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IEEE Advanced Information Technology, Electronic and Automation Control Conference (IAEAC)

A new semi-quantum key distribution protocol with high efficiency

Wei Liu, Huaijun Zhou

Published Oct 1, 2018• 2 citations
Publisher

Abstract

Boyer et al put forward the first semi-quantum key distribution (BKM2007), which is completely robust while one side is limited. However, its efficiency is not satisfactory. In this paper, we present a high-efficient semi-quantum key distribution. The efficiency for qubits is approximately 50% while that is approximately 25% in the BKM2007 protocol, which means that the sifted key proportion of the SQKD protocol is double as that in the BKM2007 protocol. Furthermore, the proportion of information bits in our SQKD protocol is not lower than that of the BKM2007 protocol. Analysis shows that our protocol is still robust.

DOI
10.1109/iaeac.2018.8577673

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•Apr 24, 2020•1 citation
Boyer et al put forward the first semi-quantum key distribution (BKM2007), which is completely robust while one side is limited. However, its efficiency is not satisfactory. In this paper, we present a high-efficient semi-quantum key distribution. The efficiency for qubits is approximately 50% while that is approximately 25% in the BKM2007 protocol, which means that the sifted key proportion of the SQKD protocol is double as that in the BKM2007 protocol. Furthermore, the proportion of information bits in our SQKD protocol is not lower than that of the BKM2007 protocol. Analysis shows that our protocol is still robust.
Recently Boyer et al. [Phys. Rev. Lett. 99, 140501 (2007)] suggested the idea of semiquantum key distribution (SQKD) in which Bob is classical and they also proposed a semiquantum key distribution protocol (BKM2007). To discuss the security of the BKM2007 protocol, they proved that their protocol is completely robust. This means that nonzero information acquired by Eve on the information string implies the nonzero probability that the legitimate participants can find errors on the bits tested by this protocol. The BKM2007 protocol uses four quantum states to distribute a secret key. In this paper, we simplify their protocol by using less than four quantum states. In detail, we present five different SQKD protocols in which Alice sends three quantum states, two quantum states, and one quantum state, respectively. Also, we prove that all the five protocols are completely robust. In particular, we invent two completely robust SQKD protocols in which Alice sends only one quantum state. Alice uses a register in one SQKD protocol, but she does not use any register in the other. The information bit proportion of the SQKD protocol in which Alice sends only one quantum state but uses a register is the double as that in the BKM2007 protocol. Furthermore, the information bit rate of the SQKD protocol in which Alice sends only one quantum state and does not use any register is not lower than that of the BKM2007 protocol.
Semi-quantum key distribution (SQKD) can share secret keys by using less quantum resource than its fully quantum counterparts, and this likely makes SQKD become more practical and realizable. In this paper, we present a new SQKD protocol by introducing the idea of B92 into semi-quantum key distribution and prove its unconditional security. In this protocol, the sender Alice just sends one qubit to the classical Bob and Bob just prepares one state in the preparation process. Indeed the classical user's measurement is not necessary either. This protocol can reduce some quantum communication and make it easier to be implemented. It can be seen as the semi-quantum version of B92 protocol, comparing to the protocol BKM2007 as the semi-quantum version of BB84 in fully quantum cryptography. We verify it has higher key rate and therefore is more efficient. Specifically we prove it is unconditionally secure by computing a lower bound of the key rate in the asymptotic scenario from information theory aspect. Then we can find a threshold value of errors such that for all error rates less than this value, the secure key can be established between the legitimate users definitely. We make an illustration of how to compute the threshold value in case of the reverse channel is a depolarizing one with parameter ppp. Though the threshold value is a little smaller than those of some existed SQKD protocols, it can be comparable to the B92 protocol in fully quantum cryptography.
Quantum cryptography has attracted much attention in recent years. In most existing quantum cryptographic protocols, players usually need the full quantum power of generating, manipulating or measuring quantum states. Semiquantum cryptography was proposed to deal with the issue that some players require only partial quantum power, such as preparing or measuring quantum states in the classical basis, which simplifies the implementations of quantum cryptography. However, the efficiency of the existing semiquantum cryptographic protocols was relatively low from a practical point of view. In this paper, we devise some new semiquantum key distribution (SQKD) protocols which highly improve the efficiency of the most well-known SQKD protocols [Phys. Rev. Lett. 99, 140501 (2007) & Phys. Rev. A 79, 052312 (2009)]. By letting players select their actions asymmetrically, the efficiency of our new protocols can be made asymptotically close to 100%. Besides, one of our proposed protocols also utilizes the discarded X-SIFT bits in the original SQKD protocol, which further improves the efficiency of SQKD. We prove that the proposed SQKD protocols are completely robust against the most general attack.
Unconditionally secure key distribution is impossible using classical communication only. However, by providing Alice and Bob with quantum capable hardware the task becomes possible. How quantum does a protocol need to be, though, in order to gain this advantage? In 2007, Boyer et al., proposed "semi-quantum key distribution" where only Alice need be quantum while Bob need only limited classical" capabilities. Several protocols were proposed and proven secure in the perfect qubit scenario" but not necessarily against realistic attacks (with one exception being recently published in (PRA 96 062335)). In this paper, we devise a new SQKD protocol and analyze its security against certain practical attacks.
Unlike purely classical communication, unconditionally secure key distribution is possible if Alice and Bob are both equipped with quantum hardware. The degree to which a protocol needs to be quantum is not only an interesting theoretical question, but also important for practical implementations. Indeed, one may wish to construct cheaper devices, or compensate for device malfunction. In this sense, studying limited resource QKD protocols is an important problem. One direction to studying this is the semi-quantum model introduced by Boyer et al. in 2007 (PRL 99 140501). Several provably secure semi-quantum protocols were put forth. However, most of these protocols were proven secure in the perfect qubit scenario and not necessarily against practical attacks. Only recently, starting with seminal work of Boyer, Katz, Liss, and Mor in (PRA 96 062335) has research in the field of semi-quantum cryptography considered practical devices and imperfections, such as multi photon sources and imperfect detectors. In this work, we present a new SQKD protocol based on an Extended B92 protocol which is able to counter certain practical attacks. Furthermore, the techniques we use may see broad application to other limited-resource (S)QKD protocols.