Optimality and beyond: The case of 4×4 S-boxes

Abstract

S-boxes with better transparency order are expected to have higher side-channel resistance. For 8×8 S-boxes this is not practical, considering the costs of lookup-table implementations and deterioration of many properties like nonlinearity or delta uniformity. However, if we concentrate on the 4×4 S-box size we can observe that it is possible to obtain S-boxes with better transparency order while maintaining proper “classical” properties. To prove this, we experiment with PRINCE and PRESENT S-boxes. We use various methods and show that evolutionary algorithms are also viable in obtaining the lowest known transparency order value for the nonlinearity value of 4. Next, we show that affine transformation changes the transparency order while keeping “classical” properties intact. By using this technique, it is possible to generate optimal S-boxes with improved DPA-related properties.