An optimal non overlapping block diffusion scheme based on genetic algorithm and its application to chaos-based image encryption

This paper presents an image encryption algorithm based on a novel discrete-time chaotic system and the evolutionary optimization of cryptographic processes. The proposed cryptosystem follows a Confusion-Diffusion-Permutation-Confusion architecture, where confusion is achieved using Arnold transform and permutation relies on the Nanfak permutation technique. The diffusion stage employs a non-overlapping block-based mechanism in which the image is randomly partitioned into k blocks during initialization, while the associated partial diffusion keys are optimized using a genetic algorithm. Unlike conventional key assignment, candidate partial keys are evaluated according to their contribution to the entropy of the globally diffused image, providing an adaptive key-selection mechanism for different image contents. The final confusion stage is independently optimized as a single-objective problem targeting the minimization of inter-pixel correlation under a local Shannon entropy constraint. All pseudo-random sequences involved in the encryption processes are generated using a three-dimensional cross-coupled trigonometric modular hyperchaotic map, which exhibits strong nonlinear dynamic, sensitivity to initial conditions, and suitable sequences for cryptographic applications. The practical feasibility of the chaotic generator is validated through field-programmable gate array implementation on a Cyclone IV DE0-Nano board. Extensive experimental and security analyses demonstrate a large key space, high resistance to statistical attacks and strong robustness against differential attacks. Moreover, the scheme exhibits resilience to noise and clipping attacks, confirming its suitability for secure image transmission.