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.

翻译：我们研究了无噪声网络中基于节点窃听者的安全多密钥分发问题，其中一个或多个源节点参与生成不同的秘密密钥，并分发给指定的终端子集，而窃听者最多可观测ℓ个节点（可能包括源节点），但无法获取任何密钥信息。针对单源场景，我们首先考虑所有节点与源节点均满足d-顶点连通性的网络，证明所有此类网络可实现d-ℓ的安全密钥速率，并通过构造d-顶点连通网络（其安全密钥分发容量至多为d-ℓ）证明该速率的优化性。随后研究仅终端节点与源节点满足d-顶点连通性、而其他网络节点可能不满足该条件且部分连通的情况，证明存在部分连通节点时仍可实现安全多密钥分发，并推导出编码方案，其速率取决于源节点的最小网络顶点连通度及特定网络属性。最后，我们将这些结论（针对d-顶点连通网络及包含部分连通节点的网络）推广至多源场景，证明即使窃听者可能观测所有（除一个源节点外）源节点，安全多密钥分发仍可实现。