Asymptotic shape synchronization in three-dimensional chaotic systems and its application in color image encryption

Distinguished from most current chaos synchronization approaches based on system states, this paper introduces a theory of asymptotic shape synchronization for three-dimensional chaotic systems based on the chaotic system’s shape dimension. Under the influence of the designed controller, the asymptotic synchronization of the shape of state trajectory curves between the drive and response systems is achieved. Building upon this, a color image encryption scheme is proposed using cross-channel pixel reorganization based on asymptotic shape synchronization. Simulation results demonstrate effective concealment of the plaintext image in the ciphertext, with successful recovery through asymptotic shape synchronization. Furthermore, a detailed analysis of the cipher is conducted using metrics such as histograms, information entropy, key space, and sensitivity, confirming the effectiveness and security of the proposed scheme.