Study On High-dimensional Chaos And Its Application On Image Encryption

Chaotic system is extremely sensitive to initial values and system parameters, whichcan produce non-periodic, broadband spectrums, noise-like and reproduced chaoticsequence. So the chaos cryptogram has many advantages in image encryption. Comparedto chaotic system, hyper chaotic system has much more complex dynamical behavior.System’s randomness and indeterminacy has enhanced much, hence hyper chaos has muchmore extensive value in engineering application. For example, recent study indicates that,hyper chaotic signal is more difficult to predict by common methods such as rebuildingphase space, regress mapping, nonlinear predict, which are usually used forlow-dimension chaos signal. So it has great application of the chaos cryptogram on imageencryption an important research field in image information science and technology,which is generated by hyper chaotic systems with at least two positive lyapunovexponents.From the theoretical point of view，this paper firstly use the non-linear statefeedback controller method and make use of external excitation of Duffing chaotic systemas a bridge, then design a new six-dimensional hyper chaotic system with multi variableparameters which comprise classic Lorenz chaotic system and Duffing chaotic system. Atthe same time some program used for analyzing characteristic of chaotic system has beenworked out, such as the program of drawing phase track figure, program of drawingPoincare sectional view, program of calculating Lyapunov exponents and so on.Secondly, according to the deficiency of the currently used method for thepretreatment of the chaos output sequence, a new method based on the idea of dynamicsegmentation mapping for the pretreatment of the sequence is proposed. The method isoperated on the real value sequence itself, so it can be applied to any data on any range.Set a six-dimensional complex hyper chaos output sequence as an example, dataprocessing, correlation comparison and random testing are done to the example. Theresults show that the data sequences behave better in cryptography performance aftertreatment. Finally, chaotic cryptography applied in digital image encryption is studied. Based onthe currently image encryption algorithm, an image encryption algorithm based onsix-dimensional complex hyper chaotic system is proposed，and according to descendingorder, this algorithm arranges hyper chaotic sequence to obtain the replacement sequenceof image location. Using Arnold map to enforce secondary scramble, then use the outputsequences of six-dimensional complex hyper chaotic system with dynamic segmentationmapping as keys for the scrambling pixels matrix based on XOR operation. Thesimulation results show that the algorithm is good at encryption performance, large inkey-space and its anti-interference is very strong. So it can commendably resist statisticalanalysis tools，and adequately protect security of the image information.