Drive–response asymptotic shape synchronization for a class of two-dimensional chaotic systems and its application in image encryption

Abstract

This paper proposes the concept of drive–response asymptotic shape synchronization for two-dimensional chaotic systems and its application in image encryption. It overcomes the limitations of traditional shape synchronization, eliminates the restrictions on the drive system’s continuous differentiability, and the response system’s specific format, while simplifying the controller design, thereby demonstrating enhanced applicability and ease of implementation. Moreover, based on the characteristics of asymptotic shape synchronization, we propose a novel image encryption scheme. In this scheme, the drive and response systems, initialized with distinct values, achieve identical chaotic attractors through rotation and translation parameters in rigid transformation, which are utilized for encryption and decryption processes, respectively. Our encryption algorithm employs DNA coding to construct a DNA plane and incorporates the concept of Rubik’s cube rotations for scrambling and diffusion. Experimental simulations and performance analysis verify the effectiveness of the proposed encryption scheme in withstanding various attacks, ensuring a high level of security.