Spatial Chaos And Its Application In Image Encryption

With the rapid development and extensive applications of computer and communication technologies, digital information is being applied more and more widely in the world. Digital information is easy to copy and distribute, this also produces many security problems in its applications. As a result, the security and protection of digital information are becoming increasingly a key problem that must be solved urgently.It's well known that cryptography is the fundamental method for information security. There is natural relationship between chaos and cryptography: such as the sensitive dependence on initial conditions and control parameters, the density of the set of all periodic points and topological transitivity which are related to some requirements such as confusion and diffusion in cryptography. Therefore, chaos-based encryption techniques play an increasing role in information security. Since 1980s, the idea of using chaotic systems to design new ciphers has attracted more and more attention, and much more contributions are made to get many promising achievements. However, recently, a majority of chaotic ciphers have been analyzed and proven not to be practicable, efficient and secure. Especially, for Encryption of images, it is different from that of texts due to some intrinsic features of images such as bulk data capacity and high redundancy, which are generally difficult to handle by traditional methods. How to design secure chaos-based encryption scheme in terms of detailed analysis is becoming a key problem that must be solved urgently.In this dissertation, we study the image cryptosystems based on high-dimensional chaotic systems in detail. Spatial chaotic systems are firstly introduced to cryptography, and several image cryptosystems based on spatial chaotic systems are designed. In addition, the nonlinear characteristics of molecular orbit are studied, and the existence of spatial chaos and bifurcation are also proven. The main achievements and originality contained in this dissertation are as follows:1. The research status and advances of chaotic ciphers has been summarized, analyzed and reviewed, and several existent key problems to be solved urgently have been pointed out;2. Chaos theory is introduced in detail. First, the research history of chaos is reviewed. Second, the definition of chaos is proposed. Third, the definitions of cryptography are aggregated. Finally, the relationship between chaos theory and cryptography is compared in detail, and some image encryption methods are introduced;3. Image encryption based on high-dimensional chaos has been suggested. This new scheme employs the Arnold cat map to shuffle the positions of image pixels and uses Lorenz chaotic map to confuse the relationship between the cipher-image and the plain-image;4. Using couple map lattices to realize image encryption, and experimental tests and security analysis are carried out, the results show the image encryption scheme is secure and fit for digital image encryption;5. The nonlinear motion forms of carrier wave functions for square-lattice conjugated molecules with rectangular boundary, straight-chain-conjugated molecules and monocyclic- ring-conjugated molecules are mainly studied. The nonlinear characteristics of molecular orbit, such as chaos, bifurcation, and other nonlinear properties, are studied. In addition, the relationship between molecular orbit and its energy level in the nonlinear dynamic system is also discussed, and the existence of spatial chaos and bifurcation are also proven;6. A scheme for pseudo-random binary sequence generation based on the spatial chaotic map is proposed. In order to face the challenge of using the proposed PRBS in cryptography, the proposed PRBS is subjected to statistical tests which are the well-known FIPS-140-1 in the area of cryptography, and correlation properties of the proposed sequences are investigated. The proposed true random bit generator successfully passes all four statistical tests for every run. The results of the tests on the sequences show the perfect cryptographic performance;7. Based on spatial chaos system, designing two image encryption methods, employing security analysis, and realizing image encryption/decryption using spatial chaos; 8. Finally, the research work of this dissertation is summarized, and the future research direction is indicated.So investigating spatial chaos system and application in image encryption, it can not only enrich chaos secrecy communication, but also understand spatial chaos from another angle. Hence there are important the theory and practical values for the thorough understanding of spatial chaos system.