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AIP conference proceedings

High-speed QKD Reconciliation using Forward Error Correction

David Pearson

Published Jan 1, 2004• 65 citations
Publisher

Abstract

We present a new error correction protocol for quantum key distribution using forward error correction techniques which is suitable for very high‐speed implementations. Using low‐density parity‐check codes, this protocol can achieve an order of magnitude greater efficiency than Cascade in communication cost and computation speed, with only slightly greater overhead in the number of parity bits revealed on the public channel. This protocol has been implemented on the DARPA quantum network between BBN, Harvard University and Boston University.

DOI
10.1063/1.1834439

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We present a new error correction protocol for quantum key distribution using forward error correction techniques which is suitable for very high‐speed implementations. Using low‐density parity‐check codes, this protocol can achieve an order of magnitude greater efficiency than Cascade in communication cost and computation speed, with only slightly greater overhead in the number of parity bits revealed on the public channel. This protocol has been implemented on the DARPA quantum network between BBN, Harvard University and Boston University.
We present the Low Density Parity Check (LDPC) forward error correction algorithm adapted for the Quantum Key Distribution (QKD) protocol in a form readily applied by developers. A sparse parity check matrix is required for the LDPC algorithm and we suggest using some that have been defined by the IEEE and ETSI standards organizations for use in various communication protocols. We evaluate the QKD performance of these various parity check matrices as a function of the quantum bit error rate. We also discuss the computational precision required for this LPDC algorithm. As QKD evolves towards deployment, complete algorithm descriptions and performance analysis, as we present, will be required.
Information reconciliation is a crucial procedure in the classical post-processing of quantum key distribution (QKD). Poor reconciliation efficiency, revealing more information than strictly needed, may compromise the maximum attainable distance, while poor performance of the algorithm limits the practical throughput in a QKD device. Historically, reconciliation has been mainly done using close to minimal information disclosure but heavily interactive procedures, like \textit{Cascade}, or using less efficient but also less interactive ---just one message is exchanged--- procedures, like the ones based in low-density parity-check (LDPC) codes. The price to pay in the LDPC case is that good efficiency is only attained for very long codes and in a very narrow range centered around the quantum bit error rate (QBER) that the code was designed to reconcile, thus forcing to have several codes if a broad range of QBER needs to be catered for. Real world implementations of these methods are thus very demanding, either on computational or communication resources or both, to the extent that the last generation of GHz clocked QKD systems are finding a bottleneck in the classical part. In order to produce compact, high performance and reliable QKD systems it would be highly desirable to remove these problems. Here we analyse the use of short-length LDPC codes in the information reconciliation context using a low interactivity, \textit{blind}, protocol that avoids an a priori error rate estimation. We demonstrate that 2×1032 \times 10^32×103 bits length LDPC codes are suitable for blind reconciliation. Such codes are of high interest in practice, since they can be used for hardware implementations with very high throughput.
Quantum Key Distribution (QKD) is a revolutionary security technology that exploits the laws of quantum mechanics to achieve information-theoretic secure key exchange. QKD enables two parties to “grow” a shared secret key without placing any limits on an adversary’s computational power. Error reconciliation protocols have been developed that preserve security while allowing a sender and receiver to reconcile the errors in their respective keys. The most famous of these is the Cascade protocol, which is effective but suffers from a high communication complexity and low throughput. The Winnow protocol reduces the communication complexity over Cascade, but has the disadvantage of introducing errors. Finally, Low Density Parity Check (LDPC) codes have been shown to reconcile errors at rates higher than those of Cascade and Winnow, but with greater computational complexity. In this paper we evaluate the effectiveness of LDPC codes by comparing the runtime, throughput and communication complexity empirically with the Cascade and Winnow algorithms. The effects of inaccurate error estimation, non-uniform error distribution and varying key length on all three protocols are evaluated for identical input key strings. Analyses are performed on the results in order to characterize the strengths and weaknesses of each protocol.
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.
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.