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SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
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Perfectly secure message transmission
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Secure hypergraphs: privacy from partial broadcast
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Efficient perfectly secure message transmission in synchronous networks
Information and Computation
Reliable communication over partially authenticated networks
Theoretical Computer Science
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On perfectly secure communication over arbitrary networks
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Private Computations in Networks: Topology versus Randomness
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Private Computation - k-Connected versus 1-Connected Networks
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Perfectly Secure Message Transmission Revisited
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Efficient reliable communication over partially authenticated networks
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Brief announcement: efficient perfectly secure communication over synchronous networks
Proceedings of the twenty-second annual symposium on Principles of distributed computing
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
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Suppose that some parties are connected by an incomplete network of reliable and private channels. The parties cooperate to execute some protocol. However, the parties are curious – after the protocol terminates each processor tries to learn information from the communication it heard. We say that a function can be computed privately in a network if there is a protocol in which each processor learns only the information implied by its input and the output of the protocol. The question we address in this paper is what functions can be computed privately in a given incomplete network. It is known that if a network is 2-connected then every pair of parties can communicate privately. Thus, the question is interesting only for non-2-connected networks. We first characterize the functions that can be computed privately in simple networks – networks with one separating vertex and two 2-connected components. We then deal with private computations in arbitrary networks: we reduce this question to private computations of related functions on trees, and give sufficient and necessary conditions on the functions that can be computed privately on trees.