Multiple color images security by SPN over the residue classes of Gaussian integer $$\:Z{\left[i\right]}_{h}$$

In this paper, the authors present the design of a new pair of 8 × 8 S-boxes over the residue classes of Gaussian integers [Formula: see text] and their usage for the encryption of multiple RGB images using a three-stage Substitution-Permutation Network (SPN). In the present work, the S-boxes are constructed using the properties of Gaussian Integers and inverse of affine then affine maps, where first S-box holds the roles of substitution layer and the second S-box looks after the permutation layer. The modulation is nonlinear by means of operating the Gaussian integer residue classes through modular arithmetic, which will greatly benefit from strong diffusion and confusion properties that are critical for cryptographic security. For even greater complexity an exclusive XOR operation on the two S-boxes is made to produce a third S-box. The third S-box is deployed in the encryption process in such manner which offers superior diffusion over all RGB image channels. When the proposed SPN framework is utilized for a set of multiple RGB images, the mappings employed involves substitution-permutation-XOR operations that are severe nonlinear functions for differential or linear attacks. The incorporation of these Gaussian-integer-based S-boxes into the SPN scheme makes it possible for each image channel to be transformed independently but mutually connected to produce a secure and efficient encryption function. The analysis of outcomes proves the efficiency of the developed method; the viability of its application for multi-image encryption with high entropy, low correlation and increased resistance to a variety of attacks. This ability to consider it as an effective tool in the sphere of secure multimedia communication.