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arXiv:2403.00192

Block-MDS QC-LDPC Codes for Information Reconciliation in Key Distribution

Lev Tauz, Debarnab Mitra, Jayanth Shreekumar, Murat Can Sarihan, Chee Wei Wong, Lara Dolecek

Published Feb 29, 2024• 1 citation
arXivHTMLPDF

Abstract

Quantum key distribution (QKD) is a popular protocol that provides information theoretically secure keys to multiple parties. Two important post-processing steps of QKD are 1) the information reconciliation (IR) step, where parties reconcile mismatches in generated keys through classical communication, and 2) the privacy amplification (PA) step, where parties distill their common key into a new secure key that the adversary has little to no information about. In general, these two steps have been abstracted as two distinct problems. In this work, we consider a new technique of performing the IR and PA steps jointly through sampling that relaxes the requirement on the IR step, allowing for more success in key creation. We provide a novel LDPC code construction known as Block-MDS QC-LDPC codes that can utilize the relaxed requirement by creating LDPC codes with pre-defined sub-matrices of full-rank. We demonstrate through simulations that our technique of sampling can provide notable gains in successfully creating secret keys.

DOI
10.48550/arxiv.2403.00192

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Quantum key distribution (QKD) is a popular protocol that provides information theoretically secure keys to multiple parties. Two important post-processing steps of QKD are 1) the information reconciliation (IR) step, where parties reconcile mismatches in generated keys through classical communication, and 2) the privacy amplification (PA) step, where parties distill their common key into a new secure key that the adversary has little to no information about. In general, these two steps have been abstracted as two distinct problems. In this work, we consider a new technique of performing the IR and PA steps jointly through sampling that relaxes the requirement on the IR step, allowing for more success in key creation. We provide a novel LDPC code construction known as Block-MDS QC-LDPC codes that can utilize the relaxed requirement by creating LDPC codes with pre-defined sub-matrices of full-rank. We demonstrate through simulations that our technique of sampling can provide notable gains in successfully creating secret keys.
High-dimensional quantum key distribution (QKD) is a popular protocol that provides information theoretically secure keys to multiple parties. Two important steps of QKD are 1) the information reconciliation (IR) step, where parties reconcile mismatches in generated keys through classical communication, and 2) the privacy amplification (PA) step, where parties distill their common key into a new secure key that the adversary has little to no information about. In general, these two steps have been abstracted as two distinct problems. In this work, we design our IR protocol to be aware of the PA step and utilize sampling to relax the requirement on the IR step without sacrificing the final key length of the PA step, allowing for more bits generated in key creation utilizing practical decoders. We provide a novel PA-aware LDPC code construction known as Block-MDS QC-LDPC codes that can utilize the relaxed requirement. We demonstrate through simulations that our technique of sampling can provide notable gains in successfully creating secret keys.
In the conventional post-processing phase of Gaussian-modulated coherent state (GMCS) quantum key distribution (QKD) systems, the processes of information reconciliation (IR) and privacy amplification (PA) are typically carried out sequentially and separately. This approach incurs substantial computational complexity and may introduce potential security risks, such as key storage risks. In this paper, we propose a more efficient and secure post-processing scheme that integrates IR and PA into a single process by utilizing well-designed spinal codes. The proposed scheme significantly reduces computational complexity by employing the linear-complexity hash function instead of the superlinear complexity Toeplitz matrices used in conventional PA schemes, and effectively mitigates potential security risks associated with conducting IR and PA as separate processes. Experimental results show that the final secret key throughput of the proposed scheme is at least 250 times higher than that of the conventional PA scheme, with the improvement in throughput becoming even greater as the block lengths increase. More importantly, owing to the rateless property and the capacity-approaching performance of spinal codes, the GMCS QKD systems can achieve reconciliation efficiencies of higher than 97% across a broad range of signal-to-noise ratios from -22.5641 to 0.122 dB.
The postprocessing or secret-key distillation process in quantum key distribution (QKD) mainly involves two well-known procedures: information reconciliation and privacy amplification. Information or key reconciliation has been customarily studied in terms of efficiency. During this, some information needs to be disclosed for reconciling discrepancies in the exchanged keys. The leakage of information is lower bounded by a theoretical limit, and is usually parameterized by the reconciliation efficiency (or inefficiency), i.e. the ratio of additional information disclosed over the Shannon limit. Most techniques for reconciling errors in QKD try to optimize this parameter. For instance, the well-known Cascade (probably the most widely used procedure for reconciling errors in QKD) was recently shown to have an average efficiency of 1.05 at the cost of a high interactivity (number of exchanged messages). Modern coding techniques, such as rate-adaptive low-density parity-check (LDPC) codes were also shown to achieve similar efficiency values exchanging only one message, or even better values with few interactivity and shorter block-length codes.
Quantum key distribution (QKD) relies on quantum and classical procedures in order to achieve the growing of a secret random string -the key- known only to the two parties executing the protocol. Limited intrinsic efficiency of the protocol, imperfect devices and eavesdropping produce errors and information leakage from which the set of measured signals -the raw key- must be stripped in order to distill a final, information theoretically secure, key. The key distillation process is a classical one in which basis reconciliation, error correction and privacy amplification protocols are applied to the raw key. This cleaning process is known as information reconciliation and must be done in a fast and efficient way to avoid cramping the performance of the QKD system. Brassard and Salvail proposed a very simple and elegant protocol to reconcile keys in the secret-key agreement context, known as Cascade, that has become the de-facto standard for all QKD practical implementations. However, it is highly interactive, requiring many communications between the legitimate parties and its efficiency is not optimal, imposing an early limit to the maximum tolerable error rate. In this paper we describe a low-density parity-check reconciliation protocol that improves significantly on these problems. The protocol exhibits better efficiency and limits the number of uses of the communications channel. It is also able to adapt to different error rates while remaining efficient, thus reaching longer distances or higher secure key rate for a given QKD system.
Quantum key distribution (QKD) relies on quantum and classical procedures in order to achieve the growing of a secret random string -the key- known only to the two parties executing the protocol. Limited intrinsic efficiency of the protocol, imperfect devices and eavesdropping produce errors and information leakage from which the set of measured signals -the raw key- must be stripped in order to distill a final, information theoretically secure, key. The key distillation process is a classical one in which basis reconciliation, error correction and privacy amplification protocols are applied to the raw key. This cleaning process is known as information reconciliation and must be done in a fast and efficient way to avoid cramping the performance of the QKD system. Brassard and Salvail proposed a very simple and elegant protocol to reconcile keys in the secret-key agreement context, known as Cascade, that has become the de-facto standard for all QKD practical implementations. However, it is highly interactive, requiring many communications between the legitimate parties and its efficiency is not optimal, imposing an early limit to the maximum tolerable error rate. In this paper we describe a low-density parity-check reconciliation protocol that improves significantly on these problems. The protocol exhibits better efficiency and limits the number of uses of the communications channel. It is also able to adapt to different error rates while remaining efficient, thus reaching longer distances or higher secure key rate for a given QKD system.
Abstract Quantum key distribution (QKD) is the most mature application of quantum information technology. Information reconciliation is a crucial step in QKD and significantly affects the final secret key rates shared between two legitimate parties. We analyze and compare various construction methods of low-density parity-check (LDPC) codes and design high-performance irregular LDPC codes with a block length of 10 6 . Starting from these good codes and exploiting the slice reconciliation technique based on multilevel coding and multistage decoding, we realize high-efficiency Gaussian key reconciliation with efficiency higher than 95% for signal-to-noise ratios above 1. Our demonstrated method can be readily applied in continuous variable QKD.