Anonymous authentication mechanisms can be used in RFID systems to preserve the privacy of the RFID tags. Scalability problem and backward privacy problem are two important issues considered in practice. In this paper, security analysis is presented on three recently proposed RFID authentication protocols satisfying scalability and backward privacy. The research shows that ACP protocol can not provide the property of backward privacy; the G-I protocol can not resist dysynchronization attack, i.e. the adversary can make the secrets stored in tag and reader unmatched, which results in the tag and the reader in a desynchronized state and renders future authentication impossible; and the MMR protocol can not resist active attack, because the adversary can extract tags all secrets via querying the tag and analyzing the messages sent by the tag. In addition, we present a modified scalable hash-based mutual authentication protocol with less storage and computation requirements than G-I. And we prove our scheme can provide the property of backward privacy and resist the desynchronization attack.