Not Optimal but Efficient: A Distinguisher Based on the Kruskal-Wallis Test

Research about the theoretical properties of side channel distinguishers revealed the rules by which to maximise the probability of first order success ("optimal distinguishers") under different assumptions about the leakage model and noise distribution. Simultaneously, research into bounding first order success (as a function of the number of observations) has revealed universal bounds, which suggest that (even optimal) distinguishers are not able to reach theoretically possible success rates. Is this gap a proof artefact (aka the bounds are not tight) or does a distinguisher exist that is more trace efficient than the "optimal" one? We show that in the context of an unknown (and not linear) leakage model there is indeed a distinguisher that outperforms the "optimal" distinguisher in terms of trace efficiency: it is based on the Kruskal-Wallis test.