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We explain the authentication and key agreement protocols for third-generation (3G) wireless communications. This protocol is known as 3GPP-AKA. We show this protocol is vulnerable to false base station attacks, and therefore, it needs synchronization between MS (mobile station) and HN (home network) that increases the complexity of system. Then, we analyze two techniques which are called adaptive protocol for AKA and extension of AKA. Any of these techniques eliminate some of the weaknesses of 3GPP-AKA. We combine these two techniques and propose a new technique, called improved adaptive protocol for AKA (IAP-AKA). We show this technique can be a good successor for 3GPP-AKA by eliminating synchronization, bandwidth wastage, and vulnerability to false base station attacks.