Design the hyperchaotic cryptosystems via the Gerschgorin theorem

In this paper, we propose a new method to design a feedback controller for synchronizing the hyperchaotic circuits. The main idea of the method is to design a controller by applying a suitable Lyapunov function and Gerschgorin theorem. Therefore, the feedback controller can guarantee that the signal by chaotic masking from the transmitter can be recovered at the receiver. A scheme of the hyperchaotic communication systems is proposed, where the transmitter and receiver are constituted of the coupled Chua’s chaotic circuits in this paper. On the other hand, to enhance the degree of security in chaotic communication systems, the techniques of cipher are also considered in this paper. Therefore, the cryptosystems can be obtained by using the encrypter, and decrypter as the chaotic transmitter–receiver pairs. To the purpose of the synchronization, the concepts of identical and generalized synchronizations are used to achieve the aim that the plaintext signals from the encrypter can be retrieved at the decrypter. Finally, the simulation results are given to demonstrate the performance of the proposed cryptosystems.