Implementation of bidirectional chaotic communication systems based on Lorenz circuits

In this paper, we proposed a scheme of the bidirectional secure communication hyperchaotic system, where the chaotic circuits are constituted by two pairs of Lorenz circuits with coupling characteristics between the transmitter and receiver. Because of the coupling relationship between the transmitter and the receiver, even if an intruder knows the coupling values of the system, he could not steal the message from the system from practical simulation results. On the other hand, to achieve the synchronization between transmitter and receiver, two methods are presented to design the feedback control gain. The design idea is to apply a suitable Lyapunov function and the property of positive definite of a matrix to satisfy the direct Lyapunov theorem. Therefore, the transmitting message masked by chaotic state from the transmitter can be guaranteed to perfectly recover in the receiver. To implement the proposed communication scheme, the pairs of Lorenz circuits designed by the operational amplifier, resistor and capacitor elements are also presented in the paper. Finally, the test results containing simulation and the circuit measurement are shown to demonstrate that the proposed method is correct and feasible.