MinMaxEntropy: Bound Model Errors for Side-Channel Leakages From Information Theory

Side-channel attacks and evaluations have been incessantly pursuing an accurate leakage model and try to address the following question: “How good is my leakage model?” However, the existing works do not well alleviate the attackers and evaluators from model assumption error and estimation error. The recent work named maximum entropy distribution (MED) model does not depend on any assumptions but uses nonlinear programming Newton-Raphson method to fit the leakage distribution, thus avoiding assumption error and making the estimation error arbitrarily small. It tries to address a more fundamental problem: “How to achieve the optimal leakage model?,” but still have to face with two issues: 1) the large deviation of MED model from leakage distribution and 2) the difficulty in determining the moments required in model profiling. In this article, we first introduce the nonlinear programming optimizations Levenberg-Marquardt and Conjugate Gradient methods to tackle the first issue. We then exploit Hopfield neural network to solve the minimum entropy for leakage model. Unlike the MED indicating the theoretically most unbiased, objective and reasonable leakage model, the minimum entropy corresponds to the theoretically most biased, subjective and unreasonable leakage model. This facilitates us to build a MinMaxEntropy bound from the maximum entropy and minimum entropy for estimation errors in leakage model, which theoretically represents the amount of information contained on unused higher moments. This bound well provides theoretical support for the moments constraints required to profile the MED model, thus well tackling the second issue. Experimental results fully demonstrate the superiority of our above schemes.