Best information is most successful: Mutual information and success rate in side-channel analysis

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 highly depends on Shannon’s 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 an additive white Gaussian noise, the bound on the probability of success of any attack is directly related to the signal to noise ratio. This leads to very easy computations and predictions of the success rate in any leakage model.