Secure (Multiple) Key-Cast over Networks: Multiple Eavesdropping 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 ℓ 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−ℓ 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−ℓ. 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.
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BibTeX
@misc{sayyari2026secure,
title = {{Secure (Multiple) Key-Cast over Networks: Multiple Eavesdropping Nodes}},
author = {Reza Sayyari and Michael Langberg},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.12209},
eprint = {2605.12209},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.12209},
}
RIS
TY - UNPB
TI - Secure (Multiple) Key-Cast over Networks: Multiple Eavesdropping Nodes
AU - Reza Sayyari
AU - Michael Langberg
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2605.12209
UR - https://arxiv.org/abs/2605.12209
AB - 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 ℓ 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−ℓ 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−ℓ. 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.
ER -