A Quantitative Approach to Noninterference for Probabilistic Systems

We present a technique for measuring the security of a system which relies on a probabilistic process algebraic formalisation of noninterference. We define a mathematical model for this technique which consists of a linear space of processes and linear transformations on them. In this model the measured quantity corresponds to the norm of a suitably defined linear operator associated to the system. The probabilistic model we adopt is reactive in the sense that processes can react to the environment with a probabilistic choice on a set of inputs; it is also generative in the sense that outputs autonomously chosen by the system are governed by a probability distribution. In this setting, noninterference is formulated in terms of a probabilistic notion of weak bisimulation. We show how the probabilistic information in this notion can be used to estimate the maximal information leakage, i.e. the security degree of a system against a most powerful attacker.