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arXiv:2005.14488

Quantum Key Recycling can share key more efficient than BB84

Yu Chin Lu, Chia‐Wei Tsai, Tzonelih Hwang

Published May 29, 2020• 0 citations
arXivHTMLPDF

Abstract

We calculate the key sharing rate of Lu et al.'s Quantum Key Recycling (QKR) protocol. The key sharing rate is another version of the key rate, but it can be calculated for both the Quantum Key Distribution (QKD) protocols and the QKR protocols. We define the key sharing rate in this study and compare the key sharing rate of the QKR protocol to the rate of the QKD protocols. We found Lu et al.'s QKR protocol can be used to share keys more efficiently than BB84 in some situations. We also compare the six-state version of Lu et al.'s QKR protocol to the six-state QKD protocol. The results of this study show the potential advantages of using pre-shared keys to replace the public discussion in quantum protocols.

DOI
10.48550/arxiv.2005.14488

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We calculate the key sharing rate of Lu et al.'s Quantum Key Recycling (QKR) protocol. The key sharing rate is another version of the key rate, but it can be calculated for both the Quantum Key Distribution (QKD) protocols and the QKR protocols. We define the key sharing rate in this study and compare the key sharing rate of the QKR protocol to the rate of the QKD protocols. We found Lu et al.'s QKR protocol can be used to share keys more efficiently than BB84 in some situations. We also compare the six-state version of Lu et al.'s QKR protocol to the six-state QKD protocol. The results of this study show the potential advantages of using pre-shared keys to replace the public discussion in quantum protocols.
Quantum Key Recycling (QKR) is a quantum cryptographic primitive that allows one to reuse keys in an unconditionally secure way. By removing the need to repeatedly generate new keys, it improves communication efficiency. Škorić and de Vries recently proposed a QKR scheme based on 8-state encoding (four bases). It does not require quantum computers for encryption/decryption but only single-qubit operations. We provide a missing ingredient in the security analysis of this scheme in the case of noisy channels: accurate upper bounds on the required amount of privacy amplification. We determine optimal attacks against the message and against the key, for 8-state encoding as well as 4-state and 6-state conjugate coding. We provide results in terms of min-entropy loss as well as accessible (Shannon) information. We show that the Shannon entropy analysis for 8-state encoding reduces to the analysis of quantum key distribution, whereas 4-state and 6-state suffer from additional leaks that make them less effective. From the optimal attacks we compute the required amount of privacy amplification and hence the achievable communication rate (useful information per qubit) of qubit-based QKR. Overall, 8-state encoding yields the highest communication rates.
Quantum-key-distribution (QKD) networks can provide absolutely secure keys for the entire communication system in theory. At present, the key-distribution rate is relatively low, and the key-distribution rate decreases exponentially as the distribution distance increases. The trusted-relay scheme commonly used in existing QKD networks achieves the purpose of extending the security distance by consuming additional keys. Since the channel is unreliable, the key-relay process will accumulate system errors to a certain extent, increasing the probability of key-relay failure. In some high-bit-error-rate network scenarios such as wireless networks and disaster environments, the channel-error rate is as high as 30–50%. And in these scenarios, there are usually a large number of confidential messages that need to be delivered. However, the key-management mechanism of the current QKD system does not consider the scenario of key-relay failure. If the key is not successfully relayed, all the keys participating in the relay process will be destroyed, including the key that has been successfully relayed before. This situation causes the key to be wasted and reduces the encryption capability of the system. In this paper, we proposed the quantum-key-recycling (QKR) mechanism to increase the number of keys available in the network and introduced a secure service grading mechanism to properly reuse the recycled keys. The QKR mechanism can be regarded as a key-management mechanism acting on the point-to-point QKD system, and the mechanism is designed for a classical channel to reuse the key resources. A post-processing method for recycled keys is proposed to improve the security of the keys. Simulation results show that the QKD network using the key-recycling strategy is about 20% higher in key-utilization rate than the traditional QKD network without the QKR mechanism, and about 10% higher in-service security coverage.
Quantum Key Recycling aims to re-use the keys employed in quantum encryption and quantum authentication schemes. QKR protocols can achieve better round complexity than Quantum Key Distribution. We consider a QKR protocol that works with qubits, as opposed to high-dimensional qudits. A security proof was given by Fehr and Salvail in the case where there is practically no noise. A high-rate scheme for the noisy case was proposed by \v{S}kori\'{c} and de Vries, based on eight-state encoding. However, a security proof was not given. In this paper we introduce a protocol modification and provide a security proof. The modified protocol has high rate not only for 8-state encoding, but also 6-state and BB84 encoding. Our proof is based on a bound on the trace distance between the real quantum state of the system and a state in which the keys are completely secure. It turns out that the rate is higher than suggested by previous results. Asymptotically the rate equals the rate of Quantum Key Distribution with one-way postprocessing.
Quantum Key Recycling aims to re-use the keys employed in quantum encryption and quantum authentication schemes. QKR protocols can achieve better round complexity than Quantum Key Distribution. We consider a QKR protocol that works with qubits, as opposed to high-dimensional qudits. A security proof was given by Fehr and Salvail [1] in the case where there is practically no noise. A high-rate scheme for the noisy case was proposed by Škorić and de Vries [2], based on eight-state encoding. However, a security proof was not given. In this paper we introduce a protocol modification to [2] and provide a security proof. The modified protocol has high rate not only for 8- state encoding, but also 6-state and BB84 encoding. Our proof is based on a bound on the trace distance between the real quantum state of the system and a state in which the keys are completely secure. It turns out that the rate is higher than suggested by previous results. Asymptotically the rate equals the rate of Quantum Key Distribution with one-way postprocessing.
We answer an open question about Quantum Key Recycling (QKR): Is it possible to put the message entirely in the qubits without increasing the number of qubits compared to existing QKR schemes? We show that this is indeed possible. We introduce a prepare-and-measure QKR protocol where the communication from Alice to Bob consists entirely of qubits. As usual, Bob responds with an authenticated one-bit accept/reject classical message. Compared to Quantum Key Distribution (QKD), QKR has reduced round complexity. Compared to previous qubit-based QKR protocols, our scheme has far less classical communication. We provide a security proof in the universal composability framework and find that the communication rate is asymptotically the same as for QKD with one-way postprocessing.