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International Symposium on Communications and Information Technologies

Performance of ½-rate convolutional code on Winnow protocol for quantum key reconciliation

Patcharapong Treeviriyanupab, Paramin Sangwongngam, Keattisak Sripimanwat, O. Sangaroon

Published Oct 1, 2010• 2 citations
Publisher

Abstract

The quantum key reconciliation is an essential step of Quantum Key Distribution (QKD) systems for correcting error in the raw keys which happens after the transmission over a quantum channel, where two legitimate parties make their correlated bits identical by exchanging messages over the public channel. This paper presents an alternative method for error correction of quantum key reconciliation by using ½-rate convolutional code, a class of forward error correcting (FEC) on Winnow for discrete-variable QKD protocol. The convolutional code can be applied to source coding with a side information problem which uses to describe quantum key reconciliation process. In the proposed scheme, it focuses on the performance evaluation of ½-rate convolutional code in quantum key reconciliation. In order to reduce an amount of interactive communication via error-free public channel for high-speed QKD applications, this proposed method is that the suitable solution.

DOI
10.1109/iscit.2010.5665052

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The quantum key reconciliation is an essential step of Quantum Key Distribution (QKD) systems for correcting error in the raw keys which happens after the transmission over a quantum channel, where two legitimate parties make their correlated bits identical by exchanging messages over the public channel. This paper presents an alternative method for error correction of quantum key reconciliation by using ½-rate convolutional code, a class of forward error correcting (FEC) on Winnow for discrete-variable QKD protocol. The convolutional code can be applied to source coding with a side information problem which uses to describe quantum key reconciliation process. In the proposed scheme, it focuses on the performance evaluation of ½-rate convolutional code in quantum key reconciliation. In order to reduce an amount of interactive communication via error-free public channel for high-speed QKD applications, this proposed method is that the suitable solution.
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.
Abstract : Currently, private communications in public and government sectors rely on methods of cryptographic key distribution that will likely be rendered obsolete the moment a full-scale quantum computer is realized, or efficient classical methods of factoring are discovered. There are alternative methods for distributing secret key material in a post-quantum era. One example of a system capable of securely distributing cryptographic key material, known as Quantum Key Distribution (QKD), is secure against quantum factorization techniques as its security rests on generally accepted laws of quantum physics. QKD protocols typically include a phase called Error Reconciliation, a clear-text classical-channel discussion between legitimate parties of a QKD protocol by which errors introduced in the quantum channel are corrected and the legitimate parties ensure they share identical key material. This work improves one such reconciliation protocol, called Winnow, by examining block-size choices for Winnow and thus increasing QKD key rate. Block sizes are chosen to maximize the probability that each block contains exactly one error. Further analyses of Winnow are provided to characterize the effects of different error distributions on protocol operation and shed light on the time and communication complexities of the Winnow secret key reconciliation protocol.
Quantum cryptography specifically called Quantum Key Distribution (QKD) provides acceptable levels of secure communications by utilising established laws of quantum mechanics. QKD protocol distributes a raw key through quantum channel between two cryptography users and then it removes errors occurred during communication from the distributed key by passing messages via public channel. Most popular error reconciliation protocols such as Binary, Cascade and Winnow are used to remove errors in a secure way. Among these three protocols, Buttler’s Winnow has the advantage of less communication complexity, however it is less effective at high error rates in a key and has the disadvantage of introducing errors during error reconciliation, and hence, causes reduction in reconciled key size and/or leave errors in the reconciled key. Winnow can handle quantum bit error rates a maximum up to 18 percent. However, after 13 percent error rate, Winnow becomes highly interactive and it may fail to reconcile the key. The deficiencies of high interactivity, reduction in reconciled key size, leaving errors in the reconciled key and failure of Winnow can be removed by enhancing the error reconciliation protocol by employing modified Bose, Chaudhuri, Hocquenghem (BCH) channel coding techniques. The enhanced BCH encoding algorithm is designed to handle a key at higher quantum bit error rates. BCH error detection and correction algorithms are enhanced to minimise the error percentage in the reconciled key. The modified block interleaver is introduced in the reconciliation protocol to obtain a long-size reconciled key with minimum iterations. The enhanced error reconciliation protocol can reconcile the key up to 50 percent initial bit error rate and reduces public channel communications. Finally, a long sized identical shared secret key with minimal error rate approaching zero is obtained within two iterations. The attained key can be used with secret key cipher to encrypt and decrypt information.
Due to imperfection in quantum key distribution (QKD) an uncorrected secret key transmitted via quantum channel exists at the receiver side. This paper presents an alternative method to recover those quantum key by using BCH codes - a class of error control coding (ECC). Application of BCH codes to source coding with side information is described for quantum key reconciliation. Unlikely to many previous protocols, the proposed scheme aims to reduce public communication with acceptable quantum bit error rate and a number of disclosed bits; therefore, it is suitable to applications of high speed QKD.
Continuous-variable quantum key distribution (CV-QKD) is a promising quantum-safe alternative to classical asymmetric cryptography that enables two authenticated parties to establish a shared secret over a potentially eavesdropped quantum channel. A key step in CV-QKD post-processing is information reconciliation, which leverages forward error correction (FEC) techniques to extract identical bit strings from noisy correlated data. In this work, we analyze the strict limitations on operating distance that are imposed by constant-rate FEC, severely limiting the practicability of CV-QKD systems in deployed optical networks. To overcome the distance limitations, we evaluate three strategies: (i) tuning modulation variance, (ii) adding controlled amounts of trusted detector loss, and (iii) the use of rate-adaptive FEC. All approaches are validated experimentally, compared in terms of performance, and we discuss implementation aspects. Our results show that while methods (i) and (ii) extend the operational distance of constant-rate FEC without the need for additional hardware components, they incur a significant penalty in secret key rate (SKR). In contrast, rate-adaptive FEC enables CV-QKD operation with performance close to the asymptotic SKR over a wide range of distances, provided that the reconciliation efficiency is chosen appropriately.
Ideally, in any quantum key distribution (QKD) communication system, each sifted key is expected to be received without error. However in practice, due to infeasibility of generating pure single photon and device impairment problem, some of the sifted key may experience errors. This results to the increment of quantum bit error rate (QBER) that requires error reconciliation for correcting error. The main concept in error reconciliation is very much related to the capability of correcting all errors while minimizing eavesdrop information. The quantum error correcting code such as Hamming code which used in Winnow protocol is found to be more attractive. However the Winnow protocol can only correct one error out of seven bits. In this paper, a modified Hamming encoder/decoder to improve Winnow protocol by correcting two errors out of seven bits which leads to reducing the QBER is presented. This design utilizes a pair of forward and reverse order syndromes for error pattern recognition. A new reconciliation protocol has been developed to enhance the error correcting capability in BB84 protocol. It is carried out in a simple structure which can correct up to double erroneous bits and detect four erroneous bits for each seven bits.