On The Communication Complexity of Perfectly Secure Message Transmission in Directed Networks.
Arpita Patra, Ashish Choudhary, Chandrasekharan Pandu Rangan
In this paper, we re-visit the problem of perfectly secure message transmission (PSMT) in a directed network under the presence of a threshold adaptive Byzantine adversary, having unbounded computing power. Desmedt et.al [5] have given the characterization for three or more phase PSMT protocols over directed networks. Recently, Patra et. al. [15] have given the characterization of two phase PSMT over directed networks. Even though the issue of tradeoff between phase complexity and communication complexity of PSMT protocols has been resolved in undirected networks, nothing is known in the literature regarding directed networks. In this paper, we completely settle down this issue. Specifically, we derive the lower bounds on communication complexity of (a) two phase PSMT protocols and (b) three or more phase PSMT protocols in directed networks. Moreover, we show that our lower bounds are asymptotically tight, by designing communication optimal PSMT protocols in directed networks, which are first of their kind. We re-visit the problem of perfectly reliable message transmission (PRMT) as well. Any PRMT protocol that sends a message containing ℓ field elements, has a trivial lower bound of Ω(ℓ) (field elements) on its communication complexity. Thus any PRMT protocol that sends a message of ℓ
•Jan 1, 2009•4 citations