Composable bounds on information flow from distribution differences

Abstract

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.