Completeness theorems for non-cryptographic fault-tolerant distributed computation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Multiparty unconditionally secure protocols
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Perfectly secure message transmission
Journal of the ACM (JACM)
Secure hypergraphs: privacy from partial broadcast
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Fault-tolerant Computation in the Full Information Model
SIAM Journal on Computing
On perfectly secure communication over arbitrary networks
Proceedings of the twenty-first annual symposium on Principles of distributed computing
Perfectly Secure Message Transmission Revisited
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Secure communication in broadcast channels: the answer to Franklin and Wright's question
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Cryptanalysis of secure message transmission protocols with feedback
ICITS'09 Proceedings of the 4th international conference on Information theoretic security
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Perfectly Secure Message Transmission Revisited
IEEE Transactions on Information Theory
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In this paper we solve the problem of secure communication in multicast graphs, which has been open for over a decade. At Eurocrypt '98, Franklin and Wright initiated the study of secure communication against a Byzantine adversary on multicast channels in a neighbor network setting. Their model requires node-disjoint and neighbor-disjoint paths between a sender and a receiver. This requirement is too strong and hence not necessary in the general multicast graph setting. The research to find the lower and upper bounds on network connectivity for secure communication in multicast graphs has been carried out ever since. However, up until this day, there is no tight bound found for any level of security. We study this problem from a new direction, i.e., we find the necessary and sufficient conditions (tight lower and upper bounds) for secure communication in the general adversary model with adversary structures, and then apply the results to the threshold model. Our solution uses an extended characterization of the multicast graphs, which is based on our observation on the eavesdropping and separating activities of the Byzantine adversary.