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To identify a mobile station (MS) and validate legal service requests, authentication functions are utilized in the location registration, call origination and call termination procedures. In GSM, the VLR requests the HLR for assistance in authenticating the visiting user. The authentication center (AuC) in the home network generates 3-tuples and sends them back to the VLR for subsequent authentications during the user’s residence. If these 3-tuples are used up before the MS’s leaving, another request is issued by the VLR. The request is expensive, because it needs to access the HLR/AuC. Traditionally, a fixed-K strategy is used. That is, K 3-tuples are sent to the VLR for each request. Lager K is preferred to reduce the number of the expensive requests for 3-tuples. However, much waste of 3-tuples is observed, especially when an inactive user is considered. Hence, K value should be determined based on the usage pattern of the user. We propose a dynamic-K (DK) strategy to reduce the waste and diminish the signaling traffic for authentication. Simulation results show that the DK strategy can effectively determine the appropriate K value. Not only the waste but also the number of requests are diminished efficiently.