Research On Some Problems In Chaos Synchronization And Encryption

Chaos theory has attached much attention since its discovery, which is seen as one of three scientific revolutions in 20th century. Chaotic system has been widely used in secure communication and encryption because of its several significant features, such as pseudo randomness, initial value sensitivity, and periodicity etc. Recently, a lot of secure communication schemes based on chaotic synchronization are proposed. However, some problems were found in the application for these synchronized schemes with the further research, such as synchronization-system’s chaotic dynamics degrade rapidly because of noise influence, the designed controller is too complex. Thus, its useful to design a robust、 universal synchronization schema. In addition, it’s a major problem to improve the robustness of chaotic cryptography. In this dissertation, by using theoretical analysis and numerical simulation, the chaos-based design of synchronization and image encryption have been studied. The main works can be summarized as follows:(1) A general modified function projective lag synchronization scheme is proposed. According to the Lyapunov stability theory, the adaptive controllers and updating law of perturbed parameter are achieved. The unique updating law of perturbed parameter ensure that the dynamical features of chaotic systems and the robustness of synchronized schemes. Moreover, the consideration of noise and time-delay make it more practical to study the synchronized schemes.(2) A novel image encryption algorithm based on chaotic system and improved gravity model is proposed. Our proposed algorithm improved the Sun’s gravity model, which avoids the defect of large key values and low sensitivity. Besides, the cipher is employed to change chaotic iterative values during encryption, which makes intermediate secret keys dependent on cipher, thus improving the robustness.(3) A novel image encryption chaotic algorithm based on hash function and cyclic shift is designed. The key streams are dependent on the hash value of the plain text and vary in each round when the initial conditions keep unchanged, which implements the principle of one-time keys.