On relationship between differential/linear clustering effects and the number of active S-boxes in block ciphers

Differential cryptanalysis and linear cryptanalysis are the two best-known cryptanalysis techniques for symmetric-key primitives. Ensuring resistance to these attacks is critical for the security of block ciphers. In this paper, we investigate the relationship between differential/linear clustering effect and the number of active S-boxes in the intermediate rounds. Our findings indicate that an increase in the number of active S-boxes in the intermediate rounds does not inherently lead to an evident improvement in EDP/ELP. Instead, the EDP/ELP remains stable once the number of active S-boxes exceeds a certain threshold. We apply our method to four lightweight SPN primitives including GIFT-64, PRESENT, RECTANGLE and KNOT-256. For GIFT-64, RECTANGLE, and KNOT-256, we obtain improvements in the best known linear propagation results, while our other results are consistent with the best known results.