An Information-Theoretic Model for Side-Channel Attacks in Embedded Hardware

Using information-theoretic tools, this paper establishes a mathematical link between the probability of success of a side-channel attack and the minimum number of queries to reach a given success rate, valid for any possible distinguishing rule and with the best possible knowledge on the attacker's side. This link is a lower bound on the number of queries, which depends on the mutual information between the traces and the secret key. This leads us to derive upper bounds on the mutual information that are as tight as possible and can be easily calculated. It turns out that, in the case of additive white Gaussian noise, the bound on the probability of success of any attack is directly related to the signal-to-noise ratio (SNR). This leads to easy computations and predictions of the success rate for any leakage model.