Multi-party semi-quantum secret sharing protocol based on measure-flip and reflect operations

Semi-quantum secret sharing (SQSS) protocols serve as fundamental frameworks in quantum secure multi-party computations, offering the advantage of not requiring all users to possess intricate quantum devices. However, current SQSS protocols mainly cater to bipartite scenarios, with few protocols suitable for multi-party scenarios. Moreover, the multi-party SQSS protocols face limitations such as low qubit efficiency and inability to share deterministic secret information. To address this gap, this paper proposes a multi-party SQSS protocol based on multi-particle GHZ states. In this protocol, the quantum user can distribute the predetermined secret information to multiple classical users with limited quantum capabilities, and only through mutual cooperation among all classical users can the correct secret information be reconstructed. By utilizing measure-flip and reflect operations, the transmitted multi-particle GHZ states can all contribute keys, thereby improving the utilization of transmitted particles. Then, security analysis shows that the protocol's resilience against prevalent external and internal threats. Additionally, employing IBM Qiskit, we conduct quantum circuit simulations to validate the protocol's accuracy and feasibility. Finally, compared to similar studies, the proposed protocol has advantages in terms of protocol scalability, qubit efficiency, and shared message types.