Study on MC-Optimal S-Box Circuits

Multiplicative complexity is one of the important properties for the efficiency of S-box. In this paper, we present a new method to find S-box circuits with optimal multiplicative complexity. Our method uses the early abortion technique to speed up finding the canonical forms of the S-box circuits. We adopted a method of grouping AND gates and searching the grouped parts. One or more component functions can be generated by searching each part, and an S-box can be generated by searching all parts. This allows a wider range of S-boxes to be investigated. We believe that our method will help S-box designers to generate efficient S-box circuits.