The Byzantine Generals Problem in Generic and Wireless Networks
In this chapter we consider the design of Secure Broadcast protocols in generic networks of known topology. Studying the problem of Secure Message Transmission (SMT) proves essential for achieving Broadcast in incomplete networks. We present a polynomial protocol that achieves parallel secure message transmissions between any two sets of nodes of an incomplete network provided that the weakest connectivity conditions which render the Broadcast problem solvable hold. Using the above, we show that the SMT protocol can be used as a subroutine for the simulation of any known protocol for complete networks, which leads us to protocols for generic networks which remain polynomial with respect to the measures of consideration. We extend our result to the case of wireless networks by exploiting the fact that participants are committed to perform local broadcasts, which greatly facilitates achieving an agreement.