Completeness theorems for non-cryptographic fault-tolerant distributed computation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Perfectly secure message transmission
Journal of the ACM (JACM)
Asynchronous secure computation
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Impossibility of distributed consensus with one faulty process
Journal of the ACM (JACM)
The Byzantine Generals Problem
ACM Transactions on Programming Languages and Systems (TOPLAS)
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
Constant phase efficient protocols for secure message transmission in directed networks
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Unconditionally reliable message transmission in directed networks
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Unconditionally Reliable and Secure Message Transmission in Directed Networks Revisited
SCN '08 Proceedings of the 6th international conference on Security and Cryptography for Networks
On Minimal Connectivity Requirement for Secure Message Transmission in Asynchronous Networks
ICDCN '09 Proceedings of the 10th International Conference on Distributed Computing and Networking
Cryptanalysis of secure message transmission protocols with feedback
ICITS'09 Proceedings of the 4th international conference on Information theoretic security
Brief announcement: synchronous Las Vegas URMT iff asynchronous Monte Carlo URMT
DISC'10 Proceedings of the 24th international conference on Distributed computing
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Reliable message transmission is a fundamental problem in distributed communication networks. Of late, several interesting results have been obtained by modelling the network as a directed graph. An important result among them was due to Bhavani et al. [Unconditionally reliable message transmission in directed networks, 18 in: SODA'08: Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, Philadelphia, PA, USA, 2008, pp. 1048-1055], where it was shown that if a negligible probability of error is allowed, the connectivity required in a synchronous network for unconditionally reliable message transmission (URMT) is significantly reduced. We refer to the variant of URMT studied by them as Monte Carlo URMT; here the receiver is allowed to output an incorrect message with small probability. Another interesting variant which has received little attention so far in the literature is the Las Vegas variant, where the receiver is allowed to abort with a small probability, but never to output an incorrect message. We show that the minimum connectivity requirements for the existence of Las Vegas URMT protocols over synchronous networks are the same as that of Monte Carlo URMT protocols over asynchronous networks-a surprising equivalence between two very different models. Furthermore, we show that the higher connectivity requirements of Las Vegas URMT over asynchronous networks match exactly with that of zero-error (perfect) variant over (a)synchronous networks. We also show that there exists a family of graphs where in the number of critical edges for the 'easier' randomized variants are asymptotically higher than that for the perfect variants. Hence, our results demonstrate an interesting interplay between (im)perfectness, synchrony and connectivity for the case of reliable message transmission.