With the rapid development of network technology and terminal devices, we have entered a digital age, where data generation and exchange have become the core of modern society. In this context, green computing and communication issues are becoming increasingly important. Traditional key management methods have some issues, including centralization risks, high energy consumption, and complex management processes. These problems are contrary to the principles of green computing and communication. The introduction of blockchain and group key technologies provides an innovative approach to solving these issues. Firstly, blockchain utilizes a decentralized distributed ledger that disperses key management tasks to multiple nodes within the network. This reduces centralization risks and enhances the security and trustworthiness of the system. Additionally, blockchain transaction records are tamper-resistant, ensuring transparency and traceability in data exchange. Moreover, blockchain-based group key management methods help reduce the need for centralized servers, thus decreasing energy consumption and aligning with the principles of green computing. In this context, this paper proposes a blockchain-based group key management method for edge device transactions. This method constructs groups based on the inherent attributes of edge device nodes, and effectively reduces the system overhead caused by rederiving new keys due to node additions or removals within the group, as well as the key transmission between nodes. The paper first utilized OpenEthereum to build a blockchain network for testing the proposed group key management algorithm, thus demonstrating the scalability of the proposed solution.