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Physical Review A

Comment on “Quantum secret sharing between multiparty and multiparty without entanglement”

Chuan-Ming Li, Chi-Chao Chang, Tzonelih Hwang

Published Jan 6, 2006• 35 citations
Publisher

Abstract

Recently, Yan and Gao [Phys. Rev. A 72, 012304 (2005)] presented a quantum secret sharing protocol which allows a secret message to be shared between two groups of parties ($m$ parties in group 1 and $n$ parties in group 2). Their protocol is claimed to be secure that, except with the cooperation of the entire group 1 or group 2, no subgroup of either group 1 or group 2 can extract the secret message. However, this study points out that the $m\text{th}$ party (the last party to process the quantum state) of group 1 can maliciously replace the secret message with an arbitrary message without the detection of the other parties.

DOI
10.1103/physreva.73.016301

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Recently, Yan and Gao [Phys. Rev. A 72, 012304 (2005)] presented a quantum secret sharing protocol which allows a secret message to be shared between two groups of parties (mmm parties in group 1 and nnn parties in group 2). Their protocol is claimed to be secure that, except with the cooperation of the entire group 1 or group 2, no subgroup of either group 1 or group 2 can extract the secret message. However, this study points out that the mthm\text{th}mth party (the last party to process the quantum state) of group 1 can maliciously replace the secret message with an arbitrary message without the detection of the other parties.
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.
This paper analyzes the security of a quantum secret sharing protocol between multiparty and multiparty, which was proposed by Yan and Gao. We show that this protocol is not secure because an external attacker can obtain the secret message shared by the two groups, making use of entanglement swapping. There are two reasons leading to this result. Firstly, the messages, which are transmitted on the quantum and classical channels, are not protected by message authentication. Secondly, the last participant in group 1 knows more information about the shared secret by the two groups. This result shows that there are some hidden security loopholes in this kind of quantum secret sharing protocols.
Security of a quantum secret sharing of quantum state protocol proposed by Guo et al. [Chin. Phys. Lett. 25 (2008) 16] is reexamined. It is shown that an eavesdropper can obtain some of the transmitted secret information by monitoring the classical channel or the entire secret by intercepting the quantum states, and moreover, the eavesdropper can even maliciously replace the secret message with an arbitrary message without being detected. Finally, the deep reasons why an eavesdropper can attack this protocol are discussed and the modified protocol is presented to amend the security loopholes.
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.