With the rapid development of the ubiquitous power Internet of Things, the trustworthiness and security of its network transmission have become the basic premise for its application in key fields. However, most of the existing solutions are not suitable for the ubiquitous power IoT environment. In this paper, a group key encryption algorithm is proposed under the framework of distributed key management and edge computing. This algorithm builds the group by using the node group construction algorithm based on the same topic, and reduces the re-derivation and new generation with the increase or decrease of nodes in the group by using algorithms such as the key distribution algorithm based on group key management. The key and the system overhead required to transfer the key between nodes, the key generation node does not need to establish a communication link with all IoT nodes. This paper also evaluates the performance indicators of the scheme, and finally proves that the key management algorithm proposed in this paper can improve device performance and reduce power consumption, and is suitable for various environments of ubiquitous power Internet of Things.