Hyperchaotic secure communication via generalized function projective synchronization

Abstract

This paper presents two different hyperchaotic secure communication schemes by using generalized function projective synchronization (GFPS), where the drive and response systems could be synchronized up to a desired scaling function matrix. The unpredictability of the scaling functions can additionally enhance the security of communication. First, a hyperchaotic secure communication scheme applying GFPS of the uncertain Chen hyperchaotic system is proposed. The transmitted information signal is modulated into the parameter of the Chen hyperchaotic system in the transmitter and it is assumed that the parameter of the receiver system is unknown. Based on the Lyapunov stability theory and the adaptive control technique, the controllers are designed to make two identical Chen hyperchaotic systems with unknown parameter asymptotically synchronized; thus, the uncertain parameter of the receiver system is identified. The information signal can be recovered accurately by the estimated parameter. Secondly, another secure communication scheme by the coupled GFPS of the Chen hyperchaotic system is introduced. The information signal transmitted can be extracted exactly through simple operation in the receiver. The corresponding theoretical proofs and numerical simulations demonstrate the validity and feasibility of the proposed hyperchaotic secure communication schemes.