An image encryption algorithm based on a novel 4D hyperchaotic system and improved Knight’s Tour scrambling algorithm

Abstract In this paper, we propose an advanced image encryption algorithm that integrates a novel 4D hyperchaotic system and an improved Knight’s Tour algorithm for enhanced security. The 4D hyperchaotic system, characterized by its complex dynamics and multiple positive Lyapunov exponents, generates pseudo-random sequences with high sensitivity to initial conditions. These sequences are utilized in both pixel-level scrambling and bit-level diffusion processes, ensuring robust encryption. The Knight’s Tour, a classical pathfinding algorithm, is enhanced through chaotic sequence-based randomization, improving path randomness and addressing traditional limitations like deadlock issues. Additionally, a nonlinear diffusion process, inspired by the Josephus ring algorithm, further strengthens the encryption scheme by introducing dynamic scrambling of pixel values. Security analysis and experimental results demonstrate that the proposed algorithm offers a large key space, excellent resistance to cryptanalysis, and robustness against various attacks such as noise and cropping. Especially in image encryption, resistance to differential attacks is a crucial performance metric, typically evaluated using NPCR and UACI. The expected values are NPCR E = 99.6094% and UACI E = 33.4635%. The NPCR and UACI values obtained from the experimental images encrypted by the proposed algorithm are close to these expected values. This work highlights the potential of integrating hyperchaotic systems in image encryption for applications requiring high levels of security, such as military communications, cloud storage, and digital healthcare systems.