This paper presents a construction of a secure image encryption scheme with graph theory, Galois field, and substitution-permutation network (SPN) for enhanced multimedia data security. First of all, the authors begin by constructing a complete graph with 8 vertices to understand the structure of the graph \(G,\) and then draw the adjacency matrix \(A\) of the graph \(G\) . An elementary finite field \(GF({2}^{8})\) by the use of the irreducible polynomial and give representation of the elements of \(GF({2}^{8})\) in a form of a binary. An affine mapping is defined using an adjacency matrix A whose entries lie in \(GF({2}^{8})\) ; each entry is transformed by computing its multiplicative inverse in \(GF({2}^{8})\) and then augmented with a parameter from \(GF({2}^{8})\) . This mapping is used to construct \(8\times 8\) S-boxes, which together with other components constitute the nonlinear portion of the SPN structure. This encryption method is applied to RGB images with three transformations proposed as below. Substitution in replacement of all the pixel’s R, G, and B channel values works with the help of S-box, which is \({S}_{1}\) . Permutation is done with the help of the second S-box ( \({S}_{2}\) ) the function of permutation is to shift the position of pixels in order to support both diffusion and confusion. Lastly, the third S-box \({S}_{3}\) is utilized for the purpose of the XOR operation on the permuted pixel values, adding one more layer of confusion to the transformation. Finally, red, green, and blue channels are used to generate an encrypted RGB image. Test results and evaluations of the proposed scheme reveal that the encrypted images achieve entropy values in the range of 7.9971–7.9994, which are very close to the ideal value of 8, and exhibit minimal pixel correlation (close to zero). Moreover, the images are resistant to differential image cryptanalysis and linear image cryptanalysis. This demonstrates that the proposed approach provides strong randomness and ensures the secure protection of multimedia information, which is of critical importance in today’s applications.
