Quantifying Information Flow Using Min-Entropy

Quantitative theories of information flow are of growing interest, due to the fundamental importance of protecting confidential information from improper disclosure, together with the unavoidability of "small" leaks in practical systems. But while it is tempting to measure leakage using classic information-theoretic concepts like Shannon entropy and mutual information, these turn out not to provide very satisfactory security guarantees. As a result, several researchers have developed an alternative theory based on Renyi\´s min-entropy. In this theory, uncertainty is measured in terms of a random variable\´s vulnerability to being guessed in one try by an adversary, note that this is the complement of the Bayes Risk. In this paper, we survey the main theory of min-entropy leakage in deterministic and probabilistic systems, including comparisons with mutual information leakage, results on min-capacity, results on channels in cascade, and techniques for calculating min-entropy leakage in systems.