Be My Guess: Guessing Entropy vs. Success Rate for Evaluating Side-Channel Attacks of Secure Chips

In a theoretical context of side-channel attacks, optimal bounds between success rate and guessing entropy 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 and guessing entropy. The intriguing approximate relation
$GE=1/SR$
is observed in the case of 8-bit bytes and low noise.