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A group key exchange protocol is a cryptographic primitive that describes how a group of parties communicating over a public network can come up with a common secret key. Due to its significance both in network security and cryptography, the design of secure and efficient group key exchange protocols has attracted many researchers' attention over the years. However, despite all the efforts undertaken, there seems to have been no previous systematic look at the growing problem of key exchange over combined wired and wireless networks which consist of both stationary computers with sufficient computational capabilities and mobile devices with relatively restricted computing resources. In this paper, we present the first group key exchange protocol that is specifically designed to be well suited for this rapidly expanding network environment. Our construction meets simplicity, efficiency, and strong notions of security.