Measuring Information Leakage in Non-stochastic Brute-Force Guessing

Abstract

This paper proposes an operational measure of nonstochastic information leakage to formalize privacy against a brute-force guessing adversary. The information is measured by non-probabilistic uncertainty of uncertain variables, the nonstochastic counterparts of random variables. For X that is related to released data Y , the non-stochastic brute-force leakage is measured by the complexity of exhaustively checking all the possibilities of the private attribute U of X by an adversary. The complexity refers to the number of trials to successfully guess U . Maximizing this leakage over all possible private attributes U gives rise to the maximal (i.e., worst-case) nonstochastic brute-force guessing leakage. This is proved to be fully determined by the minimal non-stochastic uncertainty of X given Y , which also determines the worst-case attribute U indicating the highest privacy risk if Y is disclosed. The maximal non-stochastic brute-force guessing leakage is shown to be proportional to the non-stochastic identifiability of X given Y and upper bounds the existing maximin information. The latter quantifies the information leakage when an adversary must perfectly guess U in one-shot via Y . Experiments are used to demonstrate the tradeoff between the maximal non-stochastic brute-force guessing leakage and the data utility (measured by the maximum quantization error) and to illustrate the relationship between maximin information and stochastic one-shot maximal leakage.