At present, the Universal Mobile Telecommunications System (UMTS) is very popular in most parts of the world. It is a third-generation mobile communication technique known for its ability to conduct user authentication and for its security of communication with the use of Authentication and Key Agreement (AKA) protocol. A mobile station (MS), a service network (SN) and a home environment (HE) use the protocol to authenticate each other and make an agreement with a session key. With the UMTS-AKA protocol standard, all authentication vectors (AV) produced by the HE are transferred to the SN for mutual authentication with the MS. In this scenario, authentication is exposed to two kinds of defects. One defect is computational overhead concentrating on the HE and the other is the communication overhead for delivering the AVs. To overcome these congenital defects, this study proposes a unique UMTS-AKA protocol called the cocktail-AKA protocol. The goal of this protocol is to allow the SN to share some medicated authentication vectors (MAV) that are calculated in advance and combined with a prescription at the authentication stage. So, the HE only needs to produce a prescription authentication vector (PAV). Once the authentication stage is initiated, the SN distributes MAV and PAV and produces an effective AV for mutual authentication with the MS. The cocktail-AKA protocol can overcome both the aforesaid defects.