The quantum secret sharing schemes based on hyperstar access structures

Suchandan Ghosh, Avishek Adhikari

Lei Li, Zhi Li

Quantum secret sharing is one of the core security technologies in the field of quantum communication. Aiming at the problems of high quantum resource consumption and the difficulty in balancing security and efficiency existing in current quantum secret sharing schemes under non-maximal quantum access structure(QAS), this paper focuses on the judgment criteria of non-maximal QAS and the construction methods of efficient and perfect quantum secret sharing schemes on a kind of non-maximal QAS, i.e. hyperstar with three hyperedges. Firstly, we characterizes the forbidden sets and intermediate sets within this non-maximal QAS, and provides a characterization for non-maximal QAS realizable by pure-state encoding. Secondly, the representative element QAS of hyperstar with three hyperedges is defined, which serves as a substructure of this hyperstar QAS, and belongs to non-maximal QAS. Furthermore, we propose a universal, efficient, and perfect quantum secret sharing scheme based on this hyperstar QAS using corresponding classical secret sharing scheme as an auxiliary. By deploying lightweight quantum resources to representative element access structures, the proposed scheme reduces the difficulty in quantum state preparation and distribution, and enhances its security and resource utilization efficiency.

Chen‐Ming Bai, Zhihui Li, Meng-Meng Si +1 more

Chen‐Ming Bai, Sujuan Zhang, Lu Liu

Lei Li, Zhi Li

This paper investigates the construction of efficient quantum secret sharing schemes for quantum access structures based on hypergraphs with three hyperedges. We prove that hypercycles with three hyperedges are quantum access structures if and only if they can be classified into 12 non-isomorphic types under hypergraph isomorphism, and these hypercyclic quantum access structures encompass all four hyperstars with three hyperedges.In prior work, efficient and perfect quantum secret sharing schemes were constructed for hyperstar access structures with three hyperedges using single photons in d -dimensional quantum systems. These schemes correspond to classical perfect secret sharing schemes with optimal information rates. However, for hypercyclic access structures with three hyperedges, the method described above fails to yield classical perfect secret sharing schemes with optimal information rates. In this work, we explicitly construct classical perfect secret sharing schemes with optimal information rates for these access structures by combining Simmons' geometric method with Shamir's threshold scheme. Subsequently, we employ single photons in d-dimensional quantum systems to build perfect QSS schemes upon these classical constructions.We introduce the concept of idealized information rate for minimal access structures in perfect QSS schemes. By extending the notion of efficiency proposed by Cabello [Phys. Rev. Lett., vol. 85, no. 26, p. 5635, 2000] for quantum key distribution protocols to QSS, we define the efficiency of minimally authorized subsets. Furthermore, we establish the relationship between the efficiency of minimally authorized subsets and the idealized information rate of minimal access structures. Finally, we rigorously prove that the QSS schemes constructed in this work achieve the highest efficiency among existing solutions.

Chen‐Ming Bai, Ya‐Xi Shu, Su-Juan Zhang

In this paper, drawing upon quantum state masking theory, we first propose a method that utilizes d-dimensional orthogonal arrays to encode quantum states into a multi-party quantum system. Building upon this foundation, we then design a quantum secret sharing scheme whose security is rooted in the principles of quantum information masking. This scheme is designed based on the hyperstar structure to define the access structure. Additionally, the protocol enables the transmission of arbitrary d-dimensional quantum states through quantum channels constructed using orthogonal arrays, ensuring that only participants within the access structure can recover the secret. We have thoroughly analyzed the security of this scheme against major quantum attacks, including intercept-resend attacks, entangle-measure attacks, and dishonest participant attack. In conclusion, our analysis examines the impact of four common types of noise on this protocol, confirming its immunity to dit-flip noise. Furthermore, we present a comparative analysis of the proposed scheme against existing quantum secret sharing protocols, highlighting its respective advantages.