Image Security Enhancement Using Non‐Chain Ring Algebraic Structure

ABSTRACT The substitution box (S‐box) is a core nonlinear component in modern block ciphers, providing confusion and resistance against cryptanalytic attacks. Traditionally, S‐boxes are constructed over Galois fields, which are algebraically simple but limited in structural diversity. In this work, we present a novel S‐box designed over the non‐chain ring introducing richer algebraic characteristics compared to conventional chain ring or field‐based designs. The choice of allows for a greater number of units and zero divisors, enhancing the algebraic complexity of the transformation while maintaining manageable memory requirements 24 × 2 8 bits compared to the large storage demands of GF (2 24 ). The proposed S‐box demonstrates strong algebraic complexity due to the complex algebraic operations of the ring. For validation, the S‐box is applied in a 24‐bit RGB image encryption framework, where pixels from red, green, and blue channels are combined into 24‐bit vectors, substituted, and then permuted through affine transformations defined over the ring Z 2 32 . The resulting encrypted images exhibit uniform histograms, low correlation, and high entropy, confirming the robustness of the proposed scheme. Overall, this study highlights the novel use of a non‐chain ring structure for efficient and secure S‐box design, offering a promising alternative to field‐based cryptographic constructions.