Cryptographic protection of RGB images using SPN over Eisenstein integer ring modulo Eisenstein prime

This research introduces a fortified cryptographic paradigm for safeguarding RGB image data, founded upon a substitution-permutation network (SPN) architecture defined over the residue class rings of Eisenstein integers modulo a selected prime element. The framework employs a dual-tier configuration of two independently constructed [Formula: see text] substitution boxes, each synthesized within the algebraic domain of [Formula: see text] where [Formula: see text] represents a primitive cubic root of unity. The generation process for these substitution layers leverages affine transformations and their respective inverses, ensuring the simultaneous attainment of strong nonlinearity, bijective mapping, and algebraic robustness. Within the encryption pipeline, the initial substitution box functions exclusively as the confusion layer, whereas the second is designed to integrate both permutation and diffusion properties. To further amplify cryptographic intricacy, an auxiliary substitution box is formulated through the bitwise XOR amalgamation of the two primary layers, thereby intensifying inter-channel diffusion across the RGB spectrum. By harnessing the unique arithmetic and lattice geometry of Eisenstein integer residue classes, including their modular and inherently non-Euclidean characteristics, the scheme achieves superior confusion-diffusion balance. Compared with conventional image encryption techniques that rely solely on chaotic maps, Gaussian integers, or quaternion-based transformations, the proposed system offers enhanced algebraic structure exploitation, triple-layer substitution for richer nonlinear complexity, and explicit multi-channel diffusion. This leads to higher entropy, lower adjacent-pixel correlation, and greater resilience to both differential and linear cryptanalysis. Empirical assessments confirm the effectiveness of the proposed methodology, yielding near-optimal entropy, negligible adjacent-pixel correlation, and robust defense capabilities against an extensive range of established cryptanalytic strategies, thereby positioning the scheme as a compelling solution for secure imagetransmission in modern communication networks.