Information Theoretic Distinguishers for Timing Attacks with Partial Profiles: Solving the Empty Bin Issue

In any side-channel attack, it is desirable to exploit all the available leakage data to compute the distinguisher’s values. The profiling phase is essential to obtain an accurate leakage model, yet it may not be exhaustive. As a result, information theoretic distinguishers may come up on previously unseen data, a phenomenon yielding empty bins. A strict application of the maximum likelihood method yields a distinguisher that is not even sound. Ignoring empty bins reestablishes soundness, but seriously limits its performance in terms of success rate. The purpose of this paper is to remedy this situation. In this research, we propose six different techniques to improve the performance of information theoretic distinguishers. We study them thoroughly by applying them to timing attacks, both with synthetic and real leakages. Namely, we compare them in terms of success rate, and show that their performance depends on the amount of profiling, and can be explained by a bias-variance analysis. The result of our work is that there exist use-cases, especially when measurements are noisy, where our novel information theoretic distinguishers (typically the soft-drop distinguisher) perform the best compared to known side-channel distinguishers, despite the empty bin situation.