High-dimensional Chaotic System And Its Application On Image Encryption

The modern society has entered the era of the data explosion of information, and avariety of multimedia information appear in people’s daily life. Accompanied byinformation growth from more and more serious information security threats, how toprotect information security has become an important direction of research. Digital imagewith an intuitive, image, vivid features become an important form of multimediainformation. The digital images (especially the high-definition images) are different fromthe text data. They have enormous information, two-dimensional distribution, a largenumber of redundant data. So the traditional encrypting methods can not meet therequirements of the digital image encrypted. Since chaotic system was found, the excellentcharacteristics of chaotic systems which include ergodicity，the class randomness andwhich are sensitive to initial values and system parameters are similar to cryptography，many researchs pay attention to this field. Some researchs are using chaotic system andcryptography to encryp digital images. Compared with the general chaotic system，hyperchaotic system has complex dynamical behavior, better randomness andunpredictability, larger key space, higher security，and get a wider application in imageencryption.Firstly，in this paper，a chaotic system is associated with another chaotic systems byadding state feedback. The state feedback as a bridge connect the two chaotic systems andbuild a new high-dimensional chaotic system. Through the dissipative analysis, balancepoint analysis, Lyapunov exponent analysis and the drawing of phase track figure,Poincare map and power spectra map, the dynamic characteristics of the system aredescribed in detail. The results show that the new chaotic system has complex structure,contains many system parameters and variables and through properly regulate parametersof the system which can become hyperchaotic state. And a class of multiplehigh-dimensional chaotic system is constructed in the same way which confirmed that thisis a new way to lead to high-dimensional chaotic sysstem.Secondly, study on the application of high-dimensional hyperchaotic system in color image encryption. Firstly, using the chaotic sequence generated by the Arnoldtransformation and ten-dimensional chaotic system to make the original image scrambling.Then，arranging the sequence of chaotic system after pretreatment as to encrypt the threeprimary colors matrix. The encrypted matrix synthesis of the three primary color imageobtained encrypted. The experimental results show that the algorithm is very sensitive tothe initial key, has a large key space and a good capability of resistance to noise attacking.Finally, a chaotic circuit of ten-dimensional system has been designed. Based oncircuit theory, the analog circuit’s modular of the chaotic system are designed. The circuitsimulation tests of EWB software verify that the circuits of the chaotic system can berealized.