Reversible image encryption and hiding algorithm based on fractional-order memristive Hopfield neural network

In order to protect the privacy information of images in the Industrial Internet of Things(IIoT), this paper mainly studies an image encryption and hiding method based on Fractional-Order Memristive Hopfield Neural Network (FOMHNN). Firstly, a FOMHNN model is proposed with variable neuron activation gradient and synaptic weight. Then, boundedness and symmetry of this model are studied by qualitative analysis, and stability analysis of its equilibrium point proves that it has self-excited dynamics. Moreover, bifurcation diagrams, Lyapunov exponents, phase diagrams, and local attraction basins are used to demonstrate dynamical behaviors of the FOMHNN. When parameters change, Spectral Entropy (SE) and C0 complexity are investigated to observe the complexity of the FOMHNN. Numerical results demonstrate that the FOMHNN exhibits complex initial offset behavior, and can generate an infinite number of coexisting double-scroll chaotic attractors and coexisting quasi-periodic attractors with same shape but different positions, which means the model has uniform extreme multi-stability. Therefore, a reversible image encryption and hiding algorithm is proposed based on the proposed model. The encryption process scrambles original image using a chaotic sequence randomly generated by the FOMHNN, and the finite domain bidirectional diffusion algorithm is used to diffuse the scrambled image. Bit plane decomposition and Least Significant Bit (LSB) algorithm are used for hiding process. Finally, experimental results are given to show that the algorithm has high security and robustness, which has a good application prospect in the field of image information security.