The type of centralized group key establishment protocols is the most commonly used one due to its efficiency in computation and communication. A key generation center (KGC) in this type of protocols acts as a server to register users initially. Since the KGC selects a group key for group communication, all users must trust the KGC. Needing a mutually trusted KGC can cause problem in some applications. For example, users in a social network cannot trust the network server to select a group key for a secure group communication. In this paper, we remove the need of a mutually trusted KGC by assu...