Two NP-Complete Problems in Software Security

A secure programming environment must offer protection mechanisms for regulating the interaction between mutually suspicious code units. Discretionary Capability Confinement (DCC) is a static type system recently proposed for expressing and enforcing access control policies in Java programs. This paper considers the computational complexity of the type reconstruction problem for DCC, that is, the automatic inference of DCC annotations for legacy Java code base. We model a representative subproblem of the type reconstruction problem as a graph-theoretic optimization problem. We demonstrate that this problem is NP-Complete. To strengthen the result, we further eliminate the asymmetry in the problem statement to obtain an elegant reformulation. We show that the reformulated problem is still NP-Complete. These results help identify the complexity core of the type reconstruction problem, and suggest that practical type reconstruction tool must adopt a heuristic and/or approximation approach.