Radio Frequency Identification (RFID) technology one of the most promising technologies in the field of ubiquitous computing. Indeed, RFID technology may well replace barcode technology. Although it offers many advantages over other identification systems, there are also associated security risks that are not easy to be addressed. When designing a real lightweight authentication protocol for low cost RFID tags, a number of challenges arise due to the extremely limited computational, storage and communication abilities of Low-cost RFID tags. This paper proposes a real mutual authentication protocol for low cost RFID tags. The proposed protocol prevents passive attacks as active attacks are discounted when designing a protocol to meet the requirements of low cost RFID tags. However the implementation of the protocol meets the limited abilities of low cost RFID tags. KEYWORDS RFID, Mutual Authentication, ubiquitous computing, Pervasive computing, Gossamer.