With wide applications of the radio frequency identification (RFID) technology in areas such as the supply chain, warehouse management, and so on, the privacy and security of RFID gradually become one of the hot topics. RFID privacy and security authentication protocols have been proposed to suit different scenarios. In 2014, the Alert Response Address (ARA) protocol based on the application scenario of a privileged membership club was presented, the formal definition of its privacy and security models was described, and the tag and reader's privacy were preserved. In this study, we analyze the efficiency of the ARA scheme and find that it is not very good because the scheme overuses bilinear maps. Under the premise of without losing the ARA scheme's privacy and security, we improve its two subprotocols, IARA1 and IARA2, with higher performance in the ARA protocol. The results show that the improved protocol is more efficient than the ARA protocol through the performance comparison of the protocols.