Shannon showed that to achieve perfect secrecy in point-to-point communication, the message rate cannot exceed the shared secret key rate giving rise to the simple one-time pad encryption scheme. In this paper, we extend this work from point-to-point to networks. We consider a connected network with pairwise communication between the nodes. We assume that each node is provided with a certain amount of secret bits before communication commences. An eavesdropper with unlimited computing power has access to all communication and can hack a subset of the nodes not known to the rest of the nodes. We investigate the limits on information-theoretic secure communication for this network. We establish a tradeoff between the secure channel rate (for a node pair) and the secure network rate (sum over all node pair rates) and show that perfect secrecy can be achieved if and only if the sum rate of any subset of unhacked channels does not exceed the shared unhacked-secret-bit rate of these channels. We also propose two practical and efficient schemes that achieve a good balance of network and channel rates with perfect secrecy guarantee. This work has a wide range of potential applications for which perfect secrecy is desired, such as cyber-physical systems, distributed-control systems, and ad-hoc networks.

中文翻译：

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网络信息理论安全

Shannon 表明，为了在点对点通信中实现完美的保密，消息速率不能超过共享密钥速率，从而产生了简单的一次性加密方案。在本文中，我们将这项工作从点对点扩展到网络。我们考虑节点之间成对通信的连接网络。我们假设在通信开始之前为每个节点提供了一定数量的秘密位。具有无限计算能力的窃听者可以访问所有通信，并且可以破解其余节点不知道的节点子集。我们调查了该网络信息论安全通信的限制。我们在安全通道速率（对于一个节点对）和安全网络速率（所有节点对速率的总和）之间建立了一个权衡，并表明当且仅当任何未破解通道子集的总速率满足时，才能实现完美保密不超过这些频道的共享未破解秘密比特率。我们还提出了两种实用且高效的方案，以完美的保密保证实现网络和信道速率的良好平衡。这项工作具有广泛的潜在应用，需要完美保密，例如网络物理系统、分布式控制系统和自组织网络。我们还提出了两种实用且高效的方案，以完美的保密保证实现网络和信道速率的良好平衡。这项工作具有广泛的潜在应用，需要完美保密，例如网络物理系统、分布式控制系统和自组织网络。我们还提出了两种实用且高效的方案，以完美的保密保证实现网络和信道速率的良好平衡。这项工作具有广泛的潜在应用，需要完美保密，例如网络物理系统、分布式控制系统和自组织网络。