Study On 4-D Hyper-Chaotic System And Application To Image Encryption

The construction and treatment of four-dimensional chaotic system is studied in this paper, and chaotic cryptographic technique applied to the image encryption technologies is illustrated. Chaotic system, characterized by its complex dynamical characteristics, is studied as chaotic cryptographic combined with cryptography. The formation and development of chaotic cryptographic supplies a solid foundation for the theory of security communication, especially in the aspect of image processing. Digital image is characterized by its containing of many redundancy data and strong correlation of data ,which is convenient for the usage that chaotic cryptographic applied to digital image encryption. Based on the present theory, a typical chaotic system family is illustrated; theoretical studies and simulation analysis are proceeded.Firstly, after analyzing the method of reduced dimensionality system expanding into the high dimensionality system, combining with enlarging dimension method idea, a new variable, which is the linear function of system variable, is introduced, so the new four-dimensional system is constructed. Based on the three-dimensional Lorenz chaos system, a four-dimensional Lorenz system is constructed in this paper. By observing Lyapunonv index of the system, the data range of the system parameter is given, in which the system is chaotic system or hyer-chatic system, and performance analysis of the output sequence of the system is done afterwards. According to the simulation experiment results, the chaos characteristics of the four-dimensional hyper-chaos system are approved.Secondly, according to the deficiency of the currently used method for the pretreatment of the chaos output sequence, a new method based on the subsection idea for the pretreatment of the sequence is proposed. The method is operated on the real value sequence itself, so it can be applied to any data on any range. Set a four-dimensional Lorenz hyper chaos output sequence as an example, data processing, correlation comparison and random testing are done to the example. The results show that the data sequences behave better in cryptography performance after treatment.Finally, chaotic cryptography applied in digital image encryption is studied. Based on the currently image encryption algorithm, a four-dimensional Lorenz hyper chaos system with different parameter configuration is adopted, in which point multiplication and binary addition are introduced, then image wavelet coefficients are encrypted in the wavelet domain. The performance analyses are done for the encryption results afterwards. The simulation results show that the algorithm is good at encryption performance, is large in key-space and is strong at robustness.