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The advantage of using RFID technology is gaining much attention as is seen by an increase in its deployment. However, this pervasive use of RFID tags opens up the possibility for various attacks violating user privacy. This work describes simple, inexpensive, and untraceable mutual identification protocols based on modular exponentiation for RFID tags. The proposed authentication mechanism is a low-cost but high-security for protecting consumer's information in RFID tag against unwanted read-attacks. We analyzed with issues of the security and privacy of RFID systems. This paper also showed the 8-bit architecture of a low-power and low die-size implementation of modular exponentiation. The 8-bit modular exponentiation implementation has a chip area of less than 1 K gates and the encryption of 64 bits requires about 1000 clock cycles. The executing time of the proposed protocol would range from 12.36 ms to 20.6 ms, with 6-8 tags authenticated per second.