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Physica Scripta

Multiparty quantum secret sharing based on GHZ states

Tzonelih Hwang, Cheng-Chieh Hwang, Chuan-Ming Li

Published Mar 14, 2011• 49 citations
Publisher

Abstract

Gao (2009 Commun. Theor. Phys. 52 421–4) has proposed an efficient multiparty quantum secret sharing (MQSS) with two-photon three-dimensional Einstein–Podolsky–Rosen (EPR) pairs. This work shows that a similar idea can also be used to construct an MQSS using the Greenberger–Horne–Zeilinger (GHZ) states. Compared to other MQSSs using GHZ-related states, the newly proposed protocol is more efficient in the aspect of qubit utilization.

DOI
10.1088/0031-8949/83/04/045004

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Gao (2009 Commun. Theor. Phys. 52 421–4) has proposed an efficient multiparty quantum secret sharing (MQSS) with two-photon three-dimensional Einstein–Podolsky–Rosen (EPR) pairs. This work shows that a similar idea can also be used to construct an MQSS using the Greenberger–Horne–Zeilinger (GHZ) states. Compared to other MQSSs using GHZ-related states, the newly proposed protocol is more efficient in the aspect of qubit utilization.
An efficient multiparty quantum secret sharing scheme is proposed with Greenberger–Horne–Zeilinger (GHZ) states following some ideas in quantum dense coding. The agents take the single-photon measurements on the photons received for eavesdropping check and exploit the four local unitary operations I , σ z , σ x and i σ y to code their message. This scheme has the advantage of high capacity as each GHZ state can carry two bits of information. The parties do not need to announce the measuring bases for almost all the photons, which will reduce the classical information exchanged largely. The intrinsic efficiency for qubits and the total efficiency both approach the maximal values.
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.
We proposed two multiparty quantum secret sharing schemes based on n-particle Greenberger–Horne–Zeilinger-states (GHZ states), which are transformed from Einstein–Podolsky–Rosen pairs by entanglement swapping. In our schemes, the dealer imposes messages by performing local unitary operations (I, σ x, iσ y, σ z) on the n-particle GHZ state she holds, and the agents collaborate to deduce the dealer's messages by performing local unitary operations on their own qubit. The amount of dealer's secret message is positively related with the number of agents. The need of qubits is one-third less than the former schemes and, also, they can be reused for the next new round. The scheme (II) does not have to pre-share the code table, which increases the security without the risk of being stolen.