Radio frequency identification (RFID) is a technology for automated identification, which consists of a reading device, a server and RFID tags. We are interested in authentication protocols where two tags are simultaneously scanned by an RFID reader. Although there are several authentication protocols proposed in literature, some of them are insecure. This paper analyses the security of the authentication protocols based on two possible attacks: the brute-force attack against the proof and the forgery attack by using an authorised reader interacting with RFID tags. We also evaluate these protocols in terms of computation costs, communication costs and the resources used by adversary to run the attack (e.g., the size of memories and the number of queries). The results from our analysis indicate that our proposed protocol is more secure than the others and provides a countermeasure against forgery attack. Copyright © 2010 ACM.