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Cardinality estimation and tag authentication are two major issues in large-scale Radio Frequency Identification (RFID) systems. While there exist both per-tag and probabilistic approaches for the cardinality estimation, the RFID-oriented authentication protocols are mainly per-tag based: the reader authenticates one tag at each time. For a batch of tags, current RFID systems have to identify them and then authenticate each tag sequentially, incurring large volume of authentication data and huge communication cost. We study the RFID batch authentication issue and propose the first probabilistic approach, termed as Single Echo based Batch Authentication (SEBA), to meet the requirement of prompt and reliable batch authentications in large scale RFID applications, e.g., the anti-counterfeiting solution. Without the need of identifying tags, SEBA provides a provable probabilistic guarantee that the percentage of potential counterfeit products is under the user-defined threshold. The experimental result demonstrates the effectiveness of SEBA in fast batch authentications and significant improvement compared to existing approaches.