Based on the idea of using reversible transformation and affine transformation to generate S-box, a method to produce dynamic S-box by changing the rows of affine transformation array was proposed. The cryptography properties of single S-box were analyzed. The experimental results show that the cryptography properties of single S-box achieve the security standard of S-box of AES. Moreover, the dynamic differential probability, dynamic linear probability, dynamic non-linear degree, dynamic algebra times and impossible differential numbers of the dynamic S-box produced by the proposed method were analyzed. Theoretical analysis shows that the S-box produced by proposed method possesses good cryptography properties, and experiments also prove that the S-box so produced has good dynamic non-linear degree, dynamic differential and impossible differential properties. Finally, by analyzing the hardware implementation efficiency of the generation of the dynamic S-box, the proposed method has high hardware implementation efficiency.

In order to study the problem about data combinations occurring in real life, different kinds of data information were combined together, leading to a structure called associated-combinatorial structure. Actually, the structure was constituted by a data set, an associated relation and a partition. The aim was to use the structure to set up a method of data combination. To this end, the associated-combinatorial structure was transformed into a granulation structure by granulating the associated relation. In this process, data combinations were completed in accordance with the data classifications. Moreover, because an associated-combinatorial structure or a granulation structure could be represented by the associated matrix, the transformation from a structure to another structure was characterized by algebraic calculations determined by matrix transformations. Therefore, the research not only involved theoretical analysis for the data combination, but also established the data processing method connected with matrix transformations. Accordingly, a computer program with linear complexity was formulated according to the data combinations method. The experimental result proves that the program is accurate and fast.