Multiparty quantum key agreement protocol based on logical single particle

doi:10.11772/j.issn.1001-9081.2021010176

Journal of Computer Applications ›› 2022, Vol. 42 ›› Issue (1): 157-161.DOI: 10.11772/j.issn.1001-9081.2021010176

Special Issue: 网络空间安全

• Cyber security • Previous Articles Next Articles

Multiparty quantum key agreement protocol based on logical single particle

Shengwei XU¹^,², Jie KANG¹^,²()

^1.Beijing Electronic Science and Technology Institute，Beijing 100070，China
^2.School of Telecommunications Engineering，Xidian University，Xi’an Shaanxi 710071，China

Received:2021-01-29 Revised:2021-06-05 Accepted:2021-06-10 Online:2022-01-11 Published:2022-01-10
Contact: Jie KANG
About author:XU Shengwei， born in 1976， Ph. D.， professor. His research interests include information security， cryptography.
KANG Jie， born in 1997， M. S. candidate. Her research interests include cryptography， quantum communication.
Supported by:
National Key Research and Development Program of China(2018YFB1004101)

基于逻辑单粒子的多方量子密钥协商协议

许盛伟¹^,², 康婕¹^,²()

^1.北京电子科技学院，北京 100070
^2.西安电子科技大学通信工程学院，西安 710071

通讯作者: 康婕
作者简介:许盛伟（1976—），男，江西吉安人，教授，博士，CCF会员，主要研究方向：信息安全、密码学
康婕（1997—），女，陕西咸阳人，硕士研究生，主要研究方向：密码学、量子通信。
基金资助:
国家重点研发计划项目(2018YFB1004101)

Abstract

Abstract:

The influence of collective noise on quantum cryptographic protocols can not be ignored， however there are few Multiparty Quantum Key Agreement （MQKA） protocols that can resist collective noise. In order to resist the influence of collective noise， two sets of logical unitary operators were proposed for the logical single particle which can resist collective-dephasing noise and the logical single particle which can resist collective rotation noise respectively， so that after acting them on the logical single particles， two unitary operators did not change the measurement base， while the other two would change the measurement base. Based on this property， an MQKA protocol was proposed. Firstly， a logical single particle was transmited to the next participant by each participant.Then， the logical single particle was encrypted by all other participants and returned to the participant to form a “ring”. Finally， the shared key was obtained by measurement. Security analysis shows that the proposed protocol can resist intercept-resend attack， entanglement-measurement attack and participant attack. Efficiency analysis shows that this protocol achieves higher qubit efficiency.

Key words: logical unitary operator, Multiparty Quantum Key Agreement (MQKA), collective-dephasing noise, collective-rotation noise, participant attack

摘要：

集体噪声对量子密码协议的影响不可忽视，然而可抵抗集体噪声的多方量子密钥协商（MQKA）协议还很少。为了抵抗集体噪声的影响，分别针对可抗集体退相位噪声的逻辑单粒子和可抗集体旋转噪声的逻辑单粒子提出了两组逻辑酉算符，使得将其作用在逻辑单粒子上后，其中两个酉算符不改变测量基，而另外两个会改变测量基。基于此性质提出一个MQKA协议。首先，每个参与者传输逻辑单粒子给下一位；然后，该逻辑单粒子经过其他所有参与者的加密重新回到这个参与者，形成一个“环形”；最后，通过测量来获取共享密钥。安全性分析证明，该协议能够抵抗截取重发攻击、纠缠测量攻击以及参与者攻击；效率分析表明，该协议具有较高的量子比特效率。

关键词: 逻辑酉算符, 多方量子密钥协商, 集体退相位噪声, 集体旋转噪声, 参与者攻击

CLC Number:

TP309.7

Shengwei XU, Jie KANG. Multiparty quantum key agreement protocol based on logical single particle[J]. Journal of Computer Applications, 2022, 42(1): 157-161.

许盛伟, 康婕. 基于逻辑单粒子的多方量子密钥协商协议[J]. 《计算机应用》唯一官方网站, 2022, 42(1): 157-161.

Figures/Tables 3

Tab. 1 State transformation relationship of unitary operator ULw acting on logical single particle

酉算符	$\| 0 L >$	$\| 1 L >$	$\| + L >$	$\| - L >$
$U L 00$	$\| 0 L >$	$\| 1 L >$	$\| + L >$	$\| - L >$
$U L 01$	$\| 1 L >$	$\| 0 L >$	$\| - L >$	$\| + L >$
$U L 10$	$\| + L >$	$\| - L >$	$\| 0 L >$	$\| 1 L >$
$U L 11$	$\| - L >$	$\| + L >$	$\| 1 L >$	$\| 0 L >$

Tab. 1 State transformation relationship of unitary operator ULw acting on logical single particle

酉算符	$\| 0 L >$	$\| 1 L >$	$\| + L >$	$\| - L >$
$U L 00$	$\| 0 L >$	$\| 1 L >$	$\| + L >$	$\| - L >$
$U L 01$	$\| 1 L >$	$\| 0 L >$	$\| - L >$	$\| + L >$
$U L 10$	$\| + L >$	$\| - L >$	$\| 0 L >$	$\| 1 L >$
$U L 11$	$\| - L >$	$\| + L >$	$\| 1 L >$	$\| 0 L >$

Tab. 2 Negotiation process of three-user protocol

变量用户	A（ $P 1$ ）	B（ $P 2$ ）	C（ $P 3$ ）
初始态 $S i → i + 1$	$\| + d p > \| 1 d p > \| 0 d p > \| - d p > \| - d p >$	$\| 1 d p > \| 0 d p > \| + d p > \| - d p > \| + d p >$	$\| - d p > \| + d p > \| 1 d p > \| + d p > \| 1 d p >$
$P i + 1$ 第一次编码	$U 01 ⊗ U 00 ⊗ U 10 ⊗ U 11 ⊗ U 10$	$U 11 ⊗ U 10 ⊗ U 01 ⊗ U 10 ⊗ U 01$	$U 10 ⊗ U 01 ⊗ U 00 ⊗ U 11 ⊗ U 11$
$P i + 1$ 得到的粒子序列	$\| - d p > \| 1 d p > \| + d p > \| 0 d p > \| 1 d p >$	$\| + d p > \| + d p > \| - d p > \| 1 d p > \| - d p >$	$\| 1 d p > \| - d p > \| 1 d p > \| 1 d p > \| + d p >$
$P i + 1$ 选择的测量基	$M 2 M 1 M 2 M 1 M 1$	$M 2 M 2 M 2 M 1 M 2$	$M 1 M 2 M 1 M 1 M 2$
$P i - 1$ 测量的结果 $V i - 1$	11001	00111	11110
$P i - 1$ 得到的共享密钥 $K =$ $K i - 1 ⊕ V i - 1$	01100	01100	01100

Tab. 2 Negotiation process of three-user protocol

变量用户	A（ $P 1$ ）	B（ $P 2$ ）	C（ $P 3$ ）
初始态 $S i → i + 1$	$\| + d p > \| 1 d p > \| 0 d p > \| - d p > \| - d p >$	$\| 1 d p > \| 0 d p > \| + d p > \| - d p > \| + d p >$	$\| - d p > \| + d p > \| 1 d p > \| + d p > \| 1 d p >$
$P i + 1$ 第一次编码	$U 01 ⊗ U 00 ⊗ U 10 ⊗ U 11 ⊗ U 10$	$U 11 ⊗ U 10 ⊗ U 01 ⊗ U 10 ⊗ U 01$	$U 10 ⊗ U 01 ⊗ U 00 ⊗ U 11 ⊗ U 11$
$P i + 1$ 得到的粒子序列	$\| - d p > \| 1 d p > \| + d p > \| 0 d p > \| 1 d p >$	$\| + d p > \| + d p > \| - d p > \| 1 d p > \| - d p >$	$\| 1 d p > \| - d p > \| 1 d p > \| 1 d p > \| + d p >$
$P i + 1$ 选择的测量基	$M 2 M 1 M 2 M 1 M 1$	$M 2 M 2 M 2 M 1 M 2$	$M 1 M 2 M 1 M 1 M 2$
$P i - 1$ 测量的结果 $V i - 1$	11001	00111	11110
$P i - 1$ 得到的共享密钥 $K =$ $K i - 1 ⊕ V i - 1$	01100	01100	01100

Tab. 3 Efficiency comparison of several anti-noise protocols

协议	量子资源	参与方	量子比特效率
文献［10］协议	逻辑Bell态	两方	16.67
文献［11］协议	逻辑 $χ$ 态	两方	21.05
文献［12］协议	逻辑Bell态	两方	25.57
文献［13］协议	逻辑 $χ$ 态	两方	20
文献［14］协议	逻辑Bell态	两方	27.27
文献［16］协议	逻辑W态	多方	$1 / 2 N (2 N + 3)$
文献［17］协议	多粒子纠缠态	多方	$1 / 2 N (N + 3)$
本文协议	逻辑单粒子	多方	$1 / 2 N (N + 2)$

Tab. 3 Efficiency comparison of several anti-noise protocols

协议	量子资源	参与方	量子比特效率
文献［10］协议	逻辑Bell态	两方	16.67
文献［11］协议	逻辑 $χ$ 态	两方	21.05
文献［12］协议	逻辑Bell态	两方	25.57
文献［13］协议	逻辑 $χ$ 态	两方	20
文献［14］协议	逻辑Bell态	两方	27.27
文献［16］协议	逻辑W态	多方	$1 / 2 N (2 N + 3)$
文献［17］协议	多粒子纠缠态	多方	$1 / 2 N (N + 3)$
本文协议	逻辑单粒子	多方	$1 / 2 N (N + 2)$

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酉算符	$\| 0 L >$	$\| 1 L >$	$\| + L >$	$\| - L >$
$U L 00$	$\| 0 L >$	$\| 1 L >$	$\| + L >$	$\| - L >$
$U L 01$	$\| 1 L >$	$\| 0 L >$	$\| - L >$	$\| + L >$
$U L 10$	$\| + L >$	$\| - L >$	$\| 0 L >$	$\| 1 L >$
$U L 11$	$\| - L >$	$\| + L >$	$\| 1 L >$	$\| 0 L >$

酉算符	$\| 0 L >$	$\| 1 L >$	$\| + L >$	$\| - L >$
$U L 00$	$\| 0 L >$	$\| 1 L >$	$\| + L >$	$\| - L >$
$U L 01$	$\| 1 L >$	$\| 0 L >$	$\| - L >$	$\| + L >$
$U L 10$	$\| + L >$	$\| - L >$	$\| 0 L >$	$\| 1 L >$
$U L 11$	$\| - L >$	$\| + L >$	$\| 1 L >$	$\| 0 L >$

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Multiparty quantum key agreement protocol based on logical single particle

基于逻辑单粒子的多方量子密钥协商协议

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