A popular effective countermeasure to protect block cipher implementations against differential power analysis (DPA) attacks is to mask the internal operations of the cryptographic algorithm with random numbers. While the masking technique resists against first-order (univariate) DPA attacks, higher-order (multivariate) attacks were able to break masked devices. In this paper, we formulate a statistical model for higher-order DPA attack. We derive an analytic success rate formula that distinctively shows the effects of algorithmic confusion property, signal-noise-ratio (SNR), and masking on leakage of masked devices. It further provides a formal proof for the centered product combination function being optimal for higher-order attacks in very noisy scenarios. We believe that the statistical model fully reveals how the higher-order attack works around masking, and would offer good insights for embedded system designers to implement masking techniques.
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