2004/05/11 by Xiao Li, Li Xiao, Gui Lu Long +3 · 5 citations
Computer Science · Mathematics · Physics and Astronomy · #Access structure #Basis (linear algebra) #Computer science #Computer security #Cryptography #Discrete mathematics #Encryption #Homomorphic secret sharing #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum cryptography #Quantum information #Quantum mechanics #Scheme (mathematics) #Secret sharing #Set (abstract data type) #Theoretical computer science #Verifiable secret sharing #quant-ph
paper · pdf · doi:10.1103/physreva.69.052307
published as PHYSICAL REVIEW A 69, 052307 (2004) · 7 pages
openalex publication_date 2004/05/11 · arxiv created 2004/05/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this work, we generalize the quantum-secret-sharing scheme of Hillery, Bu\ifmmode \checkz\else \vz\fiek, and Berthiaume [Phys. Rev. A 59, 1829 (1999)] into arbitrary multiparties. Explicit expressions for the shared secret bit is given. It is shown that in the Hillery-Bu\ifmmode \checkz\else \vz\fiek-Berthiaume quantum-secret-sharing scheme the secret information is shared in the parity of binary strings formed by the measured outcomes of the participants. In addition, we have increased the efficiency of the quantum-secret-sharing scheme by generalizing two techniques from quantum key distribution. The favored-measuring-basis quantum-secret-sharing scheme is developed from the Lo-Chau-Ardehali technique [H. K. Lo, H. F. Chau, and M. Ardehali, e-print quant-ph∕0011056] where all the participants choose their measuring-basis asymmetrically, and the measuring-basis-encrypted quantum-secret-sharing scheme is developed from the Hwang-Koh-Han technique [W. Y. Hwang, I. G. Koh, and Y. D. Han, Phys. Lett. A 244, 489 (1998)] where all participants choose their measuring basis according to a control key. Both schemes are asymptotically 100% in efficiency, hence nearly all the Greenberger-Horne-Zeilinger states in a quantum-secret-sharing process are used to generate shared secret information.