Multi-Variate High-Order Attacks of Shuffled Tables Recomputation.
Nicolas Bruneau, Sylvain Guilley, Zakaria Najm, Yannick Teglia · 2015
Abstract. Masking schemes based on tables recomputation are classi-cal countermeasures against high-order side-channel attacks. Still, they are known to be attackable at order d in the case the masking involves d shares. In this work, we mathematically show that an attack of order strictly greater than d can be more successful than an attack at order d. To do so, we leverage the idea presented by Tunstall, Whitnall and Oswald at FSE 2013: we exhibit attacks which exploit the multiple leak-ages linked to one mask during the recomputation of tables. Specifically, regarding first-order table recomputation, improved by a shuffled execu-tion, we show that there is a window of opportunity, in terms of noise variance, where a novel highly multivariate third-order attack is more ef-ficient than a classical bivariate second-order attack. Moreover, we show on the example of the high-order secure table computation presented by Coron at EUROCRYPT 2014 that the window of opportunity enlarges linearly with the security order d.