Quantitative information flow in interactive systems

Mário S. Alvim, Miguel E. Andrés, Catuscia Palamidessi

Abstract: We consider the problem of defining the information leakage in interactive systems where secrets and observables can alternate during the computation. We show that the information-theoretic approach which interprets such systems as (simple) noisy channels is no longer valid. However, the principle can be recovered if we consider channels of a more complicated kind, that in Information Theory are known as channels with memory and feedback. We show that there is a complete correspondence between interactive systems and such channels. Furthermore, we show that the capacity of the channels associated to such systems is a continuous function with respect to a pseudometric based on the Kantorovich metric.