Construction of S-boxes with LBN and DBN ≥ 4

There is always a need for good and safe S-boxes in block ciphers for secure communication. To improve the security of lightweight block ciphers, S-boxes with high linear and diiferential branch numbers (LBN and DBN) are utilized. Many of these S-boxes have been built in recent years. Sarkar et. al. built S-boxes with LBN and DBN both equal to 3. Kim Hangi et. al. also created 8-bit S-boxes using smaller S-boxes with at least 3 LBN and DBN. In this direction, we narrow the search space of 8 × 8 S-boxes with LBN = DBN = 4. We used the Feistel and Lai-Massey structures to build these S-boxes. We present a detailed explanation of such 8 × 8 S-boxes.