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Standard (k, n)-threshold hierarchical quantum secret sharing

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Hierarchical quantum secret sharing has important theoretical value and realistic significance in quantum secret sharing schemes. In order to expand the access structure of participants and improve the performance of schemes, this paper presents a standard (k, n)-threshold hierarchical quantum secret sharing scheme. Firstly, we construct a specific pair of orthogonal entangled states and use their local distinguishable property to achieve the standard (k, n)-threshold structure at each level in the hierarchy, which not only enhances the practical value of hierarchical quantum secret sharing schemes, but also reduces the computational expenses. Secondly, our scheme does not require any quantum operations to recover the secret during the reconstruction phase, which greatly reduces the quantum computational complexity. Finally, performance analysis shows that our scheme owns higher information efficiency compared with the existing schemes. Security analysis shows that our scheme is resistant to not only a series of typical external attacks but also both personal attacks from dishonest internal participants and collusion attacks.
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Quantum Information Processing (2024) 23:168
https://doi.org/10.1007/s11128-024-04378-x
Standard (k,n)-threshold hierarchical quantum secret
sharing
Fulin Li1,2 ·Qingao Wu1·Changlu Lin4·Shixin Zhu1,3
Received: 27 December 2023 / Accepted: 5 April 2024 / Published online: 3 May 2024
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024
Abstract
Hierarchical quantum secret sharing has important theoretical value and realistic sig-
nificance in quantum secret sharing schemes. In order to expand the access structure of
participants and improve the performance of schemes, this paper presents a standard
(k,n)-threshold hierarchical quantum secret sharing scheme. Firstly, we construct a
specific pair of orthogonal entangled states and use their local distinguishable prop-
erty to achieve the standard (k,n)-threshold structure at each level in the hierarchy,
which not only enhances the practical value of hierarchical quantum secret sharing
schemes, but also reduces the computational expenses. Secondly, our scheme does not
require any quantum operations to recover the secret during the reconstruction phase,
which greatly reduces the quantum computational complexity. Finally, performance
analysis shows that our scheme owns higher information efficiency compared with the
existing schemes. Security analysis shows that our scheme is resistant to not only a
This research was supported by the National Natural Science Foundation of China (Nos. U21A20428,
61972126, 12171134).
BQingao Wu
wqa12170@163.com
Fulin Li
lflsxx66@163.com
Changlu Lin
cllin@fjnu.edu.cn
Shixin Zhu
zhushixinmath@hfut.edu.cn
1School of Mathematics, HeFei University of Technology, Hefei 230009, China
2College of Mathematics and Physics, Xinjiang Agricultural University, Ürümqi 830052, China
3Intelligent Interconnected Systems Laboratory of Anhui Province, Hefei, China
4School of Mathematics and Statistics, Key Laboratory of Analytical Mathematics and Applications
(Ministry of Education), Fujian Normal University, Fuzhou 350117, China
123
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
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