Perfectly secure message transmission

The problem of perfectly secure communication in a general network in which processors and communication lines may be faulty is studied. Lower bounds are obtained on the connectivity required for successful secure communication. Efficient algorithms that operate with this connectivity and rely on no complexity theoretic assumptions are derived. These are the first algorithms for secure communication in a general network to achieve simultaneously the goals of perfect secrecy, perfect resiliency, and worst case time linear in the diameter of the network.