This paper takes steps toward adapting results to a quantitative treatment of disclosure. The authors generalize the cut principle to include a probabilistic analysis for quantifying information leakage.
Composable Bounds on Information Flow from Distribution Differences
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We define information leakage in terms of a "difference" between the a priori distribution over some remote behavior and the a posteriori distribution of the remote behavior conditioned on a local observation from a protocol run. Either a maximum or an average may be used. We identify a set of notions of "difference"; we show that they reduce our general leakage notion to various definitions in the literature. We also prove general composability theorems analogous to the data processing inequality for mutual information, or cascading channels for channel capacities.