Study Of Chaotic Sequence Generating Method And Its Applications

With the development of information and network technology, informationsecurity is getting much concern. As information technology is popularized anddeveloped, how to ensure the confidentiality, integrity and availability ofinformation is becoming a fundamental problem, which has made informationsecurity one of the hotspot in the current research field of information technology.In all the research areas of information security, cryptography theory andtechnology is at the core position.Chaos is a unique movement appeared in nonlinear dynamic systems. It is aseemingly irregular movement form in the determination of nonlinear systems,which can be achieved in the class of random behavior without any additionalrandom factors. Chaotic systems have some properties in common: uncertainty,initial parameter sensitivity, ergodicity, mixing, rapid decay of the autocorrelation,long-term unpredictability and pseudo-randomness. The properties of initialparameter sensitivity, ergodicity and pseudo-randomness of chaotic system aresimilar to the requirements of cryptography, thus the two basic principles ofcryptography, confusion and diffusion will have some corresponding propertiesin the chaotic system. The natural connection and structural similarity betweenchaos and cryptography provide a good foundation for the application of chaosin cryptography.Chaotic sequence generation methods based on chaotic systems and sequenceevaluation methods are studied in this dissertation. We also study Hash functionconstruction methods, image segmentation methods and digital imageprotection technologies based on chaotic systems. The specific work includesthe following aspects:1. Current cryptography works based on chaotic system are summarized,including the definition of chaos, chaotic motion properties, several commonchaotic systems and related criteria of using chaos in cryptography.2. Performance evaluation criteria of pseudo-random sequence generated bychaotic systems are studied, and a chaotic system initial parameter sensitivitycriterion, the number of bifurcation iteration, is proposed and applied into theevaluation of chaotic systems. The effectiveness of the evaluation is analyzed byexperimental simulations.3. Combined with the properties of the LFSR and chaotic systems, a sequencegeneration method is designed based on LFSR and chaotic system. Since thecombination of LFSR and the chaotic system lead to a larger key space, thechaotic system that uses the LFSR generating selection function increases thedifficulty of cryptanalysis attacks. The feedback value of the LFSR and thefeedback value of the generated binary sequence are operated with XOR way, which can achieve operation of LFSR random disturbance and make thegenerated sequence have good safety and randomness. The method can notonly generate pseudo-random binary sequences, but also generate realpseudo-random sequences. The two pseudo-random sequence generationprocesses are achieved by several simple chaotic systems and repetitioniteration, which reduces complexity of the computation process, and facilitateshardware implementation as well.4. Properties of Logistic and Tent chaotic systems are studied. On this basis, apiecewise Logistic map construction method is presented, and its performance isanalyzed by experimentations. Experimental results show that, pseudo-randomsequences generated by the piecewise Logistic chaotic map have goodrandomness, initial parameter sensitivity and other properties, and it does notrequire a corresponding disturbance in the process of generating chaoticsequence using piecewise Logistic map, which can effectively improve theefficiency of the algorithm. Because the piecewise Logistic map has goodbifurcation speed and can be used in Hash function construction method, a Hashfunction construction method based on piecewise nonlinear chaotic system ispresented.5. The properties of Bernstein basis function and the distribution of sequencesgenerated by Arnold chaotic system are studied. On this basis, apseudo-random sequence generation method is designed based on Bernsteinbasis functions and the chaotic sequence. The related properties of thegenerated pseudo-random sequence are analyzed by simulations. Experimentalresults show that, sequences generated by Bernstein basis functions andinterpolation operations have the characteristics of random distribution, and itsdistribution is also more suitable for the image segmentation method based onchaotic optimization algorithm. According to the sequence distribution properties,the generated sequence is applied to image segmentation based on chaoticoptimization algorithm, and good segmentation results are achieved.6. Digital image protection technologies based on chaotic system are studied,including an adaptive digital image encryption algorithm based on chaos, adigital image encryption algorithm that can withstand shear transform attacksbetter, and a digital image encryption algorithm based on image fusion technique,a digital image hiding algorithm based on chaotic iteration structure and animage hiding algorithm based on image fusion that can treat two images withdifferent sizes.