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The objective of private authentication for Radio Frequency Identification (RFID) systems is to allow valid readers to explicitly authenticate their dominated tags without leaking the private information of tags. In previous designs, the RFID tags issue encrypted authentication messages to the RFID reader, and the reader searches the key space to identify the tags. Without key updating, those schemes are vulnerable to many active attacks, especially the compromising attack. We propose a strong and lightweight RFID private authentication protocol, SPA. By designing a novel key updating method, we achieve the forward secrecy in SPA with an efficient key search algorithm. We also show that, compared with existing designs, (SPA) is able to effectively defend against both passive and active attacks, including compromising attacks. Through prototype implementation, we demonstrate that SPA is practical and scalable for current RFID infrastructures. [ABSTRACT FROM AUTHOR]