Quantum secret sharing (QSS) is a cryptographic protocol that leverages quantum mechanics to distribute a secret among multiple parties. With respect to the classical counterpart, in QSS the secret is encoded into quantum states and shared by a dealer such that only an authorized subsets of participants, i.e., the players, can reconstruct it. Several state-of-the-art studies aim to transpose classical Secret Sharing into the quantum realm, while maintaining their reliance on traditional network topologies (e.g., star, ring, fully-connected) and require that all the n players calculate the secret. These studies exploit the Greenberger-Horne-Zeilinger (GHZ) state, which is a type of maximally entangled quantum state involving three or more qubits. However, none of these works account for redundancy, enhanced security/privacy features or authentication mechanisms able to fingerprint players. To address these gaps, in this paper we introduce a new concept of QSS which leans on a generic distributed quantum-network, based on a threshold scheme, where all the players collaborate also to the routing of quantum information among them. The dealer, by exploiting a custom flexible weighting system, takes advantage of a newly defined quantum Dijkstra algorithm to select the most suitable subset of t players, out of the entire set on n players, to involve in the computation. To fingerprint and authenticate users, CRYSTAL-Kyber primitives are adopted, while also protecting each player's privacy by hiding their identities. We show the effectiveness and performance of the proposed protocol by testing it against the main classical and quantum attacks, thereby improving the state-of-the-art security measures.

翻译：量子秘密共享（QSS）是一种利用量子力学原理将秘密分发给多方参与者的密码学协议。相较于经典对应方案，在QSS中，秘密被编码为量子态并由分发者共享，使得只有经授权的参与者子集（即玩家）能够重构秘密。当前多项前沿研究致力于将经典秘密共享转换至量子领域，但仍依赖传统网络拓扑结构（如星型、环型、全连接型），且要求全部n名玩家参与秘密计算。这些研究利用格林伯格-霍恩-蔡林格（GHZ）态——一种包含三个或更多量子比特的最大纠缠量子态。然而，现有方案均未考虑冗余机制、增强型安全/隐私特性或能够对玩家进行身份标识的认证机制。为填补这些空白，本文提出一种基于通用分布式量子网络的新型QSS框架，该框架采用阈值方案，所有玩家共同参与量子信息的路由传输。分发者通过自定义的灵活权重系统，利用新定义的量子Dijkstra算法，从全体n名玩家中筛选出最合适的t名玩家子集参与计算。为标识和认证用户，本方案采用CRYSTAL-Kyber密码原语，同时通过隐藏玩家身份保护个体隐私。我们通过抵御主流经典与量子攻击的测试，验证了所提协议的有效性与性能，从而提升了现有安全措施的技术水平。