Side-Channel Information Leakage of Code-Based Masked Implementations

Side-channel attacks (SCAs) are among the most powerful physical attacks against cryptographic implementations. To thwart SCAs, a well-established countermeasure is random masking. A recent code-based masking formalism unifies several known masking schemes and allows one to carry out an all-in-one leakage quantification. In this paper, we investigate how a code-based masked implementation leaks in an information-theoretic setting, where the mutual information measures the impact of both number and positions of probes in the probing attack model. We also establish that the mutual information decreases as the measurement noise variance increases, with an exponent equal to the dual distance of the masking code. Our findings quantitatively connect the attacker's capability to recover secret keys with the actual mutual information leakage of the protected implementation.