一种带作弊识别的动态(t,n)门限量子秘密共享方案

doi:10.3969/j.issn.1671-1122.2024.05.008

信息网络安全 ›› 2024, Vol. 24 ›› Issue (5): 745-755.doi: 10.3969/j.issn.1671-1122.2024.05.008

一种带作弊识别的动态(t,n)门限量子秘密共享方案

郭建胜, 关飞婷(), 李志慧

陕西师范大学数学与统计学院，西安 710119

收稿日期:2023-10-17 出版日期:2024-05-10 发布日期:2024-06-24
通讯作者: 关飞婷 E-mail:ftguan123@163.com
作者简介:郭建胜（1979—），男，青海，副教授，博士，主要研究方向为密码学|关飞婷（1999—），女，山西，硕士研究生，主要研究方向为密码学|李志慧（1966—），女，陕西，教授，博士，主要研究方向为有限域和密码学
基金资助:
国家自然科学基金(12071271)

A Dynamic (t,n) Threshold Quantum Secret Sharing Scheme with Cheating Identification

GUO Jiansheng, GUAN Feiting(), LI Zhihui

School of Mathematics and Statistics, Shaanxi Normal University, Xi’an 710119, China

Received:2023-10-17 Online:2024-05-10 Published:2024-06-24
Contact: GUAN Feiting E-mail:ftguan123@163.com

摘要/Abstract

摘要：

文章基于齐次线性反馈移位寄存器（Linear Feedback Shift Register，LFSR）序列和d维单量子态提出了一种带作弊识别的动态(t,n)门限量子秘密共享方案。在该方案中，可信的分发者确定共享的秘密，并为参与者分配份额，参与者对传输中的粒子执行相应的酉操作来恢复秘密。在秘密重建阶段，通过执行量子态数字签名，不仅可以检测到作弊行为，还可以识别具体的作弊者并将其删除，最终参与者可以验证恢复秘密的正确性。该方案可以在不更改旧参与者份额的前提下，无需其他参与者的帮助便可实现参与者的动态更新。安全性分析表明，该方案能够抵抗常见的外部攻击和内部攻击。

关键词: 量子秘密共享, 动态更新, 作弊识别, 量子态数字签名

Abstract:

Based on homogeneous linear feedback shift register(LFSR) sequences and d-dimensional single quantum states, this paper proposed a dynamical (t,n) threshold quantum secret sharing scheme with cheating identification. In this scheme, a trusted dealer determined the shared secret and distributed shared to the participants, and the participants recovered the secret by performing the corresponding unitary operation on the transmitted particles. In the secret reconstruction phase, by performing quantum state digital signatures, not only the existence of cheating behavior could be detected, but also the specific cheater could be identified and removed, and finally the participants could verify the correctness of the recovered secret. The scheme allowed dynamic updating of participants without changing the shares of old participants and without the help of other participants. Security analysis shows that the scheme is resistant to common external and internal attacks.

Key words: quantum secret sharing, dynamic updating, cheating identification, quantum state digital signature

中图分类号:

TP309

郭建胜, 关飞婷, 李志慧. 一种带作弊识别的动态(t,n)门限量子秘密共享方案[J]. 信息网络安全, 2024, 24(5): 745-755.

GUO Jiansheng, GUAN Feiting, LI Zhihui. A Dynamic (t,n) Threshold Quantum Secret Sharing Scheme with Cheating Identification[J]. Netinfo Security, 2024, 24(5): 745-755.

图/表 3

参考文献 28

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	${{p}_{i}}$	${{r}_{i}}$	${{q}_{i}}$	酉操作	${{\alpha }_{i}}$	${{\beta }_{i}}$
Bob1	4	6	10	${{U}_{10,10}}$	8	6
Bob2	10	1	0	${{U}_{0,0}}$	7	5
Bob3	8	4	1	${{U}_{1,1}}$	7	5

	文献[12]方案	文献[16]方案	文献[23]方案	文献[24]方案	本文方案
所用量子态	d维 Bell态	d维 Bell态	d维 GHZ态	d维 Bell态	MUB
动态	否	否	是	是	是
作弊识别	否	是	否	否	是
抵抗伪造攻击	是	是	是	是	是
抵抗否认攻击	否	否	否	否	是
诱饵粒子数	$N(m+1)$	$N(m+1)$	$nN$	$N(m+1)$	0
所用的粒子总数	$N(m+1)+2$	$N(m+1)+n(m-1)+2$	$n(N+1)$	$N(m+1)+2$	$4m-2$
酉操作次数	$m+1$	$\frac{n}{2}(m+1)(m-1)+1$	0	$m+1$	$9m-4$
测量操作次数	$N(m+1)+1$	$N(m+1)+\frac{nm}{2}+1$	$n(N+1)$	$N(m+1)+1$	$4m-1$

一种带作弊识别的动态(t,n)门限量子秘密共享方案

A Dynamic (t,n) Threshold Quantum Secret Sharing Scheme with Cheating Identification

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[2]	杨宇光, 卢嘉煜. 一种基于星型簇态的动态的分级的量子秘密共享协议[J]. 信息网络安全, 2023, 23(6): 34-42.
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