This paper proposes a novel S-box construction method based on disjoint code theory. It aims to efficiently generate 8×8 bijective S-boxes, which have excellent cryptographic properties. The method breaks the traditional paradigm of “first designing coordinate Boolean functions and then correcting bijectivity”. We structurally partition and reorganize the vector space 𝔽82 via disjoint codes. This directly constructs a 256×8 matrix Q, with rows covering the entire space. Each column of Q naturally corresponds to the truth table of a coordinate Boolean function, thus structurally guaranteeing the bijectivity of the S-box.The cryptographic performance of the three proposed S-boxes is outstanding: the average nonlinearity values are 107.50, 107.75, and 107.50, and the overall nonlinearity (NLF) is 96, 94, and 94. The mean strict avalanche criterion (SAC) values are 0.5059, 0.5010, and 0.4946, showing only slight deviations from the ideal 0.5. Their differential probabilities (DP) are uniformly 0.0391. The average bit independence criterion-nonlinearity (BIC-NL) values are 104.93, 104.36, and 104.36, and the average bit independence criterion strict avalanche criterion (BIC-SAC) values are 0.5029, 0.4992, and 0.5052, which indicates strong independence among the output bits. Finally, the linear approximation probabilities (LAP) are 0.1250 for Scheme 1 and 0.1328 for both Schemes 2 and 3, demonstrating robust resistance to linear attacks. These properties together ensure that the constructed S-boxes can effectively resist mainstream attacks such as differential and linear cryptanalysis. The method simplifies the design process and ensures high security. It provides a new approach for the provable construction and batch generation of core confusion components in block ciphers.
CHEN et al. (Thu,) studied this question.