Easy impossibility proofs for distributed consensus problems
Distributed Computing
Fault tolerance in networks of bounded degree
SIAM Journal on Computing
Verifiable secret sharing and multiparty protocols with honest majority
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Fault-tolerant computation in the full information model (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Perfectly secure message transmission
Journal of the ACM (JACM)
Tolerating a linear number of faults in networks of bounded degree
Information and Computation
Secure hypergraphs: privacy from partial broadcast
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Efficient perfectly secure message transmission in synchronous networks
Information and Computation
Reliable communication over partially authenticated networks
Theoretical Computer Science
Distributed Algorithms
Graph Algorithms
Perfectly Secure Message Transmission Revisited
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Reliable broadcast in unknown fixed-identity networks
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Efficient reliable communication over partially authenticated networks
Distributed Computing - Special issue: PODC 02
On private computation in incomplete networks
SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
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Reliable communication between parties in a network is a basic requirement for executing any protocol. Dolev [4] and Dolev et al. [5] showed that reliable communication is possible if and only if the communication network is sufficiently connected. Beimel and Franklin [1] showed that the connectivity requirement can be relaxed if some pairs of parties share authentication keys. That is, costly communication links can be replaced by authentication keys.In this work, we continue this line of research. We consider the scenario where there is a speciiic sender and a specific receiver. In this case, the protocol of [1] has no(n) rounds even if there is a single Byzantine processor. We present a more efficient protocol with round complexity of (n/t)o(t), where n is the number of processors in the network and t is an upper bound on the number of Byzantine processors in the network. Specifically, our protocol is polynomial when the number of Byzantine processors is O(1), and for every t its round complexity is bounded by 2O(n). The same improvements hold for reliable and private communication. The improved protocol is obtained by analyzing the properties of a "communication and authentication graph" that characterizes reliable communication.