On the Success Rate of Side-Channel Attacks on Masked Implementations: Information-Theoretical Bounds and Their Practical Usage

This study derives information-theoretical bounds of the success rate (SR) of side-channel attacks on masked implementations. We first develop a communication channel model representing side-channel attacks on masked implementations. We then derive two SR bounds based on the conditional probability distribution and mutual information of shares. The basic idea is to evaluate the upper-bound of the mutual information between the non-masked secret value and the side-channel trace by the conditional probability distribution of shares given its leakage, with a help of the Walsh-Hadamard transform. With the derived theorems, we also prove the security of masking schemes: the SR decreases exponentially with an increase in the number of masking shares, under a much more relaxed condition than the previous proof. To validate and utilize our theorems in practice, we propose a deep-learning-based profiling method for approximating the conditional probability distribution of shares to estimate the SR bound and the number of traces required for attacking a given device. We experimentally confirm that our bounds are much stronger than the conventional bounds on masked implementations, which validates the relevance of our theorems to practice.