Dynamic S-box construction via rotationally nonsingular binary matrix families for symmetric-key block ciphers

Abstract

Substitution boxes are fundamental nonlinear components of symmetric-key ciphers, and dynamic S-box generation provides a means of diversifying the nonlinear layer during operation. However, many existing approaches focus on constructing or optimizing individual S-boxes and do not provide a systematic mechanism for preserving principal cryptographic characteristics across an entire generated family. To address this limitation, this study introduces a structured dynamic S-box construction based on Rotationally Nonsingular Binary Matrix Families (RNBMFs). A 64-bit binary seed is cyclically rotated to generate 64 interrelated $$8\times 8$$ binary matrices, which are used as reproducible affine layers around multiplicative inversion over $$\textrm{GF}(2^8)$$ . The admissibility condition of the complete matrix family is reduced exactly from 64 determinant checks to eight representative tests through the determinant-equivalence structure induced by cyclic row permutations. Large-scale evaluation of $$10{,}000$$ distinct generated S-boxes confirms stable nonlinearity of $$112$$ , linear approximation probability of $$0.0625$$ , differential uniformity of $$4$$ , algebraic degree of $$7$$ , and boomerang uniformity of $$6$$ , while SAC behavior, fixed-point patterns, and permutation-cycle structures remain instance-dependent and can therefore be used as additional screening criteria. As an integration-level assessment, the generated S-boxes were also evaluated in a common reversible RGB permutation–diffusion configuration, producing ciphertext entropy close to $$8$$ , near-zero adjacent-pixel correlation, NPCR and UACI values close to their theoretical references, and exact image recovery. These results show that the proposed RNBMF framework provides a compact and reproducible mechanism for affine diversification of inversion-based S-boxes while preserving their principal affine-invariant cryptographic profile and enabling structurally preferable representatives to be selected for dynamic substitution layers.