Designing key-dependent chaotic S-box with larger key space

The construction of cryptographically strong substitution boxes (S-boxes) is an important concern in designing secure cryptosystems. The key-dependent S-boxes designed using chaotic maps have received increasing attention in recent years. However, the key space of such S-boxes does not seem to be sufficiently large due to the limited parameter range of discretized chaotic maps. In this paper, we propose a new key-dependent S-box based on the iteration of continuous chaotic maps. We explore the continuous-valued state space of chaotic systems, and devise the discrete mapping between the input and the output of the S-box. A key-dependent S-box is constructed with the logistic map in this paper. We show that its key space could be much larger than the current key-dependent chaotic S-boxes.