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The prevalence of Radio Frequency Identification (RFID) technology requires Privacy-Preserving Authentication (PPA) protocols to combat the privacy leakage during authentication. Existing PPA protocols employ the per-tag authentication, in which the reader has to sequentially authenticate the tags within the detecting region. Such a processing pattern becomes a bottleneck in current RFID enabled systems, especially for batch-type processing applications. In this paper, we propose an efficient authentication protocol, which leverages the collaboration among multiple tags for accelerating the authentication speed. We also find that the collision, usually considered as a negative factor, is a helpful media to enable collaborative authentication among tags. Our protocol, termed as Multiple-tags privacy-preserving Authentication Protocol (MAP), authenticates a batch of tags concurrently with strong privacy protection and high efficiency guarantee. The analytical and simulation results show that the efficiency of MAP is better than O(logN) and asymptotically approaches O(1).