网络上的多密钥传送
Multiple Key-cast over Networks
摘要：
由Langberg和Effros [ITW 2022]引入的无噪声网络上的多播密钥传播问题，在这里称为“密钥投射”问题，捕获了在给定网络上向一组终端传播共享秘密随机密钥的任务。与传统的通信不同，其中消息必须从源传递到目的地（一个或多个）不变，键投射更灵活，因为键投射不需要在目的地节点处进行源重构。例如，分布式密钥可以是源本身可能不可恢复的源的混合。手头的工作考虑单源、多播网络编码设置中的密钥分发，即，“多键投射”问题。这里，不同的密钥将同时从单个源节点发送到多个终端集合，每个多播集合一个共享随机密钥。方案包括安全设置，其中只有源和预定目的地获得关于给定密钥的信息;和非安全设置，其中唯一的要求是一个密钥的知识不会泄露关于另一个密钥的信息。在这两种情况下，我们提出了组合条件的密钥分发和设计相应的多个密钥投方案。此外，我们还比较了有无信源重构限制下的多密钥投射率，前者对应于传统的通信形式，当信源重构放松时，密钥投射在速率上具有严格的优势。
英文摘要：
The multicast key-dissemination problem over noiseless networks, introduced by Langberg and Effros [ITW 2022], here called the ``key-cast'' problem, captures the task of disseminating a shared secret random key to a set of terminals over a given network. Unlike traditional communication, where messages must be delivered from source to destination(s) unchanged, key-cast is more flexible since key-cast need not require source reconstruction at destination nodes. For example, the distributed keys can be mixtures of sources from which the sources themselves may be unrecoverable. The work at hand considers key dissemination in the single-source, multiple-multicast network coding setting, i.e., the ``multiple key-cast'' problem. Here, distinct keys are to be simultaneously transmitted from a single source node to multiple terminal sets, one shared random key per multicast set. Scenarios include the secure setting, in which only the source and intended destinations gain information about a given key; and the non-secure setting in which the only requirement is that the knowledge of one key does not reveal information about another. In both settings, we present combinatorial conditions for key dissemination and design corresponding multiple key-cast schemes. In addition, we compare the multiple key-cast rate with and without the restriction of source reconstruction, the former corresponding to traditional forms of communication; key-cast achieves a strict advantage in rate when source reconstruction is relaxed.
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