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Recently, several authentication protocols have been proposed for wireless local area networks (WLANs) to improve security in hotspot public access and corporate networks, and some have been proposed for integrated 3G-WLAN networks. These authentication protocols are based on the extensible authentication protocol and have been directly applied to wireless networks based on their widespread use in wired networks. Depending on the 3G-WLAN architecture and how the WLAN is tied to the 3G network, these protocols could have large latency. Moreover, they do not have mechanisms for authenticating the usage time of a mobile in a WLAN. We first discuss these issues related to existing authentication protocols for a 3G-WLAN integrated network. Then, we propose a new authentication mechanism based on the dual signature concept used in secure electronic transactions that can be used in a loosely coupled architecture. Finally, we present a preliminary evaluation of the energy performance and latency of the existing and proposed protocols.