Efficient mediated semi-quantum key distribution

Highlights

• An efficient mediated semi-quantum key distribution protocol is proposed.

• The quantum capability required by TP is reduced.

• TP only needs to prepare and measure qubits in the $X$ basis.

Abstract

Mediated semi-quantum key distribution (MSQKD) allows two “classical” participants to establish a secret key with the help of an untrusted quantum third party (TP). In all existing MSQKD protocols, the quantum capability required by TP is high and thus it needs much cost in a real implementation. In this paper, we propose an efficient MSQKD protocol, where TP only needs to prepare and measure qubits in the $X$ basis and two “classical” participants just have the ability to prepare and measure qubits in the $Z$ basis. Compared with other similar MSQKD protocols, the proposed protocol reduces the capability requirements of TP without sacrificing the qubit efficiency.

Introduction

Quantum key distribution (QKD) allows two quantum participants to establish a secret key securely by using the principles of quantum mechanics. Since the first QKD protocol was proposed by Bennett and Brassard [1], various QKD protocols are proposed subsequently [2], [3], [4], [5], [6], [7], [8], [9], [10]. However, in all these QKD protocols, both participants are required to have much quantum capability such as preparing and measuring states in two different bases. Actually quantum resources are not easy to obtain under current technology and it may be unnecessary for both two participants to own many quantum resources to share a key. In 2007, Boyer et al. proposed the first semi-quantum key distribution (SQKD) protocol which reduced the quantum capability of one participant compared with QKD protocols [11]. The SQKD protocol allows a “classical” participant with limited quantum capability to share a secret key securely with a trusted quantum participant. A “classical” participant means one can only perform some of the following four operations: (1) preparing qubits in the basis {$|0〉,|1〉$}, (2) measuring qubits in the basis {$|0〉,|1〉$}, (3) reflecting qubits without disturbance, and (4) reordering the qubits. In 2009, Boyer et al. presented a novel SQKD protocol by employing four quantum states as resource states [12], each of which was randomly prepared in the $Z$ or $X$ basis. In the same year, five SQKD protocols were proposed by Zou et al. with less than four quantum states [13]. Then, Wang et al. put forward a SQKD protocol which employed entangled states as resource states and improved the qubit efficiency to 50% [14]. In 2014, Yu et al. proposed an authenticated SQKD protocol which used Bell states and was unnecessary to have access to authenticated classical channels [15]. Since then, many SQKD protocols have been proposed [16], [17], [18], [19], [20], [21], [22], [23], [24] and the security of them has been investigated [25], [26], [27], [28], [29], [30], [31]. In addition, other kinds of semi-quantum cryptographic protocols were also studied, such as semi-quantum secret sharing [32], [33], [34], semi-quantum communication [35], [36], and semi-quantum private comparisons [37], [38]. But in all the semi-quantum cryptographic protocols mentioned above, only one of the two participants is “classical”.

A mediated semi-quantum key distribution (MSQKD) protocol permits two “classical” participants to share a secret key securely with the help of an untrusted quantum third party (TP). The main difference between the QKD, SQKD, and MSQKD protocol is that the MSQKD protocol is more suitable when both two participants owning limited quantum capability want to share a key. In 2015, Krawec proposed a MSQKD protocol where TP required to prepare Bell states and two “classical” participants need to measure qubits in the $Z$ basis [39]. In 2018, Liu et al. removed the quantum measurement capability of both “classical” participants and presented a MSQKD protocol [40]. But TP needs to prepare Bell states as resource states. In 2019, Lin et al. proposed a MSQKD protocol which used single photons as resource states [41]. But the qubit efficiency of this protocol was only $\frac{1}{24}$. Recently, Massa et al. proposed a novel MSQKD protocol where “classical” participants just need to have access to superimposed single photon as a feasible quantum resource and realized it in the experiment [42].

In this paper, we propose an efficient MSQKD protocol where the quantum capability of TP will be lessened and two “classical” participants still only need to make measurements in the $Z$ basis and produce quantum states $|0〉$ and $|1〉$. The rest part of the paper is organized as follows. In Section 2, a MSQKD protocol is proposed. Section 3 analyzes the security of the proposed protocol in the ideal situation. Comparisons among similar MSQKD protocols are made in Section 4. The last section concludes the paper.