Assuring the security of the communication channel is a significant issue in the fog networks. Designing an efficient and secure key management scheme with a common key among nodes is a critical factor. The available key distribution schemes of hierarchical networks are not scalable and impose high communication and computation overhead to networks. These schemes are impractical on limited resources’ environments like the internet of things (IoT) networks. In this paper, a hierarchical key pre-distribution scheme based on the transversal design and residual theorem (TD-R) is proposed for large mobile fog networks with multi-clouds. The objective of this paper to reveal that TD-R is the key pre-distribution scheme for establishing secure intra and inter-fog nodes’ communication channels and intra and inter-end nodes with moderate network connectivity. The obtained results indicate that the TD-R scheme increases network scalability in comparison with available schemes, while it decreases memory consumption and node storage overhead.

在雾网络中，确保通信通道的安全性是一个重要问题。设计具有节点间公共密钥的高效且安全的密钥管理方案是关键因素。分层网络的可用密钥分发方案不可扩展，并且给网络带来了很高的通信和计算开销。这些方案在物联网（IoT）网络等有限资源的环境中不切实际。本文提出了一种基于横向设计和残差定理（TD-R）的层次化密钥预分配方案，用于大型多云的移动雾网络。本文旨在揭示TD-R是建立安全的内部和内部雾节点的通信通道以及具有中等网络连通性的内部和内部节点的关键预分配方案。获得的结果表明，与可用方案相比，TD-R方案增加了网络可伸缩性，同时减少了内存消耗和节点存储开销。