Characterizing positive-rate key-cast (and multicast network coding) with eavesdropping nodes

TL;DR

This paper analyzes the conditions under which secure key dissemination is possible in network coding scenarios with eavesdropping nodes, providing combinatorial characterizations for positive-rate secure multicast and key-cast.

Contribution

It introduces two combinatorial characterizations for networks supporting positive-rate secure key-cast and multicast under eavesdropping constraints, advancing understanding of secure network coding.

Findings

Characterizes networks supporting positive-rate secure key-cast.

Provides combinatorial criteria for secure multicast capacity.

Addresses open problems in secure network coding theory.

Abstract

In multi-source multi-terminal key-dissemination, here called ``key-cast,'' introduced by the authors in [ITW2022], network nodes hold independent random bits, and one seeks a communication scheme that allows all terminal nodes to share a secret key K. The work at hand addresses positive (albeit, arbitrarily small) rate key-cast under the security requirement that no single non-terminal network node can gain information about the shared key K; this scenario is useful in cryptographic settings. Specifically, key-dissemination protocols based on secure multicast network coding are designed. The analysis presented yields two combinatorial characterizations. In each, we assume a network in which an eavesdropper may access any individual network node. The first characterization captures all networks that support positive-rate secure multicast; computing the secure-multicast capacity in the setting studied is a known open problem. The second characterizes all networks that support positive-rate secure key-cast.