Radio　frequency　identification　(RFID)　system　is　a　contactless　automatic　identification　system,　which　uses　small　and　low　cost　RFID　tags.　The　primary　problem　of　current　security　and　privacy　preserving　schemes　is　that,　in　order　to　identify　only　one　single　tag,　these　schemes　require　a　linear　computational　complexity　on　the　server　side.　We　propose　an　efficient　mutual　authentication　protocol　for　passive　RFID　tags　that　provides　confidentiality,　untraceability,　mutual　authentication,　and　efficiency.　The　proposed　protocol　shifts　the　heavy　burden　of　asymmetric　encryption　and　decryption　operations　on　the　more　powerful　server　side　and　only　leaves　lightweight　hash　operation　on　tag　side.　It　is　also　efficient　in　terms　of　time　complexity,　space　complexity,　and　communication　cost,　which　are　very　important　for　practical　large-scale　RFID　applications.　©　2012　Institute　of　Automation,　Chinese　Academy　of　Sciences　and　Springer-Verlag　Berlin　Heidelberg.