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In this work, we propose a novel key reconciliation protocol for the quantum key distribution (QKD). Based on Newton's polynomial interpolation, the proposed protocol aims to correct all erroneous bits at the receiver without revealing information to the eavesdropper. We provide the exact frame error rate (FER) expression of the proposed protocol. The inherent nature of the proposed algorithm ensures correcting all erroneous bits if the algorithm succeeds. We present an information-theoretical proof that the revealed information during the key reconciliation process is equal to zero. We also provide a numerical comparison of our algorithm with the asymptotic performance of the error-correcting codes and two exemplary low-density-parity-check (LDPC) codes. The results highlight that our algorithm provides superior performance when compared to the LDPC codes, regardless of the distance between Alice and Bob. Furthermore, the proposed key reconciliation protocol is usable for the longer quantum link distances than the state-of-the-art protocols.