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RFID technology can potentially be used in many applications. A typical RFID system involves a reader and a number of tags, which may range from the battery-powered tags that have Wi-Fi capabilities, to the low-cost tags that are constrained in computation capacities and hardware resources. Keeping RFID systems secure is crucial since RFID systems are vulnerable to a number of malicious attacks. As for low-cost RFID systems, security problems become much more challenging, because traditional security mechanisms are infeasible to be used on low-cost tags due to their resource constraints. Tag search is an important functionality that a RFID system should provide. In this paper, we study how to secure tag search with a focus on low-cost RFID systems. Existing solutions are mostly based on hash functions and consume 8000 to 10000 gates, however, the low-cost tags can afford at most 2000 gates for secure features. In this paper, we propose several lightweight secure search protocols based on linear feedback shift registers (LFSR) and physically unclonable functions (PUF). Our protocols prevent adversaries from learning tag identity and impersonating RFID reader or tags. Experimental results show that our solutions have hundreds of nanoseconds processing time and require no more than 1400 hardware gates on tags.