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Leakage Squeezing of Order Two

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In masking schemes, leakage squeezing is the study of the optimal shares representation, that maximizes the resistance order against high-order side-channel attacks. Squeezing the leakage of first-order Boolean masking has been problematized and solved previously. The solution consists in finding a bijection F that modifies the mask, in such a way that its graph, seen as a code, be of greatest dual distance. This paper studies second-order leakage squeezing, i.e. leakage squeezing with two independent random masks. It is proved that, compared to first-order leakage squeezing, second-order leakage squeezing at least increments (by one unit) the resistance against high-order attacks, such as high-order correlation power analyses (HO-CPA). Now, better improvements over first-order leakage squeezing are possible by relevant constructions of the squeezing bijections pair.