Composability and robustness against physical defaults (e.g., glitches) are two highly desirable properties for secure implementations of masking schemes. While tools exist to guarantee them separately, no current formalism enables their joint investigation. In this paper, we solve this issue by introducing a new model, the robust probing model, that is naturally suited to capture the combination of these properties. We first motivate this formalism by analyzing the excellent robustness and low randomness requirements of first-order threshold implementations, and highlighting the difficulty to extend them to higher orders. Next, and most importantly, we use our theory to design and prove the first higher-order secure, robust and composable multiplication gadgets. While admittedly inspired by existing approaches to masking (e.g., Ishai-Sahai-Wagner-like, threshold, domain-oriented), these gadgets exhibit subtle implementation differences with these state-of-the-art solutions (none of which being provably composable and robust). Hence, our results illustrate how sound theoretical models can guide practically-relevant implementations.
Singular Spectrum Analysis (SSA) is a powerful data decomposition/recompose technique that can be used to reduce the noise in time series. Compared to existing solutions aiming at similar purposes, such as frequency-based filtering, it benefits from easier-to-exploit intuitions, applicability in contexts where low sampling rates make standard frequency analyses challenging, and the (theoretical) possibility to separate a signal source from a noisy source even if both run at the same frequency. In this paper, we first describe how to apply SSA in the context of side-channel analysis, and then validate its interest in three different scenarios. Namely, we consider unprotected software, masked software, and unprotected hardware block cipher implementations. Our experiments confirm significant noise reductions in all three cases, leading to success rates improved accordingly. They also put forward the stronger impact of SSA in more challenging scenarios, e.g. masked implementations (because the impact of noise increases exponentially with the number of shares in this case), or noisy hardware implementations (because of the established connection between the amount of noise and the attacks' success rate in this case). Since noise is a fundamental ingredient for most countermeasures against side-channel attacks, we conclude SSA can be an important element in the toolbox of evaluation laboratories, in order to efficiently preprocess their measurements in a black box manner.
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