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The radio frequency identification (RFID) technology is expected to play a vital role in identifying objects and serving to prevent counterfeiting and fraud. The use of RFID tags may cause privacy violation of users carrying an RFID tag. Owing to the unique identification number of the RFID tag, the possible privacy threats are information leakage of a tag, traceability of the consumer, denial of service attack and impersonation of a tag. Owing to the large number of tags in any application individual secret value for each tag requires a large number of complex hash computations in the database side. To reduce the computation overhead many protocols use a group secret value for tags in the database side. This study proposes a new authentication protocol which provides privacy and security in a more efficient manner using individual secret values for each tag and also avoids many complex hash operations in the database side. The evaluation indicates that the proposed protocol requires a low storage, computation and communication cost but offers larger ranges of privacy and security protection.