In this paper, we propose a novel radio frequency identification (RFID) infrastructure enabling multi-purpose RFID tags realized by the use of privacy preserving public key cryptography (PKC) architecture. The infrastructure ensures that the access rights of the tags are preserved based on the spatial and temporal information collected from the RFID readers. We demonstrate that the proposed scheme is secure with respect to cryptanalytic, impersonation, tracking, replay, and relay attacks. We also analyze the feasibility of PKC implementation on passive class 2 RFID tags, and show that the requirements for PKC are comparable to those of other cryptographic implementations based on symmetric ciphers. Our numerical results indicate PKC based systems can outperform symmetric cipher based systems, since the back end servers can identify RFID tags with PKC based systems approximately 57 times faster than the best symmetric cipher based systems.