Be My Guesses: The interplay between side-channel leakage metrics

In a theoretical context of side-channel attacks, optimal bounds between success rate, guessing entropy and statistical distance are derived with a simple majorization (Schur-concavity) argument. They are further theoretically refined for different versions of the classical Hamming weight leakage model, in particular assuming a priori equiprobable secret keys and additive white Gaussian measurement noise. Closed-form expressions and numerical computation are given. A study of the impact of the choice of the substitution box with respect to side-channel resistance reveals that its nonlinearity tends to homogenize the expressivity of success rate, guessing entropy and statistical distance. The intriguing approximate relation between guessing entropy and success rate $GE=1/SR$ is observed in the case of 8-bit bytes and low noise. The exact relation between guessing entropy, statistical distance and alphabet size $GE=\frac{M+1}{2}-\frac{M}{2}SD$ for deterministic leakages and equiprobable keys is proved.