S-box: L-L Cascade Chaotic Map and Line Map.

Being as an important nonlinear component of block ciphers, Substitution box (S-box) directly affect the security of the cryptographic systems. It is important and difficult to design cryptographically strong S-box that simultaneously meet with multiple cryptographic criteria such as bijection, non-linearity, strict avalanche criterion (SAC), bits independence criterion (BIC), differential probability (DP) and linear probability (LP). To address the issue, an S-box generation approach based on L-L cascade Chaotic Map and Line Map (LLCMLM) is proposed in this paper. L-L cascade chaotic map is used to generate an integer sequence ranging 0–255, and line map is applied to scramble the position of the integer sequence. A series of experiments have been conducted to compare multiple cryptographic criteria of LLCMLM with other algorithms. Simulation results indicate that LLCMLM meets well with the design criteria of the S-box.