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arXiv:0801.0177 · Journal of Physics A Mathematical and Theoretical

Three-partyd-level quantum secret sharing protocol

Dong Pyo Chi, Jeong Woon Choi, Jeong San Kim, Tae‐Wan Kim, Soojoon Lee

Published Jun 5, 2008• 6 citations
arXivHTMLPDF

Abstract

We develop a three-party quantum secret sharing protocol based on arbitrary dimensional quantum states. In contrast to the previous quantum secret sharing protocols, the sender can always control the state, just using local operations, for adjusting the correlation of measurement directions of three parties and thus there is no waste of resource due to the discord between the directions. Moreover, our protocol contains the hidden value which enables the sender to leak no information of secret key to the dishonest receiver until the last steps of the procedure.

DOI
10.1088/1751-8113/41/25/255309

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We develop a three-party quantum secret sharing protocol based on arbitrary dimensional quantum states. In contrast to the previous quantum secret sharing protocols, the sender can always control the state, just using local operations, for adjusting the correlation of measurement directions of three parties and thus there is no waste of resource due to the discord between the directions. Moreover, our protocol contains the hidden value which enables the sender to leak no information of secret key to the dishonest receiver until the last steps of the procedure.
Inspired by quantum secure direct communication, a three-party quantum secret sharing approach is proposed. In the preparation phase, the sender shares a GHZ state among users. After she ensures about the security of the channel, she generates an auxiliary GHZ state and keeps it. Then she encodes three-bit information on the GHZ states, by applying the appropriate gates on her qubits. In the decoding phase, the three parties measure their qubits. The receivers achieve no information on the encoded message individually and just when they know the others' measurement results have access to the secret message. The security of the preparation phase against various attacks is investigated. Since no qubits carrying the message are transmitted, the protocol is completely secure, if the perfect quantum channel is used. The proposed approach has a better efficiency as compared to the previous ones.
Controllable quantum secret sharing scheme on three -party entangled states can be implemented in realistic,high quantum network with three quantum units.S1,S2,S3 construct a three-party entangled state.S1 prepares 2N GHZ-like state,and sends S2 and S3 the last two particles,respectively.At last,S1,S2,S3 check together,derive the private key string through hidden value α.The scheme analyzes the security of the protocol for two cases of attacks,where one is an eavesdropping by Eve,and the other is the intercept-and-resend attack by a dishonest person.The three-party entangled state guarantees the security of the controllable secret sharing scheme.
Inspired by quantum secure direct communication and quantum dense coding, we present a three-party quantum secret sharing (QSS) scheme by quantum teleportation. After performing the rectilinear basis or diagonal basis measurement randomly for the eavesdropping check to ensure the security of the quantum channel, the sender encodes the secret messages directly on a series of Einstein-Podolsky-Rosen (EPR) pairs and transmits them to the receivers by quantum teleportation. Neither of the receivers can decode the secret messages on his own even if they collaborate. Only the two receivers combine their measurement results with the sender's result, can they recover the secret messages. In this scheme, one qubit can encode two bits of classical information because quantum dense coding is introduced. Using quantum teleportation, the distinct advantage of this scheme is that there is not the transmission of qubits carrying the secret messages in the quantum channel, it is absolutely secure for QSS if a perfect channel is used.
This study proposes quantum secret sharing protocols using product states. The first two protocols adopt the quantum key distribution protocol using product states [Guo et al.Phys. Rev. A 64, 042301 (2001)]. In these two protocols, the sender does not reveal any information about the qutrits until confirming that each receiver has received a qutrit. This study also considers the security and some possible eavesdropping strategies. In the third proposed protocol, three-level Bell states are exploited for qutrit preparation via nonlocality swapping.
Quantum secret sharing (QSS) is a cryptographic protocol that utilizes fundamental principles of quantum mechanics to securely distribute and reconstruct secret information among multiple participants. Most existing protocols rely on entangled states (such as Bell and GHZ states), but in practical applications. The preparation of entangled state is constrained by a short quantum coherence time, low state fidelity, etc., which makes it difficult to implement entangled resource-dependent QSS protocols. In this work, a novel practical and verifiable multi-party QSS protocol is proposed based on orthogonal product states, which are easier to prepare than entangled states. During the protocol preparation stage, the secret distributor first converts pre-shared classical secret information into the corresponding orthogonal product states according to the encoding rules, and pre-shares a communication key with participants via quantum key distribution (QKD), which is used to hide the initial quantum sequence information through subsequent particle transformation operations. After preparing the orthogonal product states, the distributor reorganizes the particles by position, extracting particles at the same position from each state to form new sequences, shuffling their order, then applying Hadamard operations using a pre-shared key, inserting decoy particles, and sending the sequences to the participants. After receiving it, participants conduct eavesdropping detection, use the same key for the inverse transformations, retain one particle from each sequence, and sequentially pass the remaining particles until the last participant receives a complete set, triggering state verification with the arbiter distributor. If the verification is successful, the particles will be returned to the first participant and the return stage will follow the same procedure. Only after both the transmission and return stage verifications have passed, will the distributor reveal the initial particle positions, allowing participants to collaboratively reconstruct the secret. In the protocol, the secret distributor acts as an arbitrator to verify the particle state information together with participants at designated points (the end of the transmission stage and the end of the return stage) in order to determine whether the particle-state information is error-free during transmission. If the verification fails at either stage, the protocol will be terminated immediately. Meanwhile, considering that the number of participants may change during the execution of the protocol, a dynamic scheme for personnel changes is designed to ensure the flexibility of the protocol. Through the analysis of possible internal and external attacks, It can be proven that our protocol can effectively resist the existing common attack. Using Qiskit simulation experiments, the core quantum procedures of the protocol can be successfully modeled. The experimental results provide strong computational validation of the theoretical feasibility of the protocol.