Radio Frequency Identification (RFID) is a method for automated identifying objects. One of the problems of this technology is its security. RFID tags include resource limitation; therefore, the system designers cannot implement complex circuits to enhance their security. Usually the symmetric and asymmetric encryption methods increase resources and cost. Because it is believed to increasing security is inconsistent with the simplicity, the researchers mostly use one-way encryption methods. In this paper, we propose a mutual authentication protocol based on public key cryptography. The used encryption method includes high security and low complexity. This protocol performs in few steps and is suitable for portable devices with power limitation. In terms of security, the proposed protocol is robust against known attacks. In addition, we prove the protocol is secure by an analytical method.

Residue number system is a non¬-weighted integer number system which uses the residues of division of ordinary numbers by some modules for representing that ordinary numbers. In this paper, the general three moduli set {(2^n)-1,(2^n)+1,(2^(pn+1))-1} based on CRT algorithm is proposed in which “p” is an even number greater than zero. The special case of this set for p=2 which is {(2^n)-1,(2^n)+1,(2^(pn+1))-1} is also described in this paper. Since the dynamic range of this set is odd, some difficult problems in RNS can be easily solved based on this set using parity checking. The proposed reverse converter is better in speed and hardware in comparison to reverse converters in similar dynamic range. Moreover, from the complexity point of view, the internal arithmetic circuits of this moduli set is improved and is less complex than the other sets in similar dynamic range.