ADAPTIVE SYNCHRONIZATION OF CHAOTIC LORENZ SYSTEM USING BACKSTEPPING-LIKE APPROACH WITH APPLICATION TO AN ASYMMETRIC IMAGE ENCRYPTION
J. YVES EFFA *
Department of Physics, Faculty of Science, The University of Ngaoundere, P.O. Box. 454 Ngaoundere, Cameroon
ZOURMBA KOTADAI
Department of Physics, Faculty of Science, The University of Ngaoundere, P.O. Box. 454 Ngaoundere, Cameroon and Department of Physics, Faculty of Science, The University of Maroua, P.O. Box. 46 Maroua, Cameroon
J. S. ARMAND EYEBE FOUDA
Department of Physics, Faculty of Science, University of Yaoundé 1 P.O. Box 812, Yaoundé, Cameroon
J. D. D. NKAPKOP
Department of Physics, Faculty of Science, The University of Ngaoundere, P.O. Box. 454 Ngaoundere, Cameroon
*Author to whom correspondence should be addressed.
Abstract
In this paper, we proposed an adaptive synchronization of Lorenz system with fully unknown parameters. The proposed adaptive synchronization method is based on fast state observer’s method using a backstepping-like approach. The developed adaptive synchronization method is fast and allows us to both ensure synchronization between the transmitter and the receiver, and to estimate the unknown parameters of the receiver. By using Matlab Simulink environment, the implementation of the proposed synchronization scheme is carried out. In addition, the proposed synchronization scheme is applied for encryption by using an asymmetric image cryptosystem. This method which uses different keys for decryption and encryption is less vulnerable to attacks. The key used for the asymmetric cryptosystem is based on adaptive synchronization method. Numerical simulations have each time confirmed the theoretical predictions of the proposed synchronization scheme, perfect reconstruction of the original image after the decryption process and reliability of the asymmetric chaos-based image cryptosystem used.
Keywords: Lorenz system, synchronization, observers, backstepping, asymmetric image encryption