Verifiable quantum secret sharing scheme based on orthogonal product states

doi:10.1088/1674-1056/ad342a

中国物理B ›› 2024, Vol. 33 ›› Issue (7): 70302-070302.doi: 10.1088/1674-1056/ad342a

Verifiable quantum secret sharing scheme based on orthogonal product states

Chen-Ming Bai(白晨明)†, Lu Liu(刘璐), and Sujuan Zhang(张素娟)

Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China

收稿日期:2023-12-21 修回日期:2024-03-04 接受日期:2024-03-15 出版日期:2024-06-18 发布日期:2024-06-20
通讯作者: Chen-Ming Bai E-mail:baichm@stdu.edu.cn
基金资助:
This work was supported by the National Natural Science Foundation of China (Grant No. 12301590) and the Natural Science Foundation of Hebei Province (Grant No. A2022210002).

Verifiable quantum secret sharing scheme based on orthogonal product states

Chen-Ming Bai(白晨明)†, Lu Liu(刘璐), and Sujuan Zhang(张素娟)

Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China

Received:2023-12-21 Revised:2024-03-04 Accepted:2024-03-15 Online:2024-06-18 Published:2024-06-20
Contact: Chen-Ming Bai E-mail:baichm@stdu.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (Grant No. 12301590) and the Natural Science Foundation of Hebei Province (Grant No. A2022210002).

摘要/Abstract

摘要： In the domain of quantum cryptography, the implementation of quantum secret sharing stands as a pivotal element. In this paper, we propose a novel verifiable quantum secret sharing protocol using the $d$-dimensional product state and Lagrange interpolation techniques. This protocol is initiated by the dealer Alice, who initially prepares a quantum product state, selected from a predefined set of orthogonal product states within the $\mathbb{C}^d \otimes \mathbb{C}^d$ framework. Subsequently, the participants execute unitary operations on this product state to recover the underlying secret. Furthermore, we subject the protocol to a rigorous security analysis, considering both eavesdropping attacks and potential dishonesty from the participants. Finally, we conduct a comparative analysis of our protocol against existing schemes. Our scheme exhibits economies of scale by exclusively employing quantum product states, thereby realizing significant cost-efficiency advantages. In terms of access structure, we adopt a $(t,n)$-threshold architecture, a strategic choice that augments the protocol's practicality and suitability for diverse applications. Furthermore, our protocol includes a rigorous integrity verification mechanism to ensure the honesty and reliability of the participants throughout the execution of the protocol.

关键词: quantum secret sharing, quantum product state, threshold scheme, unitary operations

Abstract: In the domain of quantum cryptography, the implementation of quantum secret sharing stands as a pivotal element. In this paper, we propose a novel verifiable quantum secret sharing protocol using the $d$-dimensional product state and Lagrange interpolation techniques. This protocol is initiated by the dealer Alice, who initially prepares a quantum product state, selected from a predefined set of orthogonal product states within the $\mathbb{C}^d \otimes \mathbb{C}^d$ framework. Subsequently, the participants execute unitary operations on this product state to recover the underlying secret. Furthermore, we subject the protocol to a rigorous security analysis, considering both eavesdropping attacks and potential dishonesty from the participants. Finally, we conduct a comparative analysis of our protocol against existing schemes. Our scheme exhibits economies of scale by exclusively employing quantum product states, thereby realizing significant cost-efficiency advantages. In terms of access structure, we adopt a $(t,n)$-threshold architecture, a strategic choice that augments the protocol's practicality and suitability for diverse applications. Furthermore, our protocol includes a rigorous integrity verification mechanism to ensure the honesty and reliability of the participants throughout the execution of the protocol.

Key words: quantum secret sharing, quantum product state, threshold scheme, unitary operations

中图分类号: (Quantum information)

03.67.-a

03.65.Ud (Entanglement and quantum nonlocality)

Chen-Ming Bai(白晨明), Lu Liu(刘璐), and Sujuan Zhang(张素娟). Verifiable quantum secret sharing scheme based on orthogonal product states[J]. 中国物理B, 2024, 33(7): 70302-070302.

Chen-Ming Bai(白晨明), Lu Liu(刘璐), and Sujuan Zhang(张素娟). Verifiable quantum secret sharing scheme based on orthogonal product states[J]. Chin. Phys. B, 2024, 33(7): 70302-070302.

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Verifiable quantum secret sharing scheme based on orthogonal product states

Verifiable quantum secret sharing scheme based on orthogonal product states

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