Information theoretic comparison of side–channel distinguishers: Inter–class distance, confusion, and success

Abstract

Different side–channel distinguishers have different efficiencies. Their fair comparison is a difficult task because many factors come into play–in particular, their intrinsic statistical properties and the quality of their estimation. In this work, we first evaluate two related information–theoretic distinguishers: mutual information analysis and inter–class information analysis. The latter requires the same underlying probability distributions but uses a different comparing strategy. These distinguishers are not only interesting on their own and suitable for a mathematical study, but they also exhibit an example where the theoretical and empirical evaluation framework agree. The IIA was found to distinguish better than MIA in theory as well as in practice. Moreover, we develop a new metric, called success metric, capturing the relevant parameters of the success rate, while providing more feedback about the distinguishing power. We additionally state closed–form expressions of the theoretical success metric for additive distinguisher like CPA and DPA and highlight that these expressions are much more convenient than for the theoretical success rate. In the case of a low signal–to–noise ratio (realistic practical condition), we derive the conditions on the cipher's substitution boxes (sboxes) to minimize the success metric (hence the success rate). This result supersedes a previous characterization on sboxes known as transparency order, which is derived from a metric on a distinguisher, and not from a success metric/rate. Moreover, we are also able to formulate a closed–form expression for MIA, which has not been shown before.