Eavesdropping games: a graph-theoretic approach to privacy in distributed systems

We initiate a graph-theoretic approach to study the (information-theoretic) maintenance of privacy in distributed environments in the presence of a bounded number of mobile eavesdroppers (“bugs”). For two fundamental privacy problems-secure message transmission and distributed database maintenance-we assume an adversary is “playing eavesdropping games,” coordinating the movement of the bugs among the sites to learn the current memory contents. We consider various mobility settings (adversaries), motivated by the capabilities (strength) of the bugging technologies (e.g., how fast can a bug be reassigned). We combinatorially characterize and compare privacy maintenance problems, determine their feasibility (under numerous bug models), suggest protocols for the feasible cases, and analyze their computational complexity