The Cardinal Abstraction for Quantitative Information Flow

Qualitative information flow aims at detecting information leaks, whereas the emerging quantitative techniques target the estimation of information leaks. Quantifying information flow in the presence of low inputs is challenging, since the traditional techniques of approximating and counting the reachable states of a program no longer suffice. This paper proposes an automated quantitative information flow analysis for imperative deterministic programs with low inputs. The approach relies on a novel abstract domain, the cardinal abstraction, in order to compute a precise upper-bound over the maximum leakage of batch-job programs. We prove the soundness of the cardinal abstract domain by relying on the framework of abstract interpretation. We also prove its precision with respect to a flow-sensitive type system for the two-point security lattice.