Multiple RGB Images Security based on Substitution–Permutation Network over the Residue Classes of Eisenstein Integer
This paper presents a multiple RGB image encryption scheme that utilizes a pair of 8 x 8 S-boxes constructed over the residue classes of Eisenstein integers ZΩπ, 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 ZΩπ, 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.
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