Optimal side-channel attacks for multivariate leakages and multiple models

Side-channel attacks allow to extract secret keys from embedded systems like smartcards or smartphones. In practice, the side-channel signal is measured as a trace consisting of several samples. Also, several sensitive bits are manipulated in parallel, each leaking differently. Therefore, the informed attacker needs to devise side-channel distinguishers that can handle both multivariate leakages and multiple models. In the state of the art, these two issues have two independent solutions: on the one hand, dimensionality reduction can cope with multivariate leakage; on the other hand, online stochastic approach can cope with multiple models. In this paper, we combine both solutions to derive closed-form expressions of the resulting optimal distinguisher in terms of matrix operations, in all situations where the model can be either profiled offline or regressed online. Optimality here means that the success rate is maximized for a given number of traces. We recover known results for uni- and bivariate models (including correlation power analysis) and investigate novel distinguishers for multiple models with more than two parameters. In addition, following ideas from the AsiaCrypt’2013 paper “Behind the Scene of Side-Channel Attacks,” we provide fast computation algorithms in which the traces are accumulated prior to computing the distinguisher values.