Fault tolerance in networks of bounded degree
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of 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
Perfectly secure message transmission
Journal of the ACM (JACM)
Reaching Agreement in the Presence of Faults
Journal of the ACM (JACM)
Almost-everywhere secure computation
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
Secure message transmission by public discussion: a brief survey
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
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We consider networks (graphs) that are notfully connected, and where some of the nodes may be corrupted (and thus misbehave in arbitrarily malicious and coordinated ways) by a computationally unbounded adversary. It is well known that some fundamental tasks in information-theoretic security, such as secure communication (perfectly secure message transmission) [4], broadcast (a.k.a. Byzantine agreement) [7], and secure multi-party computation [1,2], are possible if and only the network has very large connectivity--specifically, 茂戮驴(t), where tis an upper bound on the number of corruptions [3,4]. On the other hand, typically in practical networks most nodes have a small degree, independent of the size of the network; thus, it is unavoidable that some of the nodes will be unable to perform the required task.The notion of computation in such settings was introduced in [5], where achieving Byzantine agreement with a low number of exceptions on several classes of graphs was considered, and more recently studied in [6,8] with regards to secure multi-party computation.In this talk we review several protocols for the above tasks, and point out some interesting problems for future research.