Time and Probability-Based Information Flow Analysis

In multilevel systems, it is important to avoid unwanted indirect information flow from higher levels to lower levels, namely, the so-called covert channels. Initial studies of information flow analysis were performed by abstracting away from time and probability. It is already known that systems that are proven to be secure in a possibilistic framework may turn out to be insecure when time or probability is considered. Recently, work has been done in order to consider also aspects either of time or of probability, but not both. In this paper, we propose a general framework based on Probabilistic Timed Automata, where both probabilistic and timing covert channels can be studied. We define a Noninterference security property and a Nondeducibility on Composition security property, which allow expressing information flow in a timed and probabilistic setting. We then compare these properties with analogous ones defined in contexts where either time or probability or neither of them are taken into account. This permits a classification of the properties depending on their discerning power. As an application, we study a system with covert channels that we are able to discover by applying our techniques.