Paper 2019/683

The Notion of Transparency Order, Revisited

Huizhong Li, Yongbin Zhou, Jingdian Ming, Guang Yang, and Chengbin Jin

Abstract

We revisit the definition of Transparency Order (TO) and that of Modified Transparency Order (MTO) as well, which were proposed to measure the resistance of an S-box against Differential Power Analysis (DPA). We spot a definitional flaw in original TO, which is proved to have significantly affected the soundness of TO and hinder it to be a good quantitative security criterion. Regretfully, the flaw itself remains virtually undiscovered in MTO, either. Surprisingly, MTO overlooks this flaw and yet it happens to incur no bad effects on the correctness of its formulation, even though the start point of this formulation is highly questionable. It is also this neglect of the flaw that made MTO take a variant of multi-bit DPA attack into consideration, which was mistakenly thought to appropriately serve as an alternative powerful attack. Based on this observation, we also find that MTO introduces such an alternative adversary that it might overestimate the resistance of an S-box in some cases, as the variant of multi-bit DPA attack considered in MTO is not that powerful as one may think. This implies the soundness of MTO is also more or less arguable. Consequently, we fix this definitional flaw, and provide a revised definition in which a powerful adversary is also involved. For demonstrating validity and soundness of our revised TO (RTO), we adopt both optimal $4\times4$ S-boxes and $8\times8$ S-boxes as study cases, and present simulated and practical DPA attacks as well on implementations of those S-boxes. The results of our attacks verify our findings and analysis as well. Furthermore, as a concrete application of the revised TO, we also present the distribution of RTO values for sixteen optimal affine equivalence classes of $4\times4$ S-boxes. Finally, we give some recommended guidelines on how to select optimal $4\times4$ S-boxes in practical implementations.