Secure (Multiple) Key-Cast over Networks: Multiple Eavesdropping Nodes
This work provides fundamental limits and achievable schemes for secure key distribution in networks, addressing a key problem in information-theoretic security for network communications.
The paper studies secure multiple key-cast over noiseless networks with node-based eavesdroppers, deriving achievable secure key rates and capacity bounds. For d-vertex-connected networks, they show a secure key rate of d-ℓ is achievable and optimal, and extend results to networks with partially-connected nodes and multi-source settings.
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.