The Characteristic Analysis Of Digital Chaos And Its Research On The Applications Of Cryptography

The data of image, text and audio can be conveniently saved and transferred by multiplie terminals with the rapid development of communication technology, however, the data security issues has also followed, e.g. the personal privacy data is vulnerable to illegally stolen. In order to ensure the the relative security of data, cryptographic techniques have drawn more and more attention. Encryption algorithm and hash function are the two basis methods in the field of information security. As part of the traditional cryptography algorithms are threatened with the development of information technology, therefore, researchers gradually turn to new research field of the cryptography. As for the nonlinear science based chaos theory, which has been widely recognized due to its pseudo-randomness, ergodic, unpredictability and initial condition sensitivity since the data of its discovery, it has been an important research hotspot in the cryptography.In recent years, great progress has been made in the chaos based encryption algorithm and hash function, however, the corresponding achievements lack unitary standards up to now as the research of chaos theory is not mature yet, and there are security and efficiency problems exsit as well. Meanwhile, researchers note that the chaos degradation may reduce the security of the chaos based cryptography systems, so the phenomenon of degradation of chaotic dynamics under finite precision has received significant attention. Based on the current research findings and on the basis of reduing the chaos degradation consideration, this thesis is to investigate how to design the image encryption algorithm and build the hash function. The tent map is employed as the entry point and the main contributions of the thesis include four aspects:1. The research background of project is firstly introduced, which includes the development course of chaos theory and the chaotic cryptography, then the innovation points of this thesis are told. The basic cryptosystem model is described, the relationships and differences between chaotic characteristics and the "diffusion and confusion" based cryptography is also revealed. The current research status of the chaos degradation, the chaos based image encryption and chaos based hash function are briefly summarized, respectively. Then, the current deficiencies in the chaotic cryptography are analyzed and the corresponding solutions are also provided.2. This thesis proposed an improved system based on the tent map and Chebyshev map to reduce the degradation phenomenon, the parameter of tent map is perturbed on the basis of Lyapunov exponent. The tent map is the orginal pseudorandom numbers generator, each status value from the self-iteration of the tent map will be mapped again by the Chebyshev function. Once the output value from the Chebyshev falls into a fixed interval, this value will not only be the final output but also be transferred to the tent map to replace the original parameter. The tests result shows that the improved system has better performance than the original chaotic systems in the respects of auto-correlation, chaos attractor and approximate entropy, it also passed the SP 800-22 test and has good initial condition sensivity.3. The improved system which based on the tent map and Chebyshev map is utilized to design an image encryption algorithm. Firstly, the plain image and initial key are quantified to be a decimal in (0,1), and the decimal is used as the initial value of the improved system. Then, two one-dimensional ergodic matrix are constructed based on the chaotic orbits and will be used to scramb the pixels. The pixel-value permutation is achieved by a kind of reversible division operation, and the permutation sequential is controlled by the chaotic values. Performance analysis shows that this encryption algorithm has big key space, high efficiency and has the ability to defend the cryptanalysis based attack e.g. statistical analysis, differential attack, chosen/known plain image attack and occlusion attack etc.4. A high dimension chaos system based on the Coupled Map Lattices (CML) and tent map is implemented by the fixed point decimals in FPGAs. Then, an embedded security model with hash function is developed on the basis of the chaos system. This model can fastly generate binary code with fixed length, and the hardware resources usage is relative low. The binary codes generated by the security model are highly sensitivity to the initial conditions and also satisfies the ideal requirements of "diffusion and confusion". Finally, an information authentication rule is defined based on the security model and it will be used for the embedded copyright protection.