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International Conference on Information and Communication Technology Convergence (ICTC)

Reconciliation with polar codes constructed using Gaussian approximation for long-distance continuous-variable quantum key distribution

Yongseen Kim, Changho Suh, June‐Koo Kevin Rhee

Published Oct 1, 2017• 4 citations
Publisher

Abstract

Quantum key distribution (QKD) enables two authenticated parties to share secret keys with the ability to detect any attempts to eavesdrop the keys theoretically. Currently, QKD systems can be categorized by its source of uncertainty in nature; single photon or coherent light. As coherent light is harnessed, the overall cost for composing systems drops in general. However, more elaborate post processing is required to extract and share errorless secret keys. Such process is called reconciliation, which is critical to performance. To extend the maximum distance to distill secret keys and prevent it from being bottleneck, we propose a reconciliation protocol that combines multidimensional reconciliation and polar codes. Especially, considering some practical issues, Gaussian approximation is chosen to construct polar codes. The simulation results show that the proposed protocol can support decent performance of coherent-light-based systems at long distance with reduced complexity.

DOI
10.1109/ictc.2017.8190991

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Quantum key distribution (QKD) enables two authenticated parties to share secret keys with the ability to detect any attempts to eavesdrop the keys theoretically. Currently, QKD systems can be categorized by its source of uncertainty in nature; single photon or coherent light. As coherent light is harnessed, the overall cost for composing systems drops in general. However, more elaborate post processing is required to extract and share errorless secret keys. Such process is called reconciliation, which is critical to performance. To extend the maximum distance to distill secret keys and prevent it from being bottleneck, we propose a reconciliation protocol that combines multidimensional reconciliation and polar codes. Especially, considering some practical issues, Gaussian approximation is chosen to construct polar codes. The simulation results show that the proposed protocol can support decent performance of coherent-light-based systems at long distance with reduced complexity.
Abstract Quantum key distribution (QKD) is a secure cryptographic technology that enables two authenticated parties to share secret keys. Information reconciliation is an essential step in continuous-variable quantum key distribution (CV-QKD) protocols, which affects both the complexity and performance of the system. This paper reviews adaptive reconciliation protocols, and also proposes a new efficient scheme using systematic polar codes. Simulation results show that the proposed scheme can significantly increase reconciliation efficiency and reduce the overall computational complexity by reducing the average number of retransmissions, without significant reduction in effective secret key length.
The two-way continuous-variable quantum key distribution (CVQKD) systems allow higher key rates and improved transmission distances over standard telecommunication networks in comparison to the one-way CVQKD protocols. To exploit the real potential of two-way CVQKD systems a robust reconciliation technique is needed. It is currently unavailable, which makes it impossible to reach the real performance of a two-way CVQKD system. The reconciliation process of correlated Gaussian variables is a complex problem that requires either tomography in the physical layer that is intractable in a practical scenario, or high-cost calculations in the multidimensional spherical space with strict dimensional limitations. To avoid these issues, we propose an efficient logical layer-based reconciliation method for two-way CVQKD to extract binary information from correlated Gaussian variables. We demonstrate that by operating on the raw-data level, the noise of the quantum channel can be corrected in the scalar space and the reconciliation can be extended to arbitrary high dimensions. We prove that the error probability of scalar reconciliation is zero in any practical CVQKD scenario, and provides unconditional security. The results allow to significantly improve the currently available key rates and transmission distances of two-way CVQKD. The proposed scalar reconciliation can also be applied in oneway systems as well, to replace the existing reconciliation schemes.
We designed high-efficiency error correcting codes allowing us to extract an errorless secret key in a continuous-variable quantum key distribution (CVQKD) protocol using a Gaussian modulation of coherent states and a homodyne detection. These codes are available for a wide range of signal-to-noise ratios on an additive white Gaussian noise channel with a binary modulation and can be combined with a multidimensional reconciliation method proven secure against arbitrary collective attacks. This improved reconciliation procedure considerably extends the secure range of a CVQKD with a Gaussian modulation, giving a secret key rate of about ${10}^{\ensuremath{-}3}$ bit per pulse at a distance of 120 km for reasonable physical parameters.
Continuous variable quantum key distribution (CV-QKD) enables authenticated parties to share a key. Information reconciliation (IR) is a critical step of the post-processing in CV-QKD, significantly affecting the secret key rate (SKR) shared between the legitimate parties. To improve the SKR performance of the CV-QKD without increasing the key inconsistency rate (KIR), this paper proposes a twofold IR method by performing independent operations on the Gaussian modulated coherent states (GMCS) obtained over the quantum channel. Specifically, assuming reverse reconciliation, after the GMCS are quantized, Bob generates parity bits, which are shared with Alice to help her correct the inconsistent bits in the quantized bits to generate the partial key. At the same time, the parity bits are used as frozen bits of polar codes in the multidimensional reconciliation (MR) to generate the other partial key. Simulation results demonstrate that the proposed twofold IR method increases the SKR nearly twice without increasing the inconsistent bits. In addition, we propose to apply symbol expansion and rotation (SER) based on the mapped GMCS to reduce the amount of information to be transmitted over the public error-free channel. Simulation results demonstrate that the performance of the proposed twofold IR with SER method can achieve a higher SKR with 3dB performance gap to that of the traditional MR protocol.
Information reconciliation is a critical process of any Quantum Key Distribution (QKD) protocol, where two legitimate parties agree on a secret key. Two parties attempt to eliminate the discrepancies between their correlated keys in the presence of an adversary, while revealing a minimum amount of information. In this paper, we propose a reconciliation protocol using polar codes with a soft-output decoder. We demonstrate that our method is better than a conventional protocol using polar codes in the view of reconciliation efficiency.
We propose an efficient logical layer-based reconciliation method for continuous-variable quantum key distribution (CVQKD) to extract binary information from correlated Gaussian variables. We demonstrate that by operating on the raw-data level, the noise of the quantum channel can be corrected in the low-dimensional (scalar) space, and the reconciliation can be extended to arbitrary dimensions. The CVQKD systems allow an unconditionally secret communication over standard telecommunication networks. To exploit the real potential of CVQKD a robust reconciliation technique is needed. It is currently unavailable, which makes it impossible to reach the real performance of the CVQKD protocols. The reconciliation is a post-processing step separated from the transmission of quantum states, which is aimed to derive the secret key from the raw data. The reconciliation process of correlated Gaussian variables is a complex problem that requires either tomography in the physical layer that is intractable in a practical scenario, or high-cost calculations in the multidimensional spherical space with strict dimensional limitations. To avoid these issues, we define the low-dimensional reconciliation. We prove that the error probability of one-dimensional reconciliation is zero in any practical CVQKD scenario, and provides unconditional security. The results allow for significantly improving the currently available key rates and transmission distances of CVQKD.