The paper presents an innovative solution in the field of RFID (Radio-Frequency IDentification) smartcard authentication. Currently the smartcards are used for many purposes - e.g. employee identification, library cards, student cards or even identity credentials. Personal identity is revealed to untrustworthy entities every time we use these cards. Such information could later be used without our knowledge and for harmful reasons like shopping pattern scanning or even movement tracking. We present a communication scheme for keeping one’s identity private in this paper. Although our system provides anonymity, it does not allow users to abuse this feature. The system is based on strong cryptographic primitives that provide features never available before. Besides theoretical design of the anonymous authentication scheme and its analysis we also provide implementation results.