Minimal Connectivity for Unconditionally Secure Message Transmission in Synchronous Directed Networks

In this paper we give the minimal connectivity required in a synchronous directed network, which is under the influence of a computationally unbounded Byzantine adversary that can corrupt a subset of nodes, so that Secure Message Transmission is possible between sender S and receiver R. We also show that secure communication between a pair of nodes in a given synchronous directed network is possible in both directions if and only if reliable communication is possible between them. We assume that in a network, every node is capable of computation and we model the network along the lines of [14].

[1]  Yvo Desmedt,et al.  Cryptanalysis of Secure Message Transmission Protocols with Feedback , 2009, ICITS.

[2]  K. Srinathan,et al.  Perfectly Secure Message Transmission in Directed Networks Tolerating Threshold and Non Threshold Adversary , 2007, CANS.

[3]  K. Srinathan,et al.  Unconditionally reliable message transmission in directed networks , 2008, SODA '08.

[4]  K. Srinathan,et al.  Unconditionally secure message transmission in arbitrary directed synchronous networks tolerating generalized mixed adversary , 2009, ASIACCS '09.

[5]  Matthew K. Franklin,et al.  Secure Communication in Minimal Connectivity Models , 1998, Journal of Cryptology.

[6]  Silvio Micali,et al.  How to play ANY mental game , 1987, STOC.

[7]  K. Srinathan,et al.  On perfectly secure communication over arbitrary networks , 2002, PODC '02.

[8]  Leslie Lamport,et al.  The Byzantine Generals Problem , 1982, TOPL.

[9]  Yongge Wang,et al.  Perfectly Secure Message Transmission Revisited , 2008, IEEE Trans. Inf. Theory.

[10]  Ueli Maurer,et al.  Complete characterization of adversaries tolerable in secure multi-party computation (extended abstract) , 1997, PODC '97.

[11]  David Chaum,et al.  Multiparty Unconditionally Secure Protocols (Extended Abstract) , 1988, STOC.

[12]  K. Srinathan,et al.  Possibility and complexity of probabilistic reliable communication in directed networks , 2006, PODC '06.

[13]  Avi Wigderson,et al.  Completeness theorems for non-cryptographic fault-tolerant distributed computation , 1988, STOC '88.

[14]  Tal Rabin,et al.  Verifiable secret sharing and multiparty protocols with honest majority , 1989, STOC '89.