Lee et al. recently proposed an RFID mutual authentication scheme based on synchronized secret information. However, we found that their protocol is vulnerable to a spoofing attack in which an adversary can impersonate a legal tag to the reader by sending a malicious random number. To remedy this vulnerability, we propose two RFID authentication protocols which are secure against all possible threats including backward and forward traceability. Furthermore, one of the two proposed protocols requires only three hash operations(but, operations in resynchronization state, m is the number of tags) in the database to authenticate a tag, hence it is well suitable fur large scale RFID systems.