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IEEE Access

Syndrome-Based Multi-Bit Error Correction With Chaotic Secure Check-Sequence Sharing for Quantum Key Distribution Systems

R. K. Mugelan, N. G. Swetha

Published Jan 1, 2026• 1 citation
Publisher

Abstract

Error correction plays a central role in Quantum Key Distribution (QKD) because the raw keys produced by Alice and Bob rarely match exactly. Channel noise, detector fluctuations, and basis mismatches routinely introduce discrepancies that must be resolved before a usable secret key can be formed. Methods such as Cascade and LDPC generally perform well under moderate noise conditions; however, they depend on repeated message exchanges or computationally intensive decoding, which limits their effectiveness when several bits flip together within short time windows. These issues become particularly evident in high-noise environments where correlated errors appear in bursts. To address these challenges, this work presents a syndrome-based multi-bit error-correction technique combined with a chaotic masking approach for securely transmitting the necessary check-sequence data. The technique forms a decimal-summation matrix from each key block and extracts a compact syndrome vector capable of identifying one-, two-, or three-bit errors in a single step. To prevent classical-channel leakage, the required check-sequence is masked using a Tent-map sequence initialized from the entropy associated with the unmatched quantum indices. Simulation results demonstrate a 50–70% reduction in post-correction bit-error rate compared with Cascade, LDPC, and Polar codes across key lengths of 128 to 1024 bits and error probabilities up to 0.5. Overall, the proposed model offers a noise-tolerant and computationally lightweight reconciliation approach and forms the error-correction component of the patented Q-RAPTOR framework (Indian Patent Application No. 202541093982).

DOI
10.1109/access.2025.3650606

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Error correction plays a central role in Quantum Key Distribution (QKD) because the raw keys produced by Alice and Bob rarely match exactly. Channel noise, detector fluctuations, and basis mismatches routinely introduce discrepancies that must be resolved before a usable secret key can be formed. Methods such as Cascade and LDPC generally perform well under moderate noise conditions; however, they depend on repeated message exchanges or computationally intensive decoding, which limits their effectiveness when several bits flip together within short time windows. These issues become particularly evident in high-noise environments where correlated errors appear in bursts. To address these challenges, this work presents a syndrome-based multi-bit error-correction technique combined with a chaotic masking approach for securely transmitting the necessary check-sequence data. The technique forms a decimal-summation matrix from each key block and extracts a compact syndrome vector capable of identifying one-, two-, or three-bit errors in a single step. To prevent classical-channel leakage, the required check-sequence is masked using a Tent-map sequence initialized from the entropy associated with the unmatched quantum indices. Simulation results demonstrate a 50–70% reduction in post-correction bit-error rate compared with Cascade, LDPC, and Polar codes across key lengths of 128 to 1024 bits and error probabilities up to 0.5. Overall, the proposed model offers a noise-tolerant and computationally lightweight reconciliation approach and forms the error-correction component of the patented Q-RAPTOR framework (Indian Patent Application No. 202541093982).
Post-processing is a significant step in quantum key distribution (QKD), which is used for correcting the quantum-channel noise errors and distilling identical corrected keys between two distant legitimate parties. Efficient error reconciliation protocol, which can lead to an increase in the secure key generation rate, is one of the main performance indicators of QKD setups. In this paper, we propose a multi-low-density parity-check codes based reconciliation scheme, which can provide remarkable perspectives for highly efficient information reconciliation. By testing our approach through data simulation, we show that the proposed scheme combining multi-syndrome-based error rate estimation allows for a more accurate estimation of the error rate as compared with random sampling and single-syndrome estimation techniques before the error correction, as well as a significant increase in the efficiency of the procedure without compromising security and sacrificing reconciliation efficiency.
Quantum key distribution (QKD) is a promising technique to share unconditionally secure keys between remote parties. As an essential part of a practical QKD system, reconciliation is responsible for correcting the errors due to the quantum channel noise by exchanging information through a public classical channel. In the present work, we propose a novel syndrome-based low-density parity-check (LDPC) reconciliation protocol to reduce the information leakage of reconciliation by fully utilizing the syndrome information that was previously wasted. Both theoretical analysis and simulation results show that our protocol can evidently reduce the information leakage as well as the number of communication rounds.
Quantum cryptography is essentially the quantum key distribution (QKD). In the context of QKD, one from two partners (Alice) generates and sends a sequence of qubits through a private quantum channel to another partner (Bob) and Bob receives the sequence and measures the state of each qubit. After the quantum transmission stage, Alice and Bob have almost identical qubit sequences. The erros are due to physical imperfections in the channel and presence of an eavesdropper. The next stage in QKD is key reconciliation (i.e. finding and correcting discrepancies between Alice's string and that of Bob). This reconciliation can be done by public discussion. Let us suppose there is a secret quantum channel between Alice and Bob through which Alice transmits a n-bit string A=(A1, A2,...,An)ε{0,1}n. Then Bob receives a n-bit string B=(B1, B2,...,Bn)ε{0,1)n. The string B differs from A due to the presence of noise and eavesdropper in the channel. One can estimate the bit error probability in the channel. For example, Bob can choose a random subset from his string and send it to Alice in public. Then Alice compares the received string with her corresponding subset and calculates the total number of protocol steps. The cascade scheme uses the interaction over the public channel to correct the secret strings by dividing them into the blocks of a fixed length. The length is determined from the bit error probability. A simple interactive routine is applied in each of these blocks. An error found in some block results in some action with other blocks. It is important to optimize the error-finding routines in standalone blocks as well as to organize the effective constrution of blocks with the object of protocol benchmark, information leakage and number of interactions between partners.
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.
From the past few years, the rapid growth in quantum computing and large-scale data systems has created an important need for advanced encryption techniques that withstand quantum-level attacks. However, traditional cryptographic systems are becoming increasingly vulnerable, particularly in big-data environments. To overcome this limitation, this research proposes a secure framework for big data encryption namely Quantum-Chaotic Key-Based Encryption System (QC-KES), which combines quantum randomness and chaos theory to make highly secure encryption keys. Therefore, the methodology begins by producing a quantum random seed utilizing Quantum Random Number Generation (QRNG). It is then enhanced through a chaotic logistic map to generate unpredictable key sequences that are securely shared using Quantum Key Distribution (QKD). Subsequently, quantum optical elements are tuned based on the key sequence to encrypt data at the hardware level. Moreover, Quantum Error Correction (QEC) confirms the signal integrity, while the data are encrypted, transmitted, and later decrypted by the shared key. This system improves key security, accuracy, and resistance to quantum-based threats. Finally, the proposed QC-KES obtained better results in entropy (8.000%) and avalanche effect (52.5 bits) when compared the existing Advanced Encryption Standard (AES) model.