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In this paper we present a novel approach to authentication and privacy in RFID systems based on the minimum disclosure property and in conformance to EPC Class-1 Gen-2 specifications. We take into account the computational constraints of EPC Class-1 Gen-2 passive RFID tags and only the cyclic redundancy check (CRC) and pseudo random number generator (PRNG) functions that passive RFID tags are capable of are employed. Detailed security analysis of our scheme shows that it can offer robust security properties in terms of tag anonymity and tag untraceability while at the same time being robust to replay, tag impersonation and desynchronisation attacks. Simulations results are also presented to study the scalability of the proposed scheme and its impact on authentication delay.