  We propose an operational measure of information leakage in a non-stochastic
setting to formalize privacy against a brute-force guessing adversary. We use
uncertain variables, non-probabilistic counterparts of random variables, to
construct a guessing framework in which an adversary is interested in
determining private information based on uncertain reports. We consider
brute-force trial-and-error guessing in which an adversary can potentially
check all the possibilities of the private information that are compatible with
the available outputs to find the actual private realization. The ratio of the
worst-case number of guesses for the adversary in the presence of the output
and in the absence of it captures the reduction in the adversary's guessing
complexity and is thus used as a measure of private information leakage. We
investigate the relationship between the newly-developed measure of information
leakage with the existing non-stochastic maximin information and stochastic
maximal leakage that are shown arise in one-shot guessing.
