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.
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.
Quantum key distribution (QKD) enables unconditional secure communication by exploiting the principles of quantum mechanics. However, existing reconciliation protocols face a trade-off between error correction efficiency and information leakage. To address this challenge, we propose an enhanced QKD reconciliation scheme based on polynomial interpolation. The protocol introduces a block-wise algebraic structure to unify error detection and correction, significantly reducing interactive rounds while maintaining high efficiency. A comprehensive information-theoretic leakage model is established, covering polynomial interpolation, verification, and iterative error localization. To further ensure unconditional security, a cascaded privacy amplification mechanism is integrated, combining two compression stages tailored to reconciliation leakage and quantum channel leakage, respectively. Moreover, an adaptive parameter optimization strategy dynamically adjusts block size and polynomial order according to the quantum bit error rate (QBER), achieving robustness under diverse channel conditions. Theoretical analysis and simulations demonstrate that the proposed scheme achieves a secure key rate of 65–72% at QBER < 3%, outperforming the classical CASCADE protocol by 8–12%, and maintains 30–50% efficiency under moderate error rates. Computational complexity analysis shows performance comparable to LDPC-based approaches while offering superior leakage control. These results confirm that the proposed protocol provides a balanced trade-off among efficiency, security, and implementation complexity, making it suitable for deployment in practical QKD systems.
In this paper, we propose how to construct a reconciliation method for the BB84 Quantum Key Distribution (QKD) protocol. Theoretically, it is unconditionally secure because it is based on the quantum laws of physics, rather than the assumed computational complexity of mathematical problems. BB84 protocol performances can be reduced by various errors and information leakages such as limited intrinsic efficiency of the protocol, imperfect devices and eavesdropping. The proposed reconciliation method allowed to weed out these errors by using Turbo codes. Since their high error correction capability implies getting low errors, this method has high performance especially when compared to the last method presented in the literature based on Low-Density Parity Check codes (LDPC). In particular, we demonstrate that our method leads to a significant improvement of the protocol security and of the Bit Error Rate (BER) even with great eavesdropping capability.
In this paper, we propose how to construct a reconciliation method for the BB84 Quantum Key Distribution (QKD) protocol. Theoretically, it is unconditionally secure because it is based on the quantum laws of physics, rather than the assumed computational complexity of mathematical problems. BB84 protocol performances can be reduced by various errors and information leakages such as limited intrinsic efficiency of the protocol, imperfect devices and eavesdropping. The proposed reconciliation method allowed to weed out these errors by using Turbo codes. Since their high error correction capability implies getting low errors, this method has high performance especially when compared to the last method presented in the literature based on Low- Density Parity Check codes (LDPC). In particular, we demonstrate that our method leads to a significant improvement of the protocol security and of the Bit Error Rate (BER) even with great eavesdropping capability.
Quantum communication uses photons to transmit quantum bits (qubits) over long distances. By using this quantum technology, quantum key distribution (QKD), a secure communication protocol, ensures the security of encryption key exchange. Due to noise and eavesdropping in the quantum channel, errors can occur in the shared qubits after QKD key agreement phase. Therefore, we need a key verification phase to deal with inconsistent qubits (i.e. the wrong qubits at the receiving end). This key verification is also called information reconciliation. Recently, some reconciliation algorithms in QKD (RQKD) using polynomial consistency have been proposed. These RQKDs use the consistency property to find the correct polynomial (converted from the qubits) and then check the correctness of other qubits based on this polynomial to achieve reconciliation. All previous consistency-based RQKDs required such an extra step to check the correctness of other qubits after finding the correct polynomial. In this paper, we propose Enhanced RQKD (ERQKD), which uses consistency in a new way to improve key verification efficiency without requiring additional checking steps. Theoretical analysis and experiments indeed show that our ERQKD outperforms the two previous RQKDs.
Quantum key reconciliation is an essential process of quantum key distribution (QKD). It aims to correct the transmission errors after the distribution of quantum objects over a quantum channel, where two legitimate parties use a classical public authenticated channel to disclose correlated bits for agreeing on their common key. This work proposes an alternative promising method employing LDPC-codes bit-flipping decoding to practical implementation of quantum key reconciliation. In our proposed scheme, the low-complexity code bit-flipping decoding based on syndrome decoding is modified and applied to conventional Winnow protocol to achieve both error correcting performance and low complexity of hardware realization, i.e. FPGA logic cells and/or memory. From numerical simulation while the performance of our proposed scheme in terms of final bit error rate (BER) and disclosed bits is superior to conventional Winnow and CASCADE protocols, it yields low complexity in LDPC decoding comparable to the existing LDPC-based reconciliation protocols. Therefore, the technique is promising to high-speed discrete-variable QKD applications.
This technical report proposes a unified error correction and reconciliation framework designed specifically for improving the secure key rate of Quantum Key Distribution (QKD) protocols, particularly in Continuous-Variable (CV-QKD) systems. Problem Addressed: Existing QKD reconciliation methods rely on standard binary codes, which fail to leverage the inherent geometry of the lattice channels used in CV-QKD. This leads to reduced efficiency, especially when the signal quality is low (low SNR). Key Innovations: Lattice-Native Coding: The design employs Low-Density Parity-Check (LDPC) codes defined natively over integer rings (Z-sub-q), allowing direct alignment with the geometric structure of the quantum channel. Geometry-Preserving Interleaving: A novel, low-discrepancy interleaver is introduced to optimize error spreading while maintaining local geometric structure during encoding and decoding. Leak-Aware Reconciliation Ledger: A dynamic ledger is used to precisely track all information leakage (syndrome sum) during the error correction process. This tracked leakage directly sets the length for Privacy Amplification, ensuring rigorous and composable finite-key security bounds.