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The issue of security in fog has several challenges and one of which is to create a secure channel that connects fog layer to the end devices. Therefore, efficient and secure key distribution is very important to create this channel. One solution is key pre-distribute that the keys generation and distribution between nodes are before the network establishment. This article presents an algorithm for key pre-distribution in fog networks that focuses on the relationship between end devices and the fog layer. The proposed scheme is a hybrid scheme that uses the K-MEANS algorithm for nodes hierarchical clustering. Then the residual design is used to generate the key chain and BIBD design is used for key pre-distribution in headers. The proposed method is completely independent of the mobility model of and its communication and computation overheads are of the order of O(q). Also, the network connectivity is above 0.8 and close to the BIBD design, which is a fully connected KPS, and the probability of capturing the entire network in case of capturing the nodes is almost equal to 0. In the proposed method for a network with size N, the size of the key chain is N 4. [ABSTRACT FROM AUTHOR]