Partially Connected Networks: Information Theoretically Secure Protocols and Open Problems (Invited Talk)

Abstract

We consider networks (graphs) that are not fully 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, Ω(t), where t is 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.