A delayed error-correction (EC) reconciliation protocol for quantum key distribution (QKD) is proposed in the paper, where the error correction operation is operated after the messages have been transmitted. There are two advantages of the proposed protocol. First, it is possible for the two nodes without a direct quantum link to share secret keys, when the two nodes are separately connected to a common trusted relay in the QKD network. Besides, the reconciliation protocol with the delayed EC also simplifies the whole reconciliation process. It corrects both errors caused by communications during QKD process and that inherent in message bits. The key generation rate of the delayed EC protocol is presented. Finally, the bit error rate of the proposed protocol is analyzed when using polar codes as the error correction codes. The results show that the performance of the delayed EC reconciliation protocol with polar codes were better than those using low-density parity check code.
A delayed error-correction (EC) reconciliation protocol for quantum key distribution (QKD) is proposed in the paper, where the error correction operation is operated after the messages have been transmitted. There are two advantages of the proposed protocol. First, it is possible for the two nodes without a direct quantum link to share secret keys, when the two nodes are separately connected to a common trusted relay in the QKD network. Besides, the reconciliation protocol with the delayed EC also simplifies the whole reconciliation process. It corrects both errors caused by communications during QKD process and that inherent in message bits. The key generation rate of the delayed EC protocol is presented. Finally, the bit error rate of the proposed protocol is analyzed when using polar codes as the error correction codes. The results show that the performance of the delayed EC reconciliation protocol with polar codes were better than those using low-density parity check code.
With the rapid improvement of quantum computing technology, quantum key distribution(QKD) is a hot technology. Information reconciliation is a key step of QKD which is useful for correcting key error. Classical message interaction is necessary in a practical information reconciliation scheme, which makes the efficiency of these protocols decreased. Therefore, some one-way information reconciliation schemes based on low-density parity-check(LDPC) codes and polar codes are proposed. Here we propose a concatenated method of IR schemes which can achieve any given error rate level without the need of interactions. Compared with the one-way IR schems based on LDPC codes and polar codes, the IR schemes based on the proposed concatenated method can get lower bit error rates after error correction, which can also reduce the communication delay and system complexity of QKD, improve the final key generation rate and enhance the practicability of QKD system.
A quantum key distribution protocol(QKD), known as BB84, was developed in 1984 by Charles Bennett and Gilles Brassard. The protocol works in two phases which are quantum state transmission and conventional post processing. In the first phase of BB84, raw key elements are distributed between two legitimate users by sending encoded photons through quantum channel whilst in the second phase, a common secret-key is obtained from correlated raw key elements by exchanging messages through a public channel e.g.; network or internet. The secret-key so obtained is used for cryptography purpose. Reconciliation is a compulsory part of post processing and hence of quantum key distribution protocol. The performance of a reconciliation protocol depends on the generation rate of common secret-key, number of bits disclosed and the error probability in common secrete-key. These characteristics of a protocol can be achieved by using a less interactive reconciliation protocol which can handle a higher initial quantum bit error rate (QBER). In this paper, we use a simple Bose, Chaudhuri, Hocquenghem (BCH) error correction algorithm with simplified syndrome table to achieve an efficient reconciliation protocol which can handle a higher quantum bit error rate and outputs a common key with zero error probability. The proposed protocol efficient in removing errors such that it can remove all errors even if QBER is 60%. Assuming the post processing channel is an authenticated binary symmetric channel (BSC).
Quantum key distribution (QKD) is a cryptographic system that generates an information-theoretically secure key shared by two legitimate parties. QKD consists of two parts: quantum and classical. The latter is referred to as classical post-processing (CPP). Information reconciliation is a part of CPP in which parties are given correlated variables and attempt to eliminate the discrepancies between them while disclosing a minimum amount of information. The elegant reconciliation protocol known as \emph{Cascade} was developed specifically for QKD in 1992 and has become the de-facto standard for all QKD implementations. However, the protocol is highly interactive. Thus, other protocols based on linear block codes such as Hamming codes, low-density parity-check (LDPC) codes, and polar codes have been researched. In particular, reconciliation using LDPC codes has been mainly studied because of its outstanding performance. Nevertheless, with small block size, the bit error rate performance of polar codes under successive-cancellation list (SCL) decoding with a cyclic redundancy check (CRC) is comparable to state-of-the-art turbo and LDPC codes. In this study, we demonstrate the use of polar codes to improve the performance of information reconciliation in a QKD system with small block size. The best decoder for polar codes, a CRC-aided SCL decoder, requires CRC-precoded messages. However, messages that are sifted keys in QKD are obtained arbitrarily as a result of a characteristic of the QKD protocol and cannot be CRC-precoded. We propose a method that allows arbitrarily obtained sifted keys to be CRC precoded by introducing a virtual string. Thus the best decoder can be used for reconciliation using polar codes and improves the efficiency of the protocol.
Quantum key distribution (QKD) is a technology to securely share keys against any attack physically permitted, with the principle of quantum mechanics. In recent years, the satellite QKD, which employs artificial satellites as trusted mobile nodes, has been attracting attention in order to overcome the bottleneck of transmission distance. However, in the satellite QKD, quality degradation due to atmospheric effects is expected, as in ordinary satellite laser communications. Therefore, it is desirable to apply an error-correcting code (ECC) that has high error-correcting performance even under the atmospheric-induced effects to the error-correcting process of the satellite QKD. Therefore, in this paper, we examined the application of polar codes, which is known as an ECC with high error correction capability. First, in order to optimize the error correction efficiency, we propose a method to adaptively obtain an appropriate code rate for the received signal strength that changes momentarily due to atmospheric effects. Then, we compare the throughput performances with polar codes to it with low-density parity-check (LDPC) codes, with the numerical simulation assuming Bennett-Brassard 1984 protocol (BB84).
Key reconciliation is important for practical Quantum key distribution (QKD) systems since it corrects the error bits in a key string by sacrificing some key bits. Therefore, its performance directly affects the secret key rate of a practical QKD system. Although key reconciliation scheme based on polar codes can achieve a high coding efficiency, the high frame error rate causes discarding key strings and decreases the secret key rate. In this paper, we fist analyze the limitation of successive cancellation decoding of polar codes, and then we propose an improved key reconciliation scheme using polar codes with successive cancellation list decoding and optimized coding structures, which can decrease the frame error probability, resulting in a higher secret key rate. Numerical results show that the proposed scheme can achieve a 12.8% higher secret key rate than the previous polar codes-based scheme with a code length of 216 bits and a quantum bit error rate of 2%. Besides, the proposed scheme is robust and it can extract secret key bits even when the quantum bit error rate reaches 10.2% with a code length of 220 bits and a coding efficiency of 90.6%.
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.