Abstract: Secure and private authentication protocolis important in Radio Frequency Identification( RFID) technology． To date，researchers haveproposed many RFID authentication protocols．However，these protocols have many flaws due tolack of theoretical support in designing these protocols．In this work，first we present the security andprivacy requirements in RFID authentication protocols．Then we examine related works and point outproblems in designing RFID authentication protocols．To solve these problems，we propose andbriefly prove three theorems． We also give necessaryexamples for better understanding these theoremswith concrete protocols． At last，we give our suggestionson designing secure and private authenticationprotocols． The security and privacy requirements，theorems， and suggestions will facilitatebetter understanding and designing of RFID authenticationprotocols in the future．

?