Perfectly Secure Communication in Directed Networks

Arpita Patra, Ashish Choudhary, Kannan Srinathan +1 more

Arpita Patra, Ashish Choudhary, Kannan Srinathan +1 more

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

Jérôme Renault, Ludovic Renou, Tristan Tomala

Nkm Nieke Aerts

Ivan Damgård, Divya Ravi, Daniel Tschudi +1 more

In this paper, we explore the feasibility of reliable and private communication in dynamic networks, where in each round the adversary can choose which direct peer-to-peer links are available in the network graph, under the sole condition that the graph is k-connected at each round (for some k). We show that reliable communication is possible in such a dynamic network if and only if k > 2t. We also show that if k = cn > 2 t for a constant c, we can achieve reliable communication with polynomial round and communication complexity. For unconditionally private communication, we show that for a passive adversary, k > t is sufficient (and clearly necessary). For an active adversary, we show that k > 2t is sufficient for statistical security (and clearly necessary), while k > 3t is sufficient for perfect security. We conjecture that, in contrast to the static case, k > 2t is not enough for perfect security, and we give evidence that the conjecture is true. Once we have reliable and private communication between each pair of parties, we can emulate a complete network with secure channels, and we can use known protocols to do secure computation.