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The RFID system, a core technology used in building a ubiquitous environment utilizing radio frequency identification, is an alternative to bar-codes. The RFID system has become very popular, with various strengths such as recognition speed and non-touch method. However, there are some problems remaining as the low- cost tag can be operated through query, which leads to information exposure and privacy encroachment. Various approaches have been used to increase security of the system, but the low-cost tag, which has about 5 K-10 K gate capabilities, can only allocate 250-3 K gate to security. Therefore, the current study will provide a reciprocal authentication solution that can be used with low-cost RFID systems, by separating 64 bit keys and minimizing calculations. Existing systems divided a 96 bit key into 4 parts. However, the proposed system reduces the key to 32 bits, and reduces the communications down to 5 from 7. Also, one additional random number is added to the existing two numbers to increase security. To improve the previous system, which only provided XOR calculations, an additional hash function was added. The added procedure does not increase effectiveness, compared to the XOR calculation, but does provide more security to the RFID system, which can be used in remote distances.