A New Classification of 4-bit Optimal S-boxes and Its Application to PRESENT, RECTANGLE and SPONGENT

In this paper, we present a new classification of 4-bit optimal S-boxes. All optimal 4-bit S-boxes can be classified into 183 different categories, among which we specify 3 platinum categories. Under the design criteria of the PRESENT (or SPONGENT) S-box, there are 8064 different S-boxes up to adding constants before and after an S-box. The 8064 S-boxes belong to 3 different categories, we show that the S-box should be chosen from one out of the 3 categories or other categories for better resistance against linear cryptanalysis. Furthermore, we study in detail how the S-boxes in the 3 platinum categories influence the security of PRESENT, RECTANGLE and SPONGENT\(_{88}\) against differential and linear cryptanalysis. Our results show that the S-box selection has a great influence on the security of the schemes. For block ciphers or hash functions with 4-bit S-boxes as confusion layers and bit permutations as diffusion layers, designers can extend the range of S-box selection to the 3 platinum categories and select their S-box very carefully. For PRESENT, RECTANGLE and SPONGENT\(_{88}\) respectively, we get a set of potentially best/better S-box candidates from the 3 platinum categories. These potentially best/better S-boxes can be further investigated to see if they can be used to improve the security-performance tradeoff of the 3 cryptographic algorithms.