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In the architecture of GSM-WLAN interworking, there are drawbacks related to authentication efficiency for processing loads in the RADIUS server. Therefore, this paper presents two authentication schemes, based on the EAP-SIM mechanism, to improve the authentication efficiency by balancing the processing loads among the RADIUS server and APs. The performance evaluation on the average authentication session time and the processing time for the conventional EAP-SIM authentication schemes and the proposed authentication schemes shows the efficiency improvement of the proposed schemes. It can save about 19% authentication processing time for the proposed full authentication, and about 75% authentication processing time for the proposed iterative fast authentication scheme.