The combinatorial complexity of masterkeying

We consider the combinatorial complexity of the algorithmic design of mechanical master key locking systems. Such locking systems use pin tumblers and profile elements (wards) to realize the functional dependencies given by a key/cylinder matrix. We prove that even very restricted versions of the masterkeying problem are NP-complete. We show that the general masterkeying problem can be defined by an integer linear program whose number of variables and restrictions is polynominal in the size of the key/cylinder matrix and the size of the locking system. Heuristic solutions are also discussed.