Perfectly secure message transmission
Journal of the ACM (JACM)
Perfectly Secure Message Transmission Revisited
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Possibility and complexity of probabilistic reliable communication in directed networks
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Unconditionally Reliable and Secure Message Transmission in Directed Networks Revisited
SCN '08 Proceedings of the 6th international conference on Security and Cryptography for Networks
Unconditionally Reliable Message Transmission in Directed Hypergraphs
CANS '08 Proceedings of the 7th International Conference on Cryptology and Network Security
Brief announcement: topology knowledge affects probabilistic reliable communication
Proceedings of the 28th ACM symposium on Principles of distributed computing
Cryptanalysis of secure message transmission protocols with feedback
ICITS'09 Proceedings of the 4th international conference on Information theoretic security
International Journal of Applied Cryptography
ICITS'11 Proceedings of the 5th international conference on Information theoretic security
ICDCN'12 Proceedings of the 13th international conference on Distributed Computing and Networking
Secure message transmission in asynchronous directed graphs
INDOCRYPT'11 Proceedings of the 12th international conference on Cryptology in India
Theoretical Computer Science
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In the unconditionally reliable message transmission (URMT) problem, two non-faulty players, the sender S and the receiver R are part of a synchronous network modeled as a directed graph. S has a message that he wishes to send to R; the challenge is to design a protocol such that after exchanging messages as per the protocol, the receiver R should correctly obtain S's message with arbitrarily small error probability δ, in spite of the influence of a Byzantine adversary that may actively corrupt up to t nodes in the network (we denote such a URMT protocol as (t, (1 - δ))-reliable). While it is known that (2t + 1) vertex disjoint directed paths from S to R are necessary and sufficient for (t, 1)-reliable URMT (that is with zero error probability), we prove that a strictly weaker condition, which we define and denote as (2t, t)-special-connectivity, together with just (t+1) vertex disjoint directed paths from S to R, is necessary and sufficient for (t, (1' - δ))-reliable URMT with arbitrarily small (but non-zero) error probability, δ. Thus, we demonstrate the power of randomization in the context of reliable message transmission. In fact, for any positive integer k 0, we show that there always exists a digraph Gk such that (k, 1)-reliable URMT is impossible over Gk whereas there exists a (2k, (1 - δ))-reliable URMT protocol, δ 0 in Gk. In a digraph G on which (t, (1 - δ))-reliable URMT is possible, an edge is called critical if the deletion of that edge renders (t, (1 - δ))-reliable URMT impossible. We give an example of a digraph G on n vertices such that G has Ω(n2) critical edges. This is quite baffling since no such graph exists for the case of perfect reliable message transmission (or equivalently (t, 1)-reliable URMT) or when the underlying graph is undirected. Such is the anomalous behavior of URMT protocols (when "randomness meet directedness") that it makes it extremely hard to design efficient protocols over arbitrary digraphs. However, if URMT is possible between every pair of vertices in the network, then we present efficient protocols for the same.