DPA Attacks and S-Boxes

For the power consumption model called Hamming weight model, we rewrite DPA attacks in terms of correlation coefficients between two Boolean functions. We exhibit properties of S-boxes (also called (n, m)-functions) relied on DPA attacks. We show that these properties are opposite to the non-linearity criterion and to the propagation criterion. To quantify the resistance of an S-box to DPA attacks, we introduce the notion of transparency order of an S-box and we study this new criterion with respect to the non-linearity and to the propagation criterion.