2026-10-12T10:31:43Z https://api.figshare.com/v2/oai

oai:figshare.com:article/33810470 2026-09-15T17:32:02Z category_146 category_15 category_272 category_734 category_106 portal_5 item_type_3 month_year_09_2026

<p>Final S-box.</p> Asima Razzaque (20521431) Hafiza Zara Mustafa (24948167) Dilshad Alghazzawi (18536230) Ghaliah Alhamzi (24948170) Space Science Neuroscience Environmental Sciences not elsewhere classified Biological Sciences not elsewhere classified Science Policy zero pixel correlations various cryptanalytic attacks round grayscale image encryption scheme based based keystream whitening parameterized permutation representation stage algebraic framework refinement process via designing cryptographically strong dependent position permutation div >< p 9968 – 7 7040 %– 99 4902 %– 33 box generation exist strong bit second stage refinement increases dependent reconstruction permutation group useful attack uaci values theoretic underpinnings step approach projective line practical applicability pepper noise paper presents numerous methods npcr values moon surface main innovation introduce non independence behavior ideal value highly nonlinear first step finite field differential sensitivity density salt cryptographic strength continuous pursuit ciphertext degradation balanced profile 7559 %, 6390 %. <div><p>The security of modern block ciphers heavily relies on the cryptographic strength of Substitution boxes (S-boxes), which introduce non-linearity and confusion. While numerous methods for S-box generation exist, there is a continuous pursuit of designs that offer a superior and balanced profile against various cryptanalytic attacks. This paper presents a new, two-step approach to the construction of highly nonlinear S-boxes, with group-theoretic underpinnings. During the first step, we use a parameterized permutation representation of the triangle group on the projective line over the finite field , denoted by , to produce an initial S-box with a nonlinearity of . The second stage is the main innovation, in which we use a refinement process via the action of the permutation group on this original S-box. The refinement increases the average nonlinearity to 112 and yields differential uniformity 4, linear approximation probability 0.0625, strong bit-independence behavior, and strict avalanche characteristics close to the ideal value. The proposed S-box is then incorporated into a multi-round grayscale image-encryption scheme based on fixed S-box substitution, key- and nonce-dependent position permutation, SHA-256-based keystream whitening, and a final bidirectional nonlinear diffusion layer. Experiments on Moon Surface, Airplane, and Clock images produce ciphertext entropies of 7.9968–7.9975, near-zero pixel correlations, NPCR values of 99.7040%–99.7559%, and UACI values of 33.4902%–33.6390%. Cropping and noise experiments further show exact recovery without attack and useful attack-dependent reconstruction under ciphertext degradation, particularly under mild cropping and low-density salt-and-pepper noise. These results demonstrate strong statistical security, differential sensitivity, and practical applicability for grayscale image protection.</p></div> 2026-09-15T17:31:52Z Dataset Dataset 10.1371/journal.pone.0357107.t004 https://figshare.com/articles/dataset/_p_Final_S-box_p_/33810470 CC BY 4.0