Cryptanalysis and constructing S-Box based on chaotic map and backtracking

•Most S-Boxes contain exploitable weakness of fixed point or reverse fixed point.•An surjective improved coupling quadratic map (ICQM) is designed, which has good ergodicity.•A keyed S-Box without weakness is designed based on ICQM and backtracking.•Experiments results verified the effectiveness of the S-Box construction scheme. In recent years, a large number of S-Box design schemes have been proposed. However, after detection we found that most of them contain fixed point or reverse fixed point, which may be an exploitable weakness in cryptography. In order to design a strong S-Box construction algorithm, and eliminate fixed point and reverse fixed point intelligently, we first designed an improved coupling quadratic map (ICQM), which is surjective and has good ergodicity and randomness, verified by bifurcation diagram, Lyapunov exponent and strict randomness testing tool of TestU01. Then we reconstructed a keyed strong S-Box scheme without weakness based on ICQM and backtracking. Experiments results indicated the effectiveness of the proposed S-Box construction scheme.