S-box design method based on improved one-dimensional discrete chaotic map

A new method for obtaining random bijective S-boxes based on improved one-dimensional discrete chaotic map is presented. The proposed method uses a new special case of discrete chaotic map based on the composition of permutations, in order to overcome the problem with potentially short length of the orbits. The proposed special case is based on the composition of permutations and sine function and has a larger minimum length of the orbits compared to the previous special case of the discrete-space chaotic map. The results of performance test show that the example of S-box generated by the proposed method has good cryptographic properties. The proposed method can achieve large key space, which makes it suitable for generation of larger S-boxes, and the process of generation of S-boxes is not affected by approximations of any kind. Also, proposed method has potential to operate at greater speed and with smaller memory requirements than previous S-box generation method based on discrete space chaotic map, which can be particularly useful for lightweight devices such as wireless sensor networks.