A Chaos‐Driven Image Encryption Method With Möbius Transformations and Finite‐Ring Diffusion

ABSTRACT

This paper introduces a lightweight yet highly secure image encryption framework that combines chaotic dynamics, HKDF‐S3‐based key expansion, and Möbius‐Affine transformations to achieve strong protection with minimal computational burden. The encryption process begins with the generation of chaotic ignition values derived from a highly sensitive nonlinear chaotic system. These initial values are then expanded using a hierarchical HKDF‐S3 mechanism, producing cryptographically strong and diversified round keys. The expanded keys are subsequently mapped to affine transformation parameters and to a carefully designed Maximum Distance Separable (MDS) diffusion matrix constructed over the finite ring . The proposed design enables per‐pixel Möbius transformations followed by chaotic masking and block‐wise diffusion. By employing an MDS matrix with maximal branch number, the framework achieves strong confusion and diffusion characteristics, ensuring that even slight variations in plaintext or key values propagate rapidly throughout the encrypted image. To further enhance sensitivity to both plaintext and key modifications, rotational key updates are applied at each encryption round. This dynamic updating mechanism significantly strengthens resistance against chosen‐plaintext and differential attacks. Comprehensive experimental analysis conducted on standard color images confirms the effectiveness of the proposed scheme.