Image Encryption and Restoration Based on a Bimodal Isomorphic Dynamical System

Abstract

In this paper, an image encryption and restoration method based on a bimodal isomorphic dynamical system is proposed to address the issues of privacy security and large-scale data loss or damage in digital image transmission, particularly in scenarios characterized by high real-time requirements, unreliable links, or ongoing attacks. Unlike existing methods that treat encryption and restoration as separate modules, the proposed system achieves both functions within a unified architecture, where the same nonlinear framework can be switched between chaotic and stochastic resonance modes via parameter adjustment. Firstly, a foundational nonlinear system framework is constructed. Under the same architecture, parameters are adjusted to obtain a chaotic system for encryption and decryption, as well as a stochastic resonance system for noise reduction, followed by a characteristics analysis of these two systems. Secondly, a chaos-based encryption and decryption algorithm is investigated. In this algorithm, a random-point scrambling method combined with Latin matrix diffusion is developed to enhance the security and robustness of the encryption process. Thirdly, a restoration algorithm for extensively damaged images is studied. This algorithm integrates stochastic resonance denoising with integral restoration to suppress noise while preserving fine image details. Finally, simulation experiments are conducted: in the chaotic mode, the encryption and decryption results are evaluated through histogram analysis, correlation coefficients, information entropy, and other relevant experiments, verifying that the encryption algorithm provides excellent communication confidentiality. In the stochastic resonance mode, by comparing the restoration effects on different large-area damaged regions, it is demonstrated that the algorithm can effectively recover the image's characteristic information even under severe damage conditions.