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This paper firstly puts forward a two dimensional interworking authentication model between 3GPP and WiMAX. In the proposed model, EAP-AKA method is adopted, and the first registered 3GPP AAA server in home domain (i.e. HPLMN, Home Public Land Mobile Network) takes charge of the responsibility of authentication for 3GPP/WiMAX UE by using authentication vectors (AV) obtained from HSS (Home Subscriber Server). Furthermore, a dynamic periodic distributing scheme for AVs is brought forward. Meanwhile, an improved authentication protocol based on EAP-AKA (EAPIAKA) is proposed, and the relative security analysis is given as well. By using of the scheme, it is unnecessary to retrieve new Avs from HSS, if there are still unused AVs for the previous PLMN, when the 3GPP/WiMAX UE leaves and reenters the same PLMN within its available period of critical period interval (CPI). Finally, the simulation results prove that a long CPI results in fewer accesses to the HSS, and only through adjusting the CPI period dynamically in accordance with the system parameters, the signaling cost can be reduced further.