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Advanced Quantum Technologies

Proving the Security of Mediated Semi‐Quantum Key Distribution Using Entropic Uncertainty Relation

Zhenye Du, Youlong Yang, Tong Ning, Kaitian Gao

Published Jul 2, 2024• 2 citations
Publisher

Abstract

Abstract In recent years, mediated semi‐quantum key distribution (MSQKD) has become a hot topic in quantum cryptography. In this study, the original MSQKD protocol is revisited and a new scheme for proving security based on information theory is developed. At first, a new bound on the key rate of the protocol is derived using an entropic uncertainty relation, thus proving the unconditional security of the protocol. In addition, in the asymptotic scenario, a higher noise tolerance that improves the previous results is found. The legitimate communicating parties have to abort the protocol when they observe the error rate is larger than the noise tolerance. Furthermore, the security of a single‐state MSQKD protocol and a single‐state semi‐quantum key distribution (SQKD) protocol is proven using a similar scheme.

DOI
10.1002/qute.202400190

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Abstract In recent years, mediated semi‐quantum key distribution (MSQKD) has become a hot topic in quantum cryptography. In this study, the original MSQKD protocol is revisited and a new scheme for proving security based on information theory is developed. At first, a new bound on the key rate of the protocol is derived using an entropic uncertainty relation, thus proving the unconditional security of the protocol. In addition, in the asymptotic scenario, a higher noise tolerance that improves the previous results is found. The legitimate communicating parties have to abort the protocol when they observe the error rate is larger than the noise tolerance. Furthermore, the security of a single‐state MSQKD protocol and a single‐state semi‐quantum key distribution (SQKD) protocol is proven using a similar scheme.
Abstract Mediated semi-quantum key distribution (MSQKD) is a popular topic in quantum cryptography, which requires less quantum abilities from legitimate users, Alice and Bob, and has the advantage of high noise tolerance. In this paper, we propose a new MSQKD protocol where the third-party quantum server M can randomly send single-state and entangled-state without informing Alice and Bob of the type of qubit. In addition, in the case where M has an infinite quantum source, we derive the key rate and noise tolerance of the protocol, which proves the unconditional security of the protocol. Furthermore, as M changes the ratio of single-state and entangled-state, the noise tolerance also changes. In particular, when M sends only single-state or entangled-state, our protocol degenerates into the previous MSQKD protocols, and we derive a higher noise tolerance by analysing the mismatch terms.
Semi-quantum key distribution (SQKD) protocols allow for the establishment of a secret key between two users Alice and Bob, when one of the two users (typically Bob) is limited or “classical” in nature. Recently it was shown that protocols exists when both parties are limited/classical in nature if they utilize the services of a quantum server. These protocols are called mediated SQKD protocols. This server, however, is untrusted and, in fact, adversarial. In this paper, we reconsider a mediated SQKD protocol and derive a new proof of unconditional security for it. In particular, we derive a new lower bound on its key rate in the asymptotic scenario. Furthermore, we show this new lower bound is an improvement over prior work, thus showing that the protocol in question can tolerate higher rates of error than previously thought.
Mediated semi-quantum key distribution (M-SQKD) permits two limited "semi-quantum" or "classical" users to establish a secret key with the help of a third party (TP), in which TP has fully quantum power and may be untrusted. Several protocols have been studied recently for two-party scenarios, but no one has considered M-SQKD for multi-party scenarios. In this paper, we design a circular M-SQKD protocol based on Bell states, which offers an approach to realizing multiple "classical" users' key distribution. Then, we prove the protocol is unconditional security in the asymptotic scenario. The protocol's key rate and noise tolerance can be derived by utilizing the parameters observed in the channel. The results show that our protocol may hold similar security to a fully quantum one. We also compare the proposed protocol with similar protocols in terms of noise tolerance, qubit efficiency, communication cost, and scalability. Finally, the security proof method of this paper may contribute to studying the security of other circular semi-quantum cryptography protocols.
Semi-quantum key distribution (SQKD) protocols allow for the establishment of a secret key between two users Alice and Bob, when one of the two users (typically Bob) is limited or "classical" in nature. Recently it was shown that protocols exists when both parties are limited/classical in nature if they utilize the services of a quantum server. These protocols are called mediated SQKD protocols. This server, however, is untrusted and, in fact, adversarial. In this paper, we reconsider a mediated SQKD protocol and derive a new proof of unconditional security for it. In particular, we derive a new lower bound on its key rate in the asymptotic scenario. Furthermore, we show this new lower bound is an improvement over prior work, thus showing that the protocol in question can tolerate higher rates of error than previously thought.
Most prior semi-quantum key distribution (SQKD) protocols are designed in the context of qubits. In this paper, we proposed an SQKD protocol using ([Formula: see text]+1) quantum states in two mutually unbiased bases in the context of qudits without invoking the classical party’s measurement capability. It not only decreases the quantum states sent by quantum party by half, but also improves the efficiency of key rate than qubits do. To prove the security of present protocol, we first illustrate that the present protocol is completely robust, and then prove its unconditional security from information theoretical perspective by computing its key rate and noise tolerance against cloning-based individual attack. The unconditional security proof demonstrates that the higher dimension of quantum system is, the higher key rate can be obtained and the higher noise tolerance is allowed in depolarization channel.