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RFID technology can be found in the most fields of our daily life, e.g. personal identification, supply-chain management, access control etc. For the sake of small computational capacity of RFID Tags, at first, only mathematical and logical operations and lightweight authentication methods could be used. However, thanks to the evolution of RFID technology, nowadays PKI infrastructure is also usable in this environment. In this paper we present our elliptic curve cryptography based mutual authentication protocol which proofs against the well-known attacks. We give a brief comparison with other EC based protocols in the point of view of security. Moreover, we show that our protocol is better than the others in case of performance, too. In order to measure the performance characteristics of our proposed ECC based authentication protocol and to make a comparison with others we implemented these algorithms in OMNeT++.