A fundamental problem in decentralized networked systems is to coordinate actions of different agents so that they reach a state of agreement. In such applications, it is additionally desirable that the actions at various nodes may not be anticipated by malicious eavesdroppers. Motivated by this, we investigate the problem of secure multi-terminal strong coordination aided by a multiple-access wiretap channel. In this setup, independent and identically distributed copies of correlated sources are observed by two transmitters who encode the channel inputs to the MAC-WT. The legitimate receiver observing the channel output and side information correlated with the sources must produce approximately i.i.d. copies of an output variable jointly distributed with the sources. Furthermore, we demand that an external eavesdropper learns essentially nothin g about the sources and the simulated output sequence by observing its own MAC-WT output. This setting is aided by the presence of independent pairwise shared randomness between each encoder and the legitimate decoder, that is unavailable to the eavesdropper. We derive an achievable rate region based on a combination of coordination coding and wiretap coding, along with an outer bound. The inner bound is shown to be tight and a complete characterization is derived for the special case when the sources are conditionally independent given the decoder side information and the legitimate channel is composed of deterministic links. Further, we also analyze a more general scenario with possible encoder cooperation, where one of the encoders can non-causally crib from the other encoders input, for which an achievable rate region is proposed. We then explicitly compute the rate regions for an example both with and without cribbing between the encoders, and demonstrate that cribbing strictly improves upon the achievable rate region.

翻译：在去中心化网络系统中，一个基本问题是如何协调不同智能体的行为以达成一致状态。在此类应用中，通常还期望各节点的行为不会被恶意窃听者预判。受此启发，我们研究了借助多接入窃听信道实现安全多终端强协调的问题。在此设置中，两个发送端观测到相关源的独立同分布副本，并将信道输入编码至MAC-WT。合法接收端通过观测信道输出以及与源相关的边信息，必须生成与源联合分布的输出变量的近似独立同分布副本。此外，我们要求外部窃听者通过观测其自身的MAC-WT输出，本质上无法获知源及仿真输出序列的任何信息。该设置得益于每个编码器与合法解码器之间存在独立的成对共享随机性，而窃听者无法获取该随机性。我们基于协调编码与窃听编码的组合推导出可达速率区域及外边界。证明内边界是紧致的，并在源给定解码器边信息条件下条件独立且合法信道由确定性链路组成的特殊情况下，给出了完整的表征。此外，我们还分析了编码器间可能存在协作的更一般场景，其中一个编码器可以非因果地窃取其他编码器的输入，并为此提出了可达速率区域。随后，我们通过实例分别计算了编码器间存在与不存在窃取机制时的速率区域，并证明窃取机制能严格改善可达速率区域。