Quantum Identity Authentication Protocol without Entanglement in d-Dimensional Quantum System

doi:10.3969/j.issn.1671-1122.2024.09.005

Abstract

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

CLC Number:

TP309

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.

Figures/Tables 14

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

协议	维数	量子资源	可供选择的量子比特数目 /个	抗冒充攻击	抗纠缠测量攻击	抗拦截测量重发攻击	抗CNOT 攻击	量子比特效率
文献[14]协议	2维	单光子	4	是	否	是	否	50%
文献[18]协议	2维	单光子	4	是	是	是	否	$\frac{n-c}{n}$
文献[19]协议	2维	单光子	4	是	是	是	是	$\frac{n-c}{n}$
本文协议	$d$ 维	单光子	${{d}^{2}}$	是	是	是	是	$\frac{n-c}{n}$

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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