Information Flow in Interactive Systems

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 not valid anymore. However, the principle can be recovered if we consider more complicated types of channels, 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 kind of channels. Furthermore, we show that the capacity of the channels associated to such systems is a continuous function of the Kantorovich metric.