Formal Analysis of Information Flow Using Min-Entropy and Belief Min-Entropy

Abstract

Abstract. Information flow analysis plays a vital role in obtaining quantitative bounds on information leakage due to external attacks. Traditionally, information flow analysis is done using paper-and-pencil based proofs or computer simulations based on the Shannon entropy and mutual information. However, these metrics sometimes provide misleading information while dealing with some specific threat models, like when the secret is correctly guessed in one try. Min-Entropy and Belief Minentropy metrics have been recently proposed to address these problems. But the information flow analysis using these metrics is done by simulation and paper-and-pencil approaches and thus cannot ascertain accurate results due to their inherent limitations. In order to overcome these shortcomings, we formalize Min-Entropy and Belief-Min-Entropy in higher-order logic and use them to perform information flow analysis within the sound core of the HOL theorem prover. For illustration purposes, we use our formalization to evaluate the information leakage of a cascade of channels in HOL.