Confused yet successful: Theoretical comparison of distinguishers for monobit leakages in terms of confusion coefficient and SNR

Many side-channel distinguishers (such as DPA/DoM, CPA, Euclidean Distance, KSA, MIA, etc.) have been devised and studied to extract keys from cryptographic devices. Each has pros and cons and find applications in various contexts. These distinguishers have been described theoretically in order to determine which distinguisher is best for a given context, enabling an unambiguous characterization in terms of success rate or number of traces required to extract the secret key. In this paper, we show that in the case of monobit leakages, the theoretical expression of all distinguishers depend only on two parameters: the confusion coefficient and the signal-to-noise ratio. We provide closed-form expressions and leverage them to compare the distinguishers in terms of convergence speed for distinguishing between key candidates. This study contrasts with previous works where only the asymptotic behavior was determined—when the number of traces tends to infinity, or when the signal-to-noise ratio tends to zero.