We propose a novel quantum-resistant mutual authentication scheme for radio-frequency identification (RFID) systems. Our scheme uses lattice-based cryptography and, in particular, achieves quantum-resistance by leveraging the hardness of the inhomogeneous short integer solution (ISIS) problem. In contrast to prior work, which assumes that the reader-server communication channel is secure, our scheme is secure even when both the reader-server and tag-reader communication channels are insecure. Our proposed protocol provides robust security against man-in-the-middle (MITM), replay, impersonation, and reflection attacks, while also ensuring unforgeability and preserving anonymity. We present a detailed security analysis, including semi-formal analysis and formal verification using the Automated Validation of Internet Security Protocols and Applications (AVISPA) tool. In addition, we analyze the storage, computation, and communication costs of the proposed protocol and compare its security properties with those of existing protocols, demonstrating that our scheme offers strong security guarantees. To the best of our knowledge, this paper is the first quantum-resistant authentication protocol for RFID systems that comprehensively addresses the insecurity of both the reader-server and tag-reader communication channels.

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