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It is necessary to authenticate users who attempt to access resources in Wireless Local Area Networks (WLANs). Extensible Authentication Protocol (EAP) is an authentication framework widely used in WLANs. Authentication mechanisms built on EAP are called EAP methods. The requirements for EAP methods in WLAN authentication have been defined in RFC 4017. To achieve user efficiency and robust security, lightweight computation and forward secrecy, excluded in RFC 4017, are desired in WLAN authentication. However, all EAP methods and authentication protocols designed for WLANs so far do not satisfy all of the above properties. This manuscript will present a complete EAP method that utilizes stored secrets and passwords to verify users so that it can 1) fully meet the requirements of RFC 4017, 2) provide for lightweight computation, and 3) allow for forward secrecy. In addition, we also demonstrate the security of our proposed EAP method with formal proofs.