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.
翻译:由 Langberg 和 Effros 推出的无噪音网络的多播关键传播问题[ITW 2022] 由 Langberg 和 Effros 介绍的多播关键传播问题由无噪音网络[ITW 2022] 提出,这里称为“ 密播” 问题, 捕捉了在特定网络上传播一组终端的共享秘密随机密钥的任务。 与传统通信不同, 信息必须从源传到目的地, 关键播送必须保持不变, 因为关键播送不需要在目的地节点进行源重建。 例如, 分布密钥可以是来源的混合来源, 来源本身可能无法恢复。 手头的工作考虑的是单一源、 多个多播的网络编码设置的关键传播问题, 即“ 多发密钥” 问题。 这里, 不同的密钥将同时从单一来源传到多个终端, 每个多播报的共享的密钥。 设想包括安全设置, 只有源和预定的目的地才能获得关于某个钥匙的信息; 以及非安全设置的唯一要求是, 一个密钥的知识不会揭示另一个信息。 在两种设置中, 我们对一个安全的设置进行更精确的配置中, 将一个关键的基路路段的更新, 与前的基路路段 将比 将比 将一个主端的校比 进行前的校比 。