A Novel RGB Image Encryption Scheme using Operations on Residue Classes of Eisenstein Integers Z[ω]π

Abstract

This article presents a novel concept for enhancing multimedia security based on Eisenstein integers. The proposed approach is divided into two primary stages. In the first stage, S-boxes are constructed over the residue classes of Eisenstein integers using affine transformations, with all parameters derived from Eisenstein integers. This construction leverages the unique properties of
Eisenstein integers, resulting in strong confusion and diffusion characteristics—essential elements of any secure cryptographic system. The second stage incorporates RGB image encryption using a Substitution-Permutation Network (SPN) framework, modified to operate over Eisenstein integers. This modification increases the complexity of image data transformations, thereby enhancing security. A comprehensive analysis of the proposed scheme’s security and performance demonstrates its robustness against most known cryptographic attacks, along with greater efficiency in terms of computational and communication costs. The results clearly indicate that the integration of Eisenstein integers into SPN structures is a promising direction for developing effective and secure multimedia encryption methods.