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An accurate leakage model is critical to side-channel attacks and evaluations. Leakage certification plays an important role to address the following question: “how good is my leakage model?” Moreover, most of the current leakage model profiling only exploit the information from lower orders of moments. They still need to tolerate assumption error and estimation error from unknown leakage models. There are many probability density functions (PDFs) satisfying given moment constraints. As such, finding an unbiased, objective, and reasonable model still remains an unresolved problem. In this article, we address a more fundamental question: “which model can approach the leakage infinitely and is the optimal in theory?” In particular, we extract information from higher order moments and propose maximum entropy distribution (MED) to estimate the leakage model as MED is an unbiased, objective, and theoretically the most reasonable PDF conditioned upon the available information. MED is a moment-based statistical PDF model in side-channel attacks. It can theoretically use information on arbitrary higher order moments to infinitely approximate the leakage distribution, and well compensates the theory vacancy of model profiling and evaluation. Experimental results demonstrate the superiority of our proposed method for approximating the leakage model using MED estimation. [ABSTRACT FROM AUTHOR]