  This paper proposes an operational measure of non-stochastic information
leakage to formalize privacy against a brute-force guessing adversary. The
information is measured by non-probabilistic uncertainty of uncertain
variables, the non-stochastic 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)
non-stochastic 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.
