d维量子系统中无需纠缠的量子身份认证协议

doi:10.3969/j.issn.1671-1122.2024.09.005

摘要/Abstract

摘要：

单光子量子身份认证协议不需要任何纠缠光子源，在一定程度上节省了量子资源。目前已有研究证明了在2维量子系统中，单光子量子身份认证协议在CNOT攻击下的安全性。文章基于奇素数d维计算基的受控非门与受控非门的相位反冲，证明了d维相互无偏基的受控非门的输出结果，即目标比特选择第一组相互无偏基中的向量时，控制比特发生改变，而目标比特选择其余d-1组相互无偏基中的任一向量时，产生纠缠态。基于此输出结果，文章提出了在奇素数d维量子系统中的量子身份认证协议，该协议可以在不泄露通信双方认证的预共享密钥的前提下验证双方的身份，且可以使用随机生成的密钥检测敌手的存在。在d维的协议中，通信双方选择的量子比特数目越多，协议成功的概率越高。安全性分析表明，该协议可以抵御冒充攻击、拦截测量重发攻击、纠缠测量攻击以及CNOT攻击。

关键词: d维相互无偏基, CNOT门, 量子身份认证, 单光子

Abstract:

The single photon quantum identity authentication protocol does not require any source of entangled photons, which saves quantum resources to some extent. Existing studies have demonstrated the security of single-photon quantum identity authentication protocols in 2-dimensional quantum systems under CNOT attack. In this paper, based on the CNOT gate of the odd-prime dimensional computational basis and its phase kickback, we proved that the output result of the d-dimension CNOT gate, that is, when we choose the vector in the first group of mutually unbiased basis as the target bit, the control bit changes, and when we choose any vector in the remaining d-1 group of mutually unbiased basis as the target bit, an entangled state is generated. Based on this output, the article proposed a quantum identity authentication protocol in odd prime dimensional quantum system, which can verify the identity of the two parties without revealing the pre-shared key authenticated by the communicating parties and can detect the presence of the adversary using a randomly generated key. In d-dimensional protocol, the higher the number of qubits chose by communicating parties, the higher the success probability of protocol. Security analysis indicates that the protocol can resist impersonation attack, interception measure-resend attack, entanglement measurement attack, and CNOT attack.

Key words: d-dimensional mutual unbiased bases, CNOT gate, quantum identity authentication, single photon

中图分类号:

TP309

段昊哲, 李志慧, 韦性佳, 胡珂欣. d维量子系统中无需纠缠的量子身份认证协议[J]. 信息网络安全, 2024, 24(9): 1364-1374.

DUAN Haozhe, LI Zhihui, WEI Xingjia, HU Kexin. Quantum Identity Authentication Protocol without Entanglement in d-Dimensional Quantum System[J]. Netinfo Security, 2024, 24(9): 1364-1374.

图/表 14

图1

图2

图3

图4

图5

图6

图7

表1

Eve增益与检测的概率

Bob 控制比特	Eve目标比特
	$\left\| e_{0}^{\left( 0 \right)} \right\rangle $		$\left\| e_{1}^{\left( 0 \right)} \right\rangle $		$\left\| e_{2}^{\left( 0 \right)} \right\rangle $		…	$\left\| e_{d-1}^{\left( 0 \right)} \right\rangle $		$\left\| e_{0}^{\left( 1 \right)} \right\rangle $		…	$\left\| e_{d-1}^{\left( d-1 \right)} \right\rangle $
		Alice	Eve	Alice	Eve	Alice	Eve	…	Alice	Eve	Alice	Eve	…	Alice	Eve
$\left\| e_{0}^{\left( 0 \right)} \right\rangle $	$\left\| e_{0}^{\left( 0 \right)} \right\rangle $	$\left\| e_{0}^{\left( 0 \right)} \right\rangle $	$\left\| e_{d-1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{d-2}^{\left( 0 \right)} \right\rangle $	$\left\| e_{2}^{\left( 0 \right)} \right\rangle $	…	$\left\| e_{1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{d-1}^{\left( 0 \right)} \right\rangle $	E	E	…	E	E
$\left\| e_{1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{0}^{\left( 0 \right)} \right\rangle $	$\left\| e_{0}^{\left( 0 \right)} \right\rangle $	$\left\| e_{1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{d-1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{2}^{\left( 0 \right)} \right\rangle $	…	$\left\| e_{2}^{\left( 0 \right)} \right\rangle $	$\left\| e_{d-1}^{\left( 0 \right)} \right\rangle $	E	E	…	E	E
$\left\| e_{2}^{\left( 0 \right)} \right\rangle $	$\left\| e_{2}^{\left( 0 \right)} \right\rangle $	$\left\| e_{0}^{\left( 0 \right)} \right\rangle $	$\left\| e_{1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{0}^{\left( 0 \right)} \right\rangle $	$\left\| e_{2}^{\left( 0 \right)} \right\rangle $	…	$\left\| e_{3}^{\left( 0 \right)} \right\rangle $	$\left\| e_{d-1}^{\left( 0 \right)} \right\rangle $	E	E	…	E	E
…	…	…	…	…	…	…	…	…	…	E	E	…	E	E
$\left\| e_{d-1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{d-1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{0}^{\left( 0 \right)} \right\rangle $	$\left\| e_{d-2}^{\left( 0 \right)} \right\rangle $	$\left\| e_{1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{d-3}^{\left( 0 \right)} \right\rangle $	$\left\| e_{2}^{\left( 0 \right)} \right\rangle $	…	$\left\| e_{0}^{\left( 0 \right)} \right\rangle $	$\left\| e_{d-1}^{\left( 0 \right)} \right\rangle $	E	E	…	E	E
$\left\| e_{0}^{\left( 1 \right)} \right\rangle $	$\left\| e_{0}^{\left( 1 \right)} \right\rangle $	$\left\| e_{0}^{\left( 0 \right)} \right\rangle $	$\left\| e_{d-1}^{\left( 1 \right)} \right\rangle $	$\left\| e_{1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{d-2}^{\left( 1 \right)} \right\rangle $	$\left\| e_{2}^{\left( 0 \right)} \right\rangle $	…	$\left\| e_{1}^{\left( 1 \right)} \right\rangle $	$\left\| e_{d-1}^{\left( 0 \right)} \right\rangle $	E	E	…	E	E
$\left\| e_{1}^{\left( 1 \right)} \right\rangle $	$\left\| e_{1}^{\left( 1 \right)} \right\rangle $	$\left\| e_{0}^{\left( 0 \right)} \right\rangle $	$\left\| e_{0}^{\left( 1 \right)} \right\rangle $	$\left\| e_{1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{d-1}^{\left( 1 \right)} \right\rangle $	$\left\| e_{2}^{\left( 0 \right)} \right\rangle $	…	$\left\| e_{2}^{\left( 1 \right)} \right\rangle $	$\left\| e_{d-1}^{\left( 0 \right)} \right\rangle $	E	E	…	E	E
$\left\| e_{2}^{\left( 1 \right)} \right\rangle $	$\left\| e_{2}^{\left( 1 \right)} \right\rangle $	$\left\| e_{0}^{\left( 0 \right)} \right\rangle $	$\left\| e_{1}^{\left( 1 \right)} \right\rangle $	$\left\| e_{1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{0}^{\left( 1 \right)} \right\rangle $	$\left\| e_{2}^{\left( 0 \right)} \right\rangle $	…	$\left\| e_{3}^{\left( 1 \right)} \right\rangle $	$\left\| e_{d-1}^{\left( 0 \right)} \right\rangle $	E	E	…	E	E
…	…	…	…	…	…	…	…	…	…	E	E	…	E	E
$\left\| e_{d-1}^{\left( d-1 \right)} \right\rangle $	$\left\| e_{d-1}^{\left( d-1 \right)} \right\rangle $	$\left\| e_{0}^{\left( 0 \right)} \right\rangle $	$\left\| e_{d-2}^{\left( d-1 \right)} \right\rangle $	$\left\| e_{1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{d-3}^{\left( d-1 \right)} \right\rangle $	$\left\| e_{2}^{\left( 0 \right)} \right\rangle $	…	$\left\| e_{0}^{\left( d-1 \right)} \right\rangle $	$\left\| e_{d-1}^{\left( 0 \right)} \right\rangle $	E	E	…	E	E

表1

表2

表3

表4

表5

表6

表7

参考文献 29

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Bob 控制比特	Eve目标比特
	$\left\| e_{0}^{\left( 0 \right)} \right\rangle $		$\left\| e_{1}^{\left( 0 \right)} \right\rangle $		$\left\| e_{2}^{\left( 0 \right)} \right\rangle $		…	$\left\| e_{d-1}^{\left( 0 \right)} \right\rangle $		$\left\| e_{0}^{\left( 1 \right)} \right\rangle $		…	$\left\| e_{d-1}^{\left( d-1 \right)} \right\rangle $
		Alice	Eve	Alice	Eve	Alice	Eve	…	Alice	Eve	Alice	Eve	…	Alice	Eve
$\left\| e_{0}^{\left( 0 \right)} \right\rangle $	$\left\| e_{0}^{\left( 0 \right)} \right\rangle $	$\left\| e_{0}^{\left( 0 \right)} \right\rangle $	$\left\| e_{d-1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{d-2}^{\left( 0 \right)} \right\rangle $	$\left\| e_{2}^{\left( 0 \right)} \right\rangle $	…	$\left\| e_{1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{d-1}^{\left( 0 \right)} \right\rangle $	E	E	…	E	E
$\left\| e_{1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{0}^{\left( 0 \right)} \right\rangle $	$\left\| e_{0}^{\left( 0 \right)} \right\rangle $	$\left\| e_{1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{d-1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{2}^{\left( 0 \right)} \right\rangle $	…	$\left\| e_{2}^{\left( 0 \right)} \right\rangle $	$\left\| e_{d-1}^{\left( 0 \right)} \right\rangle $	E	E	…	E	E
$\left\| e_{2}^{\left( 0 \right)} \right\rangle $	$\left\| e_{2}^{\left( 0 \right)} \right\rangle $	$\left\| e_{0}^{\left( 0 \right)} \right\rangle $	$\left\| e_{1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{0}^{\left( 0 \right)} \right\rangle $	$\left\| e_{2}^{\left( 0 \right)} \right\rangle $	…	$\left\| e_{3}^{\left( 0 \right)} \right\rangle $	$\left\| e_{d-1}^{\left( 0 \right)} \right\rangle $	E	E	…	E	E
…	…	…	…	…	…	…	…	…	…	E	E	…	E	E
$\left\| e_{d-1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{d-1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{0}^{\left( 0 \right)} \right\rangle $	$\left\| e_{d-2}^{\left( 0 \right)} \right\rangle $	$\left\| e_{1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{d-3}^{\left( 0 \right)} \right\rangle $	$\left\| e_{2}^{\left( 0 \right)} \right\rangle $	…	$\left\| e_{0}^{\left( 0 \right)} \right\rangle $	$\left\| e_{d-1}^{\left( 0 \right)} \right\rangle $	E	E	…	E	E
$\left\| e_{0}^{\left( 1 \right)} \right\rangle $	$\left\| e_{0}^{\left( 1 \right)} \right\rangle $	$\left\| e_{0}^{\left( 0 \right)} \right\rangle $	$\left\| e_{d-1}^{\left( 1 \right)} \right\rangle $	$\left\| e_{1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{d-2}^{\left( 1 \right)} \right\rangle $	$\left\| e_{2}^{\left( 0 \right)} \right\rangle $	…	$\left\| e_{1}^{\left( 1 \right)} \right\rangle $	$\left\| e_{d-1}^{\left( 0 \right)} \right\rangle $	E	E	…	E	E
$\left\| e_{1}^{\left( 1 \right)} \right\rangle $	$\left\| e_{1}^{\left( 1 \right)} \right\rangle $	$\left\| e_{0}^{\left( 0 \right)} \right\rangle $	$\left\| e_{0}^{\left( 1 \right)} \right\rangle $	$\left\| e_{1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{d-1}^{\left( 1 \right)} \right\rangle $	$\left\| e_{2}^{\left( 0 \right)} \right\rangle $	…	$\left\| e_{2}^{\left( 1 \right)} \right\rangle $	$\left\| e_{d-1}^{\left( 0 \right)} \right\rangle $	E	E	…	E	E
$\left\| e_{2}^{\left( 1 \right)} \right\rangle $	$\left\| e_{2}^{\left( 1 \right)} \right\rangle $	$\left\| e_{0}^{\left( 0 \right)} \right\rangle $	$\left\| e_{1}^{\left( 1 \right)} \right\rangle $	$\left\| e_{1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{0}^{\left( 1 \right)} \right\rangle $	$\left\| e_{2}^{\left( 0 \right)} \right\rangle $	…	$\left\| e_{3}^{\left( 1 \right)} \right\rangle $	$\left\| e_{d-1}^{\left( 0 \right)} \right\rangle $	E	E	…	E	E
…	…	…	…	…	…	…	…	…	…	E	E	…	E	E
$\left\| e_{d-1}^{\left( d-1 \right)} \right\rangle $	$\left\| e_{d-1}^{\left( d-1 \right)} \right\rangle $	$\left\| e_{0}^{\left( 0 \right)} \right\rangle $	$\left\| e_{d-2}^{\left( d-1 \right)} \right\rangle $	$\left\| e_{1}^{\left( 0 \right)} \right\rangle $	$\left\| e_{d-3}^{\left( d-1 \right)} \right\rangle $	$\left\| e_{2}^{\left( 0 \right)} \right\rangle $	…	$\left\| e_{0}^{\left( d-1 \right)} \right\rangle $	$\left\| e_{d-1}^{\left( 0 \right)} \right\rangle $	E	E	…	E	E

密钥	${{T}_{1}}$	${{T}_{2}}$	${{T}_{3}}$	${{T}_{4}}$	${{T}_{6}}$
认证密钥${{B}_{K}}$	4	1	2	3	3
诱饵密钥${{D}_{AK}}$	1	1	2	4	2
诱饵密钥${{D}_{BK}}$	3	2	1	4	1

迭代次数$T$	Alice与Bob制备基						Bob编码
$m=6,r=11$	${{k}_{i-r}}$	${{k}_{i}}$	${{k}_{i+r}}$	${{x}_{i}}$	${{y}_{i}}$	${{z}_{i}}$	$Q{{B}_{{{k}_{t}}}}$	$Q{{D}_{A{{k}_{t}}}}$	$Q{{D}_{B{{k}_{t}}}}$
$T=1$	3	1	2	0	4	3	$\left\| e_{4}^{\left( 0 \right)} \right\rangle $	$\left\| e_{1}^{\left( 4 \right)} \right\rangle $	$\left\| e_{3}^{\left( 3 \right)} \right\rangle $
$T=2$	1	2	0	1	3	2	$\left\| e_{1}^{\left( 1 \right)} \right\rangle $	$\left\| e_{1}^{\left( 3 \right)} \right\rangle $	$\left\| e_{2}^{\left( 2 \right)} \right\rangle $
$T=3$	2	0	2	4	2	2	$\left\| e_{2}^{\left( 4 \right)} \right\rangle $	$\left\| e_{2}^{\left( 2 \right)} \right\rangle $	$\left\| e_{1}^{\left( 2 \right)} \right\rangle $
$T=4$	0	2	0	0	2	2	$\left\| e_{3}^{\left( 0 \right)} \right\rangle $	$\left\| e_{4}^{\left( 2 \right)} \right\rangle $	$\left\| e_{4}^{\left( 2 \right)} \right\rangle $
$T=5$	2	0	0	2	2	0	$\left\| e_{0}^{\left( 2 \right)} \right\rangle $	$\left\| e_{0}^{\left( 2 \right)} \right\rangle $	$\left\| e_{0}^{\left( 0 \right)} \right\rangle $
$T=6$	4	0	1	0	4	1	$\left\| e_{3}^{\left( 0 \right)} \right\rangle $	$\left\| e_{2}^{\left( 4 \right)} \right\rangle $	$\left\| e_{1}^{\left( 1 \right)} \right\rangle $

迭代次数$T$	Alice解码所用基			Alice测量结果
$m=6,r=11$	${{x}_{i}}$	${{y}_{i}}$	${{z}_{i}}$	$B{{'}_{{{k}_{t}}}}$	$D{{'}_{A{{k}_{t}}}}$	$D{{'}_{B{{k}_{t}}}}$
$T=1$	$j=0$	$j=4$	$j=3$	4	1	3
$T=2$	$j=1$	$j=3$	$j=2$	1	1	2
$T=3$	$j=4$	$j=2$	$j=2$	2	2	1
$T=4$	$j=0$	$j=2$	$j=2$	3	4	4
$T=5$	$j=2$	$j=2$	$j=0$	0	0	0
$T=6$	$j=0$	$j=4$	$j=1$	3	2	1

${{A}_{{{k}_{t}}}}$	$D{{'}_{B{{k}_{t}}}}\oplus B{{'}_{{{k}_{t}}}}$	Alice解码	Bob解码所用基	Bob测量结果$A{{'}_{{{k}_{t}}}}$
2	2	$\left\| e_{2}^{\left( 2 \right)} \right\rangle $	$j=2$	2
4	3	$\left\| e_{4}^{\left( 3 \right)} \right\rangle $	$j=3$	4
1	3	$\left\| e_{1}^{\left( 3 \right)} \right\rangle $	$j=3$	1
2	2	$\left\| e_{2}^{\left( 2 \right)} \right\rangle $	$j=2$	2
3	0	$\left\| e_{3}^{\left( 0 \right)} \right\rangle $	$j=0$	3
0	4	$\left\| e_{0}^{\left( 4 \right)} \right\rangle $	$j=4$	0