Intermittent Impulsive Synchronization of Hyperchaos with Application to Secure Communication

In this paper, a hyperchaotic system is presented as the chaotic carrier to encrypt information in secure communication. The sensitivity to the system parameters and delay of the hyperchaotic system, i.e., its chaotic degree indicated by the number of positive Lyapunov exponents, increases with its system parameter and delay, guaranteeing a large enough key space when one selects its system parameter and delay as the secret key. Furthermore, we develop an intermittent impulsive synchronization scheme (IISS) to achieve chaos synchronization, a crucial process in chaos-based secure communication. In our scheme, impulsive control is only activated in the control windows, not during the whole time, which breaks through the limitation on the upper bound of the impulsive intervals in the general impulsive synchronization scheme (GISS). Specifically, IISS improves the security of the chaos-based secure communication scheme since the encrypted signal (cipher) is transmitted in the free windows, different from the synchronization signal in the control windows. Finally, a secure communication scheme employing our hyperchaotic system and IISS technique is proposed and numerical results are given to demonstrate the performance of this scheme.