An ATPAF-based multi-scroll memristive hopfield neural network and its application to image encryption

Abstract

To address the limitation of traditional activation functions for the dynamical complexity generation of Hopfield neural networks, an antisymmetric tunable potential activation function (ATPAF)-based memristive Hopfield neural network (ATP-MHNN) is proposed in this work. By integrating a non-polynomial memristor, the system generates controlled unidirectional multi-scroll attractors under external stimuli, exhibiting enhanced chaotic behaviors compared to classical models. These theoretical findings are systematically validated via FPGA hardware implementation. Furthermore, to overcome the hardware overhead of static lookup tables (LUTs) and the spatial locality vulnerabilities inherent in traditional raster-scan stream ciphers, a multi-granularity state-dependent encryption (MGSE) architecture driven by the ATP-MHNN is designed. This scheme decomposes image data into a fine-grained quaternary representation, introducing an entropy-driven dynamic substitution mechanism and variable-length block permutation. By chaining these lightweight sub-pixel algebraic operations with a global spiral topology diffusion, the encryption system achieves an S-box-LUT-free encryption transform, high-dimensional nonlinear mapping. This purely algebraic approach systematically avoids computationally expensive operations, effectively reconciling robust cryptographic security with optimal hardware execution efficiency.