Control, Synchronization And Encryption Of Chaos

Nowadays, chaos has been intensively studied within physics, mathematics and so on. It has been realized that chaos research has great potential in many technological disciplines. The relative problems of chaos control and chaos synchronization are studied in this thesis using the methods of theoretical derivation and numerical simulation. The main achievements contained in the research are as follows:Control for Chen systems subject to uncertainties has been analyzed. Based on theories of sliding mode, it designs a sliding mode controller which can regulate the state vector to a desired point in the state space or to a predictable neighborhood of an arbitrary desired point. The proposed controller is guaranteed by the rigorous mathematical analysis. Finally, the effectiveness of this controller is proved by numerical simulations.A class of autonomous chaotic systems has been analysed. Based on the stability criterion of linear systems, a new approach for constructing complete synchronization and complete anti-synchronization is proposed. The complete synchronizations and complete anti-synchronizations of the coupled dynamos system are achieved via the proposed method. Finally, the method is applied in security communication, and numerical simulations are provided for illustration and verification of the proposed method.Based on the reaserch work by Baptista, Kocarev, Tang and Pareek et al, a symmetric key block re-encryption algorithm using multiple one-dimensional chaotic maps has been proposed. However, we also use an external secret key of variable length (maximum 128-bits). In the present cryptosystem, multiple one-dimensional chaotic maps construct a system group, and plainttext is divided into blocks of 8-bit length in order, and the other sections into subgroup and finally encrypt the subgroups in order. The number of the plaintext blocks of each subgroup and which chaotic map is selected and the parameters and the number of iteration for seletion are all generated dynamically. The whole process of encryption or decryption is governed by two dynamical tables. Finally, the author processes text, image, video and so on with the proposed method and also analyzes the safety of the proposed cryptosystem. The result is that, compared with method of Baptista and others, the proposed method is safer, faster and more powerful against force attack.