The growing use of Radio Frequency Identification (RFID) technology to enhance ubiquitous computing environments has only begun to be realized. It allows for the identification of objects and/or subjects remotely using attached RFID tags via a radio frequency channel, hence identification is achieved in a contactless manner. This paper presents issues concerning security and privacy of RFID Systems which are heavily discussed in public and introduces Authentication Protocol for a RFID security protocol which serves as a proof of concept for authentication an RFID tag to a reader device using the vernam and standard encryption as a cryptographic primitive. To verify our protocol, we use model checking methodology, that is, Casper(A Compiler for Security Protocol), CSP(Communicating Sequential Processes) and then verify security properties such as secrecy and authentication using FDR(Failure Divergence Refinement) tool.