A 4D discrete Hopfield neural network-based image encryption scheme with multiple diffusion modes

Abstract

A novel 4D chaotic map is proposed in this paper using the model of a self-feedback Discrete Hopfield Neural Network (DHNN) with nonlinear synaptic ICMIC (4D-IDHNN). Based on an analysis of chaos characteristics, including attractors, Lyapunov exponents, Bifurcation, Sample Entropy and CO algorithms, the 4D-IDHNN system demonstrates reasonable stochasticity and ergodicity, alongside a broad spectrum of hyperchaotic parameters. Based on the 4D-IDHNN system, we design a new Pixel-dependent bit-plane Chaotic random Diffusion (PbCrD) algorithm with high diffusion capability and security. To begin, the 4D-IDHNN system generates pseudo-random sequences to confuse the plaintext image pixel positions with Chaotic Magic Random Scramble (CMRS). Subsequently, the PbCrD algorithm can be employed to diffuse pixel values. With the initial value of 4D-IDHNN generated using the SHA-256 hash of plaintext image, the ability to resist plaintext attacks can be enhanced. The algorithm includes 24 diffusion modes, which is three times greater than the number of DNA rules, thereby enhancing the complexity of decryption. The proposed encryption algorithm has good effectiveness, robustness, and resistance to differential attacks based on simulations and security analyses.