Unconditionally Reliable and Secure Message Transmission in Directed Networks Revisited

In this paper, we re-visit the problem of unconditionally reliable message transmission (URMT) and unconditionally secure message transmission (USMT) in a directed network under the presence of a threshold adaptive Byzantine adversary, having unbounded computing power. Desmedt et.al [5] have given the necessary and sufficient condition for the existence of URMT and USMT protocols in directed networks. Though their protocols are efficient, they are not communication optimal. In this paper, we prove for the first time the lower bound on the communication complexity of URMT and USMT protocols in directed networks. Moreover, we show that our bounds are tight by giving efficient communication optimal URMT and USMT protocols, whose communication complexity satisfies our proven lower bounds.