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Chinese Physics Letters

Cryptanalysis and Improvement of a Quantum Secret Sharing Protocol between Multiparty and Multiparty with Single Photons and Unitary Transformations

Zhen-Chao Zhu, Yuqing Zhang

Published Jun 1, 2010• 11 citations
Publisher

Abstract

In a recent paper [ Chin. Phys. Lett 25(2008)1187 ], a quantum secret sharing scheme between multiparty and multiparty was presented. We show that the protocol is not secure because the last member in Alice's group can illegally obtain most secret messages without introducing any error. Finally, a possible way to avoid the security flaw is suggested.

DOI
10.1088/0256-307x/27/6/060303

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In a recent paper [ Chin. Phys. Lett 25(2008)1187 ], a quantum secret sharing scheme between multiparty and multiparty was presented. We show that the protocol is not secure because the last member in Alice's group can illegally obtain most secret messages without introducing any error. Finally, a possible way to avoid the security flaw is suggested.
We propose a scheme of quantum secret sharing between Alice's group and Bob's group with single photons and unitary transformations. In the protocol, one member in Alice's group prepares a sequence of single photons in one of four different states, while other members directly encode their information on the sequence of single photons via unitary operations; after that, the last member sends the sequence of single photons to Bob's group. Then Bob's, except for the last one, do work similarly. Finally the last member in Bob's group measures the qubits. If the security of the quantum channel is guaranteed by some tests, then the qubit states sent by the last member of Alice's group can be used as key bits for secret sharing. It is shown that this scheme is safe.
Recently, Yan and Gao proposed a quantum secret sharing protocol between multiparty (mmm members in group 1) and multiparty (nnn members in group 2) using a sequence of single photons (Phys. Rev. A \textbf{72}, 012304 (2005)). We find that it is secure if the quantum signal transmitted is only a single photon but insecure with a multi-photon signal as some agents can get the information about the others' message if they attack the communication with a Trojan horse. However, security against this attack can be attained with a simple modification.
We propose a quantum secret sharing protocol between multiparty (mmm members in group 1) and multiparty (nnn members in group 2) using a sequence of single photons. These single photons are used directly to encode classical information in a quantum secret sharing process. In this protocol, all members in group 1 directly encode their respective keys on the states of single photons via unitary operations; then, the last one (the mthm\mathrm{th}mth member of group 1) sends 1∕n1∕n1∕n of the resulting qubits to each of group 2. Thus the secret message shared by all members of group 1 is shared by all members of group 2 in such a way that no subset of each group is efficient to read the secret message, but the entire set (not only group 1 but also group 2) is. We also show that it is unconditionally secure. This protocol is feasible with present-day techniques.
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).
Recently, Gao et al.'s [ Commun. Theor. Phys. 52 (2009) 421 ] multiparty quantum secret sharing (MQSS) protocol with two-photon three-dimensional Bell states was enhanced by Hwang et al. [ Commun. Theor. Phys. 56 (2011) 79 ]. The improved protocol removes some unnecessary unitary operations, devices, and transmissions by the technique of decoy single photons and careful modification. However, in this paper, we investigate the security of the improved protocol and find it is insecure. The eavesdropper can steal all Alice's secret information. Furthermore, a feasible modification to remedy the security loophole is put forward. Our improved protocol provides a basic method to modify a kind of MQSS protocols which cannot resist the collusion attack.