Lag matrix projection synchronization for discrete chaotic systems and its application to image encryption

Chaotic systems are widely used in the field of secure communications due to their initial value sensitivity, long-term unpredictability and other characteristics. In this paper, a Lag Matrix Projection Synchronization (LMPS) scheme based on discrete chaotic system is proposed, which can adapt to a variety of synchronization including lag synchronization, simultaneous synchronization, projection synchronization, inverse synchronization, and complete synchronization. In order to verify the feasibility of the scheme, we also design a new four-dimensional discrete chaotic system, which is fully analyzed by numerical simulation. Simulation results show that the LMPS synchronization scheme can achieve synchronization with an average of only 8 iterations, and the synchronization error is controlled within the range of 10^–10, which reflects the high efficiency and accuracy of the scheme. In addition, we apply it to the field of image encryption, and the security analysis shows that the system performs well in terms of encryption effect, key space size, and resistance to noise attack, and can effectively guarantee the confidentiality and integrity of data.