Multiple RGB Images Security based on Substitution–Permutation Network over the Residue Classes of Eisenstein Integer Z[Ω]π

Abstract

This paper presents a multiple RGB image encryption scheme that utilizes a pair of 8×8 S-boxes constructed over the residue classes of Eisenstein integers Z[Ω]π, implemented within a three-stage Substitution–Permutation Network (SPN) architecture. The S-boxes are generated using Eisenstein integer algebra through affine transformations and their corresponding inverse functions, ensuring strong nonlinearity. The first S-box serves as a substitution function, while the second contributes to both permutation and diffusion. Enhanced cryptographic strength is achieved through modular arithmetic in Z[Ω]π, which supports essential encryption properties such as confusion and diffusion. Further complexity is introduced by combining the two S-boxes
via an XOR operation to construct a third S-box, promoting greater inter-channel diffusion among the RGB components. The proposed SPN framework is designed to resist differential and linear cryptanalysis through its layered substitution, permutation, and XOR-based mixing operations. Separate yet interlinked processing pathways for each image channel ensure secure and efficient encryption. Experimental evaluations validate the proposed method, demonstrating high entropy, low inter-channel correlation, and robust resistance to various attacks, making it a strong candidate for secure multimedia communication applications.