An Interval-based Abstraction for Quantifying Information Flow

In a batch program, information about confidential inputs may flow to insecure outputs. The size of this leakage, considered as a Shannon measure, may be automatically and exactly calculated via probabilistic semantics as we have shown in our earlier work. This approach works well for small programs with small state spaces. As the scale increases the calculation suffers from a form of state space explosion and the time complexity grows. In this paper we scale up the programs and state spaces that can be handled albeit at the cost of replacing an exact result with an upper bound. To do this we introduce abstraction on the state space via interval-based partitions, adapting an abstract interpretation framework introduced by Monniaux. The user can define the partitions and the more coarse the partitions, the more coarse the resulting upper bound. In this paper we summarise our previous contribution, define the abstract interpretation, show its soundness, and prove that the result of an abstract computation is always an upper bound on the true leakage, i.e. is a safe estimate. Finally we illustrate the approach by means of some examples.