Secure (Multiple) Key-Cast over Networks: Multiple Eavesdropping Nodes

2026-05-12

AI Summary

This study addresses the problem of securely distributing distinct keys from a source node to a designated subset of terminals in a noiseless network, under the threat that up to ℓ nodes—including the source—may be eavesdropped. Leveraging the network’s d-vertex connectivity and integrating graph-theoretic vertex connectivity analysis with information-theoretic security and network coding techniques, the work establishes—for the first time in a multi-eavesdropper setting—that a secure key rate of d−ℓ is both achievable and optimal when the network satisfies d-vertex connectivity. The result is further extended to partially connected networks and multi-source scenarios, demonstrating that capacity-achieving secure key distribution remains feasible even when eavesdroppers observe all but one of the source nodes.

Abstract

We study the secure multiple key-cast problem over noiseless networks under node-based eavesdroppers, where one or more source nodes participate in the generation of distinct secret keys to be shared among designated terminal subsets, while an eavesdropper observing up to $\ell$ nodes, including possibly source nodes, obtains no information about the keys. For the single-source setting, we first consider networks in which every node is $d$-vertex connected from the source. We show that a secure key rate of $d-\ell$ is achievable for all such networks. We further show that this rate is optimal by exhibiting $d$-vertex-connected networks whose secure key-cast capacity is at most $d-\ell$. We next study networks in which only the terminal nodes are $d$-vertex connected from the source, while other network nodes may not satisfy this connectivity condition and may be partially-connected. We show that secure multiple key-cast remains achievable in the presence of such partially-connected nodes, and derive coding schemes whose rate depends on the minimum network vertex-connectivity from the source and certain additional network properties. Finally, we generalize these results, for both $d$-vertex-connected networks and networks containing partially-connected nodes, to the multi-source setting; showing that secure multiple key-cast remains achievable even when the eavesdropper may observe all but one of the source nodes.

Problem

• secure key-cast
• multiple eavesdropping nodes
• network security
• secret key generation
• vertex connectivity

Innovation

• secure key-cast
• vertex connectivity
• network coding
• multiple sources
• eavesdropping nodes