Easy impossibility proofs for distributed consensus problems
Distributed Computing
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
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
A zero-one law for Boolean privacy
SIAM Journal on Discrete Mathematics
Fault-tolerant computation in the full information model (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Privacy and communication complexity
SIAM Journal on Discrete Mathematics
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
On perfectly secure communication over arbitrary networks
Proceedings of the twenty-first annual symposium on Principles of distributed computing
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
CRYPTO '91 Proceedings of the 11th 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
Brief announcement: efficient perfectly secure communication over synchronous networks
Proceedings of the twenty-second annual symposium on Principles of distributed computing
Efficient reliable communication over partially authenticated networks
Distributed Computing - Special issue: PODC 02
Weakly-private secret sharing schemes
TCC'07 Proceedings of the 4th conference on Theory of cryptography
Practical private information aggregation in large networks
NordSec'10 Proceedings of the 15th Nordic conference on Information Security Technology for Applications
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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 party 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 function (in the information theoretic sense). The question we address in this paper is what functions can be privately computed in a given incomplete network. Every function can be privately computed in two-connected networks with at least three parties. Thus, the question is interesting only for non two-connected networks. Generalizing results of (Bläser et al. in J. Cryptol, 19(3):341-357, 2006), we characterize the functions that can be computed privately in simple networks--networks with one separating vertex and no leaves. We then deal with private computations in arbitrary non two-connected networks: we reduce this question to private computations of related functions on trees, and give some sufficient conditions and necessary conditions on the functions that can be privately computed on trees.