Harnessing Complex-Valued Chaos in Discrete-Time Hopfield Neural Network for Secure Image Encryption

The secure transmission of images in critical applications like smart healthcare and autonomous driving demands encryption schemes that are both highly secure and efficient. While chaos-based systems are promising, their security is fundamentally limited by the complexity of the underlying chaotic generator. This paper introduces a novel complex-valued discrete-time Hopfield neural network (CVDHNN) to address this challenge. We demonstrate that the CVDHNN exhibits rich hyperchaotic dynamics through various numerical analyses. The network is successfully implemented on an FPGA, verifying its capability for chaotic sequence generation. Leveraging this complex chaos, we design a robust image encryption algorithm that integrates multi-stage confusion and diffusion. Security analysis confirms the cipher’s excellence, achieving favorable statistical properties, high key sensitivity, and strong resistance to various attacks.