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Communications in Theoretical Physics

Sequential Quantum Secret Sharing Using a Single Qudit*

Chen‐Ming Bai, Zhihui Li, Yongming Li

Published May 1, 2018• 17 citations
Publisher

Abstract

Abstract In this paper we propose a novel and efficient quantum secret sharing protocol using d-level single particle, which it can realize a general access structure via the thought of concatenation. In addition, Our scheme includes all advantages of Tavakoli’s scheme [Phys. Rev. A 92 (2015) 030302(R)]. In contrast to Tavakoli’s scheme, the efficiency of our scheme is 1 for the same situation, and the access structure is more general and has advantages in practical significance. Furthermore, we also analyze the security of our scheme in the primary quantum attacks.

DOI
10.1088/0253-6102/69/5/513

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Quantum secret sharing (QSS) protocols between NNN players, for sharing classical secrets, either use multipartite entangled states or use sequential manipulation of single ddd-level states only when ddd is prime (A. Tavakoli et al., arXiv:1501.05582). We propose a sequential scheme which is valid for any value of ddd. In contrast to A. Tavakoli et al. whose efficiency (number of valid rounds) is 1d\frac{1}{d}d1​, the efficiency of our scheme is 12\frac{1}{2}21​ for any ddd. This, together with the fact that in the limit $d\ensuremath{\longrightarrow}\ensuremath{\infty}$ the scheme can be implemented by continuous variable optical states, brings the scheme into the domain of present day technology.
(ttt, nnn) Threshold Quantum Secret Sharing based on a Single ddd-level Quantum System
A (ttt, nnn) threshold quantum secret sharing (QSS) is proposed based on a single ddd-level quantum system. It enables the (ttt, nnn) threshold structure based on Shamir's secret sharing and simply requires sequential communication in the ddd-level quantum system to recover secret. Besides, the scheme employs an additional qudit to detect cheats and eavesdropping during secret reconstruction, and allows a participant to use the share repeatedly. Analyses show that the proposed scheme is resistant to typical attacks. The scheme is scalable in the number of participants and easier to realize compared to related schemes. More generally, our scheme also presents a generic method to construct new (ttt, nnn) threshold QSS schemes based on ddd-level quantum system with other classical threshold secret sharing.
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Abstract In the paper (EPJ Quant. Technol. 10:29, 2023), Kuo et al. proposed a multiparty quantum secret sharing protocol based on a novel structure and single qubits. Owing to the absence of an entanglement state, the proposed protocol is more practical than other quantum secret sharing protocols which use entanglement properties. Therefore, we study the security of the proposed protocol and find there exists a security loophole in the n-party ( n≥4n\geq 4n≥4 n ≥ 4 ) secret sharing case in it, that is, two dishonest agents can collude to obtain (part of) Alice’s secret without the help of the other agents. In order to overcome the security loophole, we give an improved protocol and make a security analysis for it. By calculating, the qubit efficiency of the three-party case in it is equal to 18\frac{1}{8}81​ 1 8 , which is higher than that in Hillery et al.’s protocol (Phys. Rev. A 59:1829, 1999).