On the resistance of Serpent-type 4 bit S-boxes against differential power attacks

The transparency order is a parameter to quantify the resistance of S-boxes against the differential power analysis (DPA). S-boxes that have lower transparency order are proved to be more resistant to DPA. In this paper, we propose theoretical methods to examine the invariant of the transparency order of S-boxes under the permutation transformations. We also use the proposed methods to investigate the transparency order of all Serpent-type 4-bit S-boxes, commonly used the lightweight block ciphers, in order to identify the good candidate S-boxes which have a low transparency order.