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This work considers identity attack on a radio-frequency identification (RFID)-based backscatter communication system. Specifically, we consider a single-reader, single-tag RFID system whereby the reader and the tag undergo two-way signaling which enables the reader to extract the tag ID in order to authenticate the legitimate tag (L-tag). We then consider a scenario whereby a malicious tag (M-tag)---having the same ID as the L-tag programmed in its memory by a wizard---attempts to deceive the reader by pretending to be the L-tag. To this end, we counter the identity attack by exploiting the non-reciprocity of the end-to-end channel (i.e., the residual channel) between the reader and the tag as the fingerprint of the tag. The passive nature of the tag(s) (and thus, lack of any computational platform at the tag) implies that the proposed light-weight physical-layer authentication method is implemented at the reader. To be concrete, in our proposed scheme, the reader acquires the raw data via two-way (challenge-response) message exchange mechanism, does least-squares estimation to extract the fingerprint, and does binary hypothesis testing to do authentication. We also provide closed-form expressions for the two error probabilities of interest (i.e., false alarm and missed detection). Simulation results attest to the efficacy of the proposed method.