基于偶数维上单量子系统的秘密共享方案

量子电子学报

基于偶数维上单量子系统的秘密共享方案

白海艳, 李志慧, 郝娜

陕西师范大学数学与信息科学学院，陕西西安710119

出版日期:2019-03-28 发布日期:2019-03-20
通讯作者: 李志慧E-mail：lizhihui@snnu.edu.cn
作者简介:白海艳（1992-），女，陕西榆林人，研究生，主要从事有限域和密码学方面的研究。E-mail：2794383583@qq.com
基金资助:
Supported by the National Natural Science Foundation of China (国家自然科学基金资助项目,61373150，61602291), The Fundamental Research Funds for the Central Universities (中央高校基本科研业务费专项资金资助, GK201603087)

Secret sharing scheme based on even-dimensional single-quantum system

BAI Hai-yan，LI Zhi-hui，HAO Na

College of Mathematics and Information science, Shaanxi Normal University, Xi’an 710119, China

Published:2019-03-28 Online:2019-03-20

摘要/Abstract

摘要： (陕西师范大学数学与信息科学学院，陕西西安710119) 摘要: Tavakoli等人利用奇素数维量子系统上互相无偏基以及基上酉变换的循环性质,设计了一个基于互相无偏基上的维单量子系统的秘密共享方案。文中首先构造了偶数维量子系统上的一类标准正交基，并给出相应结论，然后利用这类标准正交基和基上酉变换的性质提出了一个量子门限秘密共享方案。该方案与奇素数维系统上的量子秘密共享方案相比，在测量方面的有效性提高为原来的倍。作为特例，给出了时对应的基，酉阵及对应方案，最后就该方案相关的攻击进行了安全性讨论。

关键词: 量子光学, 量子秘密共享方案, 互相无偏基, 门限方案

Abstract: Tavakoli et al. used the cyclic property of the mutually unbiased basis and unitary transformations on it for the odd prime dimension, and designed a secret sharing scheme for d dimensional single quantum systems based on the mutually unbiased basis.Firstly, the class of standard orthogonal basis on even dimensional quantum systems is constructed, and relevant conclusions are given, and then an threshold quantum secret sharing scheme based on the properties of the basis and unitary transformations on it is proposed. In contrast to Tavakoli’s scheme, the measurement efficiency of the proposed scheme has been doubled. And here are the corresponding basis, unitary matrix and related results about for illustration. Finally, the security of scheme related attacks is discussed.

Key words: quantum optics, quantum secret sharing scheme, mutually unbiased basis, threshold scheme

白海艳, 李志慧, 郝娜. 基于偶数维上单量子系统的秘密共享方案[J]. 量子电子学报.

BAI Hai-yan，LI Zhi-hui，HAO Na. Secret sharing scheme based on even-dimensional single-quantum system[J]. Chinese Journal of Quantum Electronics.

参考文献

[1] Cleve R, Gottesman D, Lo H K. How to Share a quantum Secret[J]. Physical Review Letters, 1999, 83(3): 648-651. [2] Hillery M, Buzek V, and Berthiaume A. Quantum secret sharing[J]. Physical Review A, 1998, 59(3): 1829-1834. [3] Cheng Zi, Jin Lirong, Shi Jinjing. (k,n) Threshold Quantum Secret Sharing Scheme Based on the Generation of Reed Solomon Code[J]. Netinfo Security(信息网络安全), 2016(4): 44-49(in Chinese). [4] Schmid C, Trojek P, Bourennane M, et al. Experimental single qubit quantum secret sharing[J]. Physical Review Letters, 2005, 95(23): 230505. [5] Bai Chenming, Li Zhihui, Si Mengmeng, et al. Quantum secret sharing for a general quantum access structure[J]. European Physical Journal D, 2017, 71(10): 255. [6] Liu Linyao, Hu Mengjun, Lv Hongjun, et al. Quantum key distribution protocol based on any Bell states[J]. Chinese Journal of Quantum Electronics(量子电子学报), 2013, 30(4): 439-444(in Chinese). [7] Xiao Li, Long Guilu, Deng Fuguo, et al. Efficient multiparty quantum-secret-sharing schemes[J]. Physics, 2004, 69(5): 521-524. [8] Gottesman D. On the Theory of Quantum Secret Sharing[J]. Physical Review A, 2012, 61(4). [9] Wang Jindong, Zhang Zhiming. Unconditional security of quantum key distribution based on practical devices[J].Chinese Journal of Quantum Electronics(量子电子学报), 2014, 31(4): 449-458(in Chinese). [10]Chen Xiaofeng, Liu Xiaofen. Mutual authenticated multiparty quantum key distribution based on single particle state[J]. Chinese Journal of Quantum Electronics(量子电子学报), 2017, 34(3): 369-373(in Chinese). [11]Wootters W K, Fields B D. Optimal state-determination by mutually unbiased measurements[J]. Annals of Physics, 1989, 191(2): 363-381. [12]Adamson R B A, Steinberg A M. Experimental quantum state estimation with mutually unbiased bases[J]. Physical Review Letters, 2010, 105 (3): 030406. [13]Cerf N J,Bourennane M,Karlsson A, et al. Security of quantum key distribution using d-level systems[J]. Physical Review Letters, 2002, 88(12): 127902. [14]Durt T. About mutually unbiased bases in even and odd prime power dimensions[J]. Journal of Physics A General Physics, 2005, 38(23): 5267. [15]Raynali P, Xin L,Englert B G. Mutually Unbiased bases in dimension six: The four most distant bases[J]. Physical Review A, 2012, 83(6): 5693-5707. [16]Appleby D M.SIC-POVMS and MUBS: Geometrical Relationships in Prime Dimension[C]// American Institute of Physics, 2009: 223-232. [17]Durt T, Englert B G, Bengtsson I. On mutually unbiased bases[J]. International Journal of Quantum Information, 2010, 08(4): 535-640. [18]Tavakoli A, Herbauts I, ?ukowski M, et al. Secret Sharing with a single d-level quantum system[J]. Physical Review A, 2015, 92(3). [19]Bai Chenming,Li Zhihui,Li Yongming. Sequential Quantum Secret Sharing Using a single Qudit*[J].Communications in Theoretical Physics, 2018,69(5):513-518.