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Fit The Joint Moments
Authors: Valence Cristiani, Maxime Lecomte, Thomas Hiscock, and Philippe MaurineAbstract:
Side-Channel Analysis (SCA) allows extracting secret keys manipulated by cryptographic primitives through leakages of their physical implementations. Supervised attacks, known to be optimal, can theoretically defeat any counter-measure, including masking, by learning the dependency between the leakage and the secret through the profiling phase. However, defeating masking is less trivial when it comes to unsupervised attacks. While classical strategies such as CPA or LRA have been extended to masked implementations, we show that these extensions only hold for Boolean and arithmetic schemes. Therefore, we propose a new unsupervised strategy, the Joint Moments Regression (JMR), able to defeat any masking schemes (multiplicative, affine, polynomial, inner product…), which are gaining popularity in real implementations. The main idea behind JMR is to directly regress the leakage model of the shares by fitting a system based on higher-order joint moments conditions. We show that this idea can be seen as part of a more general framework known as the Generalized Method of Moments (GMM). This offers strong mathematical foundations on which we can rely on to derive optimizations of JMR. Simulation experiments show that our proposal outperforms state-of-the-art attacks, even in the case of Boolean and arithmetic masking. Eventually, we apply this strategy to provide, to the best of our knowledge, the first unsupervised attack (successful in practice) on the protected AES implementation proposed by the ANSSI for SCA research, which embed an affine masking and shuffling counter-measures.
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