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arXiv:cs/0406001

Side-Information Coding with Turbo Codes and its Application to Quantum Key Distribution

Nguyen, Kim-Chi, Gilles Van Assche, Nicolas J. Cerf

Published Jun 1, 2004• 38 citations
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Abstract

Turbo coding is a powerful class of forward error correcting codes, which can achieve performances close to the Shannon limit. The turbo principle can be applied to the problem of side-information source coding, and we investigate here its application to the reconciliation problem occurring in a continuous-variable quantum key distribution protocol.

DOI
10.48550/arxiv.cs/0406001

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Turbo coding is a powerful class of forward error correcting codes, which can achieve performances close to the Shannon limit. The turbo principle can be applied to the problem of side-information source coding, and we investigate here its application to the reconciliation problem occurring in a continuous-variable quantum key distribution protocol.
Abstract Quantum key distribution (QKD) can provide information-theoretically secure keys for two parties of legitimate communication, and information reconciliation, as an indispensable component of QKD systems, can correct errors present in raw keys based on error-correcting codes. In this paper, we first describe the basic knowledge of information reconciliation and its impact on continuous variable QKD. Then we introduce the information schemes and the corresponding error correction codes employed. Next, we introduce the rate-compatible codes, the hardware acceleration of the reconciliation algorithm, the research progress of information reconciliation, and its application in continuous variable QKD. Finally, we discuss the future challenges and conclude.
Two legitimate users of an encryption system,Alice and Bob,want to acquire the key from the related Gaussian continuous variables X and Y transferred through a quantum channel,by exchanging parts of information through an ideal public authorized channel,and they get consistent binary keys from the inconsistent X and Y.This process is referred to reconciliation.This paper builds a reconciliation scheme for continuous-variables quantum key distribution using Turbo codes as the primitive code,on the basis of Sliced Error Correction(SEC) and Multi Level coding/Multi Stage Decoding(MLC/MSD).Parity bits of Turbo code are employed as the redundant information in the Slepian-Wolf encoding and decoding scheme.The simulation results show that the reconciliation convergences when the SNR is 7dB above whilst the block size is 20000.
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.
This paper investigates further on Quantum Key Distribution (QKD) protocols based on classical error-correcting codes, previously proposed by the authors. In [1], the classic channel coding techniques were shown to be suitable, in particular conditions, instead of quantum error-correcting codes, for correcting errors that occur during the exchange of a cryptographic key between two authorized users. To this end, systematic parallel concatenated codes, also known as turbo codes, were proposed in [1]. In this paper we address the properties that the systematic parallel concatenated codes must have in order to be successfully used in a QKD protocol. In particular, we address the problem, not considered in [1], that the constituent codes used in the parallel concatenation scheme must be such that the information sequence cannot be easily recovered from the encoder output sequences. In fact, the parallel classical channel on which to transmit only the redundancy bits is highly reliable but also public, i.e., very vulnerable as far as the attack attempts of a possible attacker are concerned.
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.