Chaotic Projective Lag Synchronization And Its Application In Secure Communication

Chaotic signals have many inherent features, such as pseudo randomness and ergodic property, thus they are particularly suitable for secure communication. In recent years, using chaotic synchronization to achieve secure communication has become a hot research topic in the world. At present, most of the researches in chaotic secure communication are mainly concentrated on low dimensional chaotic systems in an ideal situation. However, the low-dimensional chaotic systems is easy to crack, and the communication would be affected by the noise, disturbance, time delay, and so on.Therefore, in order to overcome the shortcomings of existing research, this paper studies the projective lag synchronization of hyperchaotic systems in the case of external disturbance, and applies this method to chaotic secure communication. The main research results in this paper are as follows:First, the concept and mathematic model of chaotic projective lag synchronization are introduced. Chaotic projective lag synchronization is the combination of chaotic projective synchronization and the chaotic lag synchronization. This paper has studied the projective lag synchronization problem of delayed chaotic system with parameter mismatch. The research results have shown that the synchronization error can be converge to a very small region under the condition of proper control.Second, the projective lag synchronization mode is improved, the modified projective lag synchronization mode is proposed. Through setting the parameters of the proposed synchronization mode, it can switch between several different synchronizations.Then, the modified projective lag synchronization of hyperchaotic complex-valued Lorenz and Lü system has been presented. Numerical simulation has shown that throughsetting the different parameters, the lag synchronization, the projective synchronization and modified projective lag synchronization of two chaotic systems have been achieved respectively. What’s more, theoretical analysis has indicated that the modified projective lag synchronization has a variety of characteristics, and the complexity of chaotic system has an influence on the synchronization effect.Third, we have designed a chaotic secure communication scheme using chaotic projective lag synchronization technology. Two examples of chaotic masking secret communication and image encryption have been done. Numerical simulation proved the effectiveness and security of this secure communication scheme.