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Chinese Physics Letters

Efficient Multiparty Quantum Secret Sharing with Greenberger–Horne–Zeilinger States

Deng Fu-Guo, Ping Zhou, Xihan Li, Chunyan Li, Hong-Yu Zhou

Published Apr 28, 2006• 56 citations
Publisher

Abstract

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.

DOI
10.1088/0256-307x/23/5/006

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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.
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.
In this paper, we present an (n, n) threshold quantum secret sharing scheme of secure direct communication using Greenberger-Horne-Zeilinger state. The present scheme is efficient in that all the Greenberger-Horne-Zeilinger states used in the quantum secret sharing scheme are used to generate shared secret messages except those chosen for checking eavesdropper. In our scheme, the measuring basis of communication parties is invariable and the classical information used to check eavesdropping needs only the results of measurements of the communication parties. Another nice feature of our scheme is that the sender transmit her secret messages to the receivers directly and the receivers recover the sender's secret by combining their results, different from the QSS scheme whose object is essentially to allow a sender to establish a shared key with the receivers. This feature of our scheme is similar to that of quantum secret direct communication.
A multiparty quantum secret report scheme is proposed with quantum encryption. The boss Alice and her M agents first share a sequence of ( M +1)-particle Greenberger–Horne–Zeilinger (GHZ) states that only Alice knows which state each ( M +1)-particle quantum system is in. Each agent exploits a controlled-not (CNot) gate to encrypt the travelling particle by using the particle in the GHZ state as the control qubit. The boss Alice decrypts the travelling particle with a CNot gate after performing a σ x operation on her particle in the GHZ state or not. After the GHZ states (the quantum key) are used up, the parties check whether there is a vicious eavesdropper, say Eve, monitoring the quantum line, by picking out some samples from the GHZ states shared and measuring them with two measuring bases. After confirming the security of the quantum key, they use the remaining GHZ states repeatedly for the next round of quantum communication. This scheme has the advantage of high intrinsic efficiency for the qubits and total efficiency.
Abstract In this paper, two new efficient multiparty quantum direct secret sharing schemes are proposed via a six-particle GHZ state and Bell measurements. In the first scheme, based on the theory of security cryptanalysis, the secret message of the sender is directly encoded into the transmitted particles, and all the agents can obtain their information by performing bell measurement on the received particles, and then cooperate to recover the information of the sender. In the second scheme, we define a new secret shared coding method by performing local unitary operations on the transmitted particles, then agents perform Bell measurements on their own particles respectively, and feedback the measurement to the dealer. If the agent’s results are matched with the previous coding method, the protocol will work out. In addition, the proposed two schemes have the following common advantages: the sender can send all prepared particles to the receiver, and can send an arbitrary key to the receiver, rather than a random secret key; the proposed schemes do not need to insert any detection sets to detect eavesdropping and can resist both existing attacks and spoofing attacks by dishonest agents. The sender need not to retain any photons, so the sender’s quantum memory could be omitted here.
We propose a new multiparty simultaneous quantum direct communication scheme based on Green–Horne–Zeilinger (GHZ) states and dense coding. For achieving high efficiency without leaking any information, four encoding schemes are prepared in advance. The present scheme has the capacity of transmitting (M + 1)M classical bits per group of M-particle GHZ states when there exist M parties. The technique of rearranging particles makes the legal users coequally exchange their messages in the same length. Both high efficiency and excellent security against the common attacks are virtues of this new scheme.