A variable feedback synchronization theorem for hyperchaotic systems is proposed and applied to hyperchaotic systems numerically. It is also demonstrated that the given method can be applied for some other concrete systems. A chaotic secure communication scheme is proposed by introducing a concept of key function (KF) and key initial conditions (KICs). By using KF, secret signal is compounded with complex chaotic signal in order to enhance the security of transmitted signal. KICs are used to enlarge minor mismatch of drive signal so as to increase initial conditions sensitivity of the auxiliary driver system. At encrypter, based on encryption key functions (EKFs), a sufficiently complicated chaotic signal is generated which consists of masked secret information and chaotic system signals. In this system, making use of an auxiliary chaotic system to drive two identical chaotic systems, so the two embedded chaotic systems in encrypter and decrypter can be synchronized. During decryption processing, if and only if decrypter offer the same KICs and right DKF corresponding to EKF, it can retrieve secret information. This method is also effectively used to sender-to-group-to-receivers (SGR) transmission scheme. Finally, the work of this dissertation is summarized and the prospective of future research is discussed.