Distribution of Signal to Noise Ratio and Application to Leakage Detection

Abstract

In the context of side-channel attacks, the Signal to Noise Ratio (SNR) is a widely used metric for characterizing the information leaked by a device when handling sensitive variables. In this paper, we derive the probability density function (p.d.f.) of the signal to noise ratio (SNR) for the byte value and Hamming Weight (HW) models, when the number of traces per class is large and the target SNR is small. These findings are subsequently employed to establish an SNR threshold, guaranteeing minimal occurrences of false positives. Then, these results are used to derive the theoretical number of traces that are required to remain below pre-defined false negative and false positive rates. The sampling complexity of the T-test, ρ-test and SNR is evaluated for the byte value and HW leakage model by simulations and compared to the theoretical predictions. This allows to establish the most pertinent strategy to make use of each of these detection techniques.