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Journal of Xidian University

Application of quantum LDPC codes to quantum key distribution

Wang Xiao

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

In this paper,the security of BB84 key distribution protocol is considered.We assume that in the protocol the eavesdropper Eve intercepts/resends photons transmitted between Alice and Bob with probability e.First,the BB84 key distribution protocol will be made equivalent to a special Wire-tap channel model,where the main channel is a binary symmetric channel with probability of flipping bits 0.25e and the eavesdropper's channel is a binary erasure channel with probability of erasure 1-e.Using the coding method and properties of quantum LDPC codes CSS(C1,C2) for secure communication across the Wire-tap channel in the BB84 protocol is an equivalent proof of the security of BB84 protocol.Finally,the tolerable error rate of the BB84 protocol based on quantum LDPC codes can be obtained by calculating the secrecy capacity of this special Wire-tap channel.

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In this paper,the security of BB84 key distribution protocol is considered.We assume that in the protocol the eavesdropper Eve intercepts/resends photons transmitted between Alice and Bob with probability e.First,the BB84 key distribution protocol will be made equivalent to a special Wire-tap channel model,where the main channel is a binary symmetric channel with probability of flipping bits 0.25e and the eavesdropper's channel is a binary erasure channel with probability of erasure 1-e.Using the coding method and properties of quantum LDPC codes CSS(C1,C2) for secure communication across the Wire-tap channel in the BB84 protocol is an equivalent proof of the security of BB84 protocol.Finally,the tolerable error rate of the BB84 protocol based on quantum LDPC codes can be obtained by calculating the secrecy capacity of this special Wire-tap channel.
This article will BB84 key distribution protocol seen as a Wire-tap channel model, the main channel is a binary symmetric channel, bit flipping rate 0.25e, Wire-tap channel is a binary erasure channel, deleted probability 1-e, through quantum LDPC coding way, in the BB84 write about the main channel to achieve secure communication, while the security of the BB84 protocol proof. Finally, the Wire-tap channel capacity of safety is calculated, and ultimately get the BB84 protocol of quantum LDPC codes under the tolerable error rate.
With the advent of quantum key distribution (QKD) systems, perfect (i.e. information-theoretic) security can now be achieved for distribution of a cryptographic key. QKD systems and similar protocols use classical errorcorrecting codes for both error correction (for the honest p arties to correct errors) and privacy amplification (to make an eavesdropper fully ignorant). From a coding perspective, a good model for such a setting is the wire tap channel introduced by Wyner in 1975. In this paper, we study fundamental limits and coding methods for wire tap channels. We provide a novel proof for the secrecy capacity theorem for wire tap channels and show how capacity achieving codes can be used to achieve the secrecy capacity for any wiretap channel. We also consider binary erasure channel and binary symmetric channel special cases for the wiretap channel and propose specific practical codes. In some cases our designs achieve the secrecy capacity and in others the codes provide complete security at rates below secrecy capacity in some specific cases.
Considering noise in the quantum channel of BB84 quantum key distribution protocol,an improved model of BB84 protocol with quantum error correction code,such as Quantum Low Density Parity Check code(QLDPC) is proposed in this paper.By numerical simulation,the effect of quantum error correction code on BB84 protocol is analyzed in the case of the efficiency of transmission rate.The results show that quantum LDPC codes have good ability to overcome the noise,raise the efficiency of transmission rate and verify the availability of the improved model.
Quantum cryptography uses quantum mechanics to guarantee secure communication. BB84 is a widely used quantum key distribution that provides a way for two parties, a sender, Alice, and a receiver, Bob, to share an unconditionally secure key in the presence of an eavesdropper, Eve. Three different criteria can be assumed to study the BB84 protocol. They are the efficiency of the protocol, the probability that Eve remains undetected, and the amount of knowledge Eve has about Alice's bit sequence. In a previous approach, we only considered the probability that Eve remains undetected. We viewed this protocol as a three player static game in which Alice and Bob were two cooperative players and Eve was a competitive one. In our game model, Alice's and Bob's objective was to maximize the probability of detecting Eve, while Eve's objective was to minimize this probability. In this paper, our previous effort is extended and we also consider the other two criteria, i.e. the efficiency of the protocol and the amount of knowledge Eve has about Alice's bit sequence. Using these models, we show how game theory can be used to find the strategies for Alice, Bob and Eve.
In this article, a model of secure key exchange based on the BB84 protocol of quantum cryptography was developed and simulated. In the study, photons transmitted through a quantum channel between Alice and Bob were encoded in quantum states, and security was ensured by random selection of bases when reading them. An error indicator was calculated to detect Eavesdropping (Eve) interference. After generating the key, a simple ECC encryption algorithm based on XOR was used to transmit data in a protected manner. The results showed that it is possible to effectively maintain information confidentiality using a key formed through the BB84 protocol.
Quantum Key Distribution (QKD) is a technique that enables secure communication between two parties by sharing a secret key. One of the most well-known QKD protocols is the BB84 protocol, proposed by Charles Bennett and Gilles Brassard in 1984. In this protocol, Alice and Bob use a quantum channel to exchange qubits, allowing them to generate a shared key that is resistant to eavesdropping. This paper presents a comparative study of existing QKD schemes, including the BB84 protocol, and highlights the advancements made in the BB84 protocol over the years. The study aims to provide a comprehensive overview of the different QKD schemes and their strengths and weaknesses and demonstrate QKDs working principles through existing simulations and implementations. Through this study, we show that the BB84 protocol is a highly secure QKD scheme that has been extensively studied and implemented in various settings. Furthermore, we discuss the improvements made to the BB84 protocol to enhance its security and practicality, including the use of decoy states and advanced error correction techniques. Overall, this paper provides a comprehensive analysis of QKD schemes, focusing on the BB84 protocol in secure communication technologies.