We propose a novel RFID infrastructure design, which foresees the usage of a single RFID tag within different contexts and for multiple purposes. We show that an infrastructure for multi-purpose RFID tags to be used in different contexts can be implemented in a privacy-preserving manner. We address security attacks such as impersonation, tracking, and replay. We also introduce spatio-temporal attacks as an important threat against privacy. We propose a methodology to thwart or alleviate these kinds of attacks. We develop our multi-context RFID infrastructure relying on usage of public key cryptography (PKC), which presents more scalable solutions in the sense that the backend servers can identify the tags 75 times faster than best symmetric cipher based systems when there are a million tags in the system. We demonstrate that the requirements for PKC are comparable to those for other cryptographic implementations based on symmetric ciphers proposed for RFID use