Statistical Analysis of Non-Profiling Higher-Order Distinguishers Against Inner Product Masking

Inner Product Masking (IPM) is one representative masking scheme, which captivates by so-called Security Order Amplification (SOA) property. It is commonly recognized that SOA holds under linear leakages. In this paper, we revisit SOA from a non-profiling attack perspective. Specifically, we conduct statistical analyses on three non-profiling distinguishers, including Pearson Coefficient Distinguisher (PCD), Spearman Coefficient Distinguisher (SCD) and Kruskal-Wallis Distinguisher (KWD). We find a fundamental connection between SCD and KWD such that SCD is a more generic distinguisher which encompasses KWD. Theoretical explanations for why KWD outperforms SCD under non-linear leakages are provided. We also propose a new adjusted SCD and present its optimal form, which bridges the efficiency gap with KWD. Grounded on this, SOA is extensively assessed and the observations are two-fold. On the one hand, we confirm again the effectiveness of SOA under Hamming weight leakage through the statistical analysis of PCD. On the other hand, we show that SOA can not resist rank-based distinguishers even under linear leakages, which has never been revealed before (to the best of our knowledge). At last, we verify the theoretical findings through both simulated and real-world measurements. Our results demonstrate the advantage of rank-based distinguishers in uncovering non-linear relationships hidden in leakage, enriching the tool-set for non-profiling class of side-channel attacks. Remarkably, we provide an adversary perspective to investigate SOA, highlighting that the side-channel resistance promised by SOA is vulnerable even considering the ideal linear leakage models.