Paper 2015/837

Multi-Variate High-Order Attacks of Shuffled Tables Recomputation

Nicolas BRUNEAU and Sylvain GUILLEY and Zakaria NAJM and Yannick TEGLIA

Abstract

Masking schemes based on tables recomputation are classical 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 leakages linked to one mask during the recomputation of tables. Specifically, regarding first-order table recomputation, improved by a shuffled execution, we show that there is a window of opportunity, in terms of noise variance, where a novel highly multivariate third-order attack is more efficient 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 $d$.

Note: Like in the CHES '15 paper, but where Alg. 1 and Fig. 1 have been made compatible.