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International Conference on Network Communication and Information Security (ICNCIS)

Quantum secret sharing scheme with single quantum state

Wei Li

Published Jan 16, 2025• 1 citation
Publisher

Abstract

A quantum secret sharing (QSS) scheme with single photons was proposed, the trusted third party (TTP) encoded the secret value into conjugate single quantum states, in the revealing phase each participant performs the corresponding unitary operation on the single photon sequence sequentially according to its’ private key, and the participants can recover the secret value only through one round of interaction with the TTP and two round of interactions between themselves, further more any dishonest action and malicious attack can be detected.

DOI
10.1117/12.3052198

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A quantum secret sharing (QSS) scheme with single photons was proposed, the trusted third party (TTP) encoded the secret value into conjugate single quantum states, in the revealing phase each participant performs the corresponding unitary operation on the single photon sequence sequentially according to its’ private key, and the participants can recover the secret value only through one round of interaction with the TTP and two round of interactions between themselves, further more any dishonest action and malicious attack can be detected.
A scheme for three-party quantum secret sharing of a private key is presented with single photons. The agent Bob first prepares a sequence of single photons with two biased bases and then sends them to the boss Alice who checks the security of the transmission with measurements and produces some decoy photons by rearranging the orders of some sample photons. Alice encodes her bits with two unitary operations on the photons and then sends them to the other agent. The security of this scheme is equivalent to that in the modified Bennett–Brassard 1984 quantum key distribution protocol. Moreover, each photon can carry one bit of the private key and the intrinsic efficiency for qubits and the total efficiency both approach the maximal value 100% when the number of the bits in the key is very large.
Based on the Einstein-Podolsky-Rosen (EPR) entangled state and the unitary operation, a quantum secret-sharing (QSS) scheme on access structure is proposed. The participants randomly choose their private keys themselves. Each participant keeps one private key even though he belongs to several qualified subsets. In the recovery, the participants in the qualified subset perform the unitary operations on the EPR pairs, and recover the secret through the Bell-state measurement. Compared to the existing QSS schemes on (n, n) or (t, n) structure, the proposed scheme on access structure is more flexible in practice.
A d-dimensional quantum state secret sharing scheme without entanglement is proposed. In the proposed scheme, the dealer generates a single quantum state in d-dimensional Hilbert space, and performs the Pauli unitary operation on the quantum state according to the private keys of the participants. In the recovery phase, each participant performs the Pauli operation on the quantum state according to his private key, and the last participant will recover the original quantum state. Compared to the existing quantum secret sharing schemes, the main contribution of the proposed scheme is that the quantum state can be shared without the entanglement, so the sharing of the quantum state is more practical.
Most semi-quantum secret sharing protocols are suitable for the application with three participants. Based on the n-level states, a multiparty semi-quantum secret sharing protocol is proposed. Compared with similar protocols, it has the merits as follows. (1) The dealer only needs to prepare the single photon sequence without using any product state or entangle state. (2) To share a secret, the classical parties need not have the ability of measurement. They only need to reorder the photon sequence and send it to the receiver. (3) The dealer knows nothing about any agent’s secret shadow. Therefore, it is infeasible for the dealer to impersonate the classical participant to pool the secret shadow during the secret recovering phase. (4) Theoretically, the qubit efficiency of the proposed protocol is asymptotically 100%. The protocol is secure against famous attacks such as intercept-resend attack, measurement-resend attack and entangle-measure attack.
The security of a secret sharing protocol is compromised if one or more dishonest participants can reconstruct the secret by deviating from the prescribed protocol, particularly when such malicious behavior remains undetected. Semi-Quantum Secret Sharing (SQSS) is a variant of secret sharing in which the participants possess only classical capabilities, such as preparing and measuring qubits in the computational (ZZZ) basis, while a quantum-capable third party assists the dealer in generating and distributing quantum shares of a classical secret. The limited quantum capabilities of the participants in SQSS protocols may introduce vulnerabilities to collusion attacks, enabling an assisting quantum third party, in collaboration with a dishonest classical participant, to jointly recover the secret even without detection. In this work, we propose a novel SQSS protocol that eliminates this vulnerability and achieves information-theoretic security against collusion attacks. We further prove that the proposed protocol is secure against a broad class of external and internal attacks. Finally, a comparative analysis demonstrates that our construction advances existing SQSS protocols by simultaneously optimizing qubit efficiency, involves a classical dealer, and resilience against DCNA attacks using basic Bell states.
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.