基于逻辑$\chi $态的三方半量子密钥协商协议

doi:10.3969/j.issn.1671-1122.2025.01.003

摘要/Abstract

摘要：

半量子密钥协商适用于参与者能力较低或承担不起昂贵设备的情况，比传统的量子密钥协商更符合实际需求。然而，目前三方半量子密钥协商协议的研究较少且普遍存在效率较低的问题。为此，文章提出一种基于逻辑六比特$\chi $型态的三方半量子密钥协商协议，该协议充分利用了逻辑六比特$\chi $型态的纠缠特性，通过简单的幺正操作和粒子测量，实现了在无需可信第三方介入的情况下两个半量子方与一个全量子方之间公平的密钥协商。该协议不仅提高了量子比特效率还具备抵御参与者攻击和外部攻击的能力。

关键词: 量子密码, 半量子密钥协商, $\chi $型态, Bell态, 量子比特效率

Abstract:

The semi-quantum key agreement protocol is suitable for scenarios where participants have limited capabilities or cannot afford expensive equipment, making it more aligned with practical requirements than quantum key agreement. However, current research on three-party semi-quantum key agreement protocols is limited, and they commonly suffer from the issue of low efficiency. To solve this problem, the paper proposed a three-party semi-quantum key agreement which is based on the logical six-qubit $\chi $-state. The protocol leverages the entanglement properties of the logical six-qubit $\chi $-state, achieving fair key agreement between two semi-quantum parties and one fully quantum party through straightforward unitary operations and particle measurements, without the need for a trusted third party. The protocol not only enhances quantum bit efficiency but also possesses the capability to resist participant and external attacks.

Key words: quantum cryptography, semi-quantum key agreement, $\chi $-type states, Bell states, quantum efficiency

中图分类号:

TP309

何业锋, 蔡明月, 梁熙媛. 基于逻辑$\chi $态的三方半量子密钥协商协议[J]. 信息网络安全, 2025, 25(1): 27-35.

HE Yefeng, CAI Mingyue, LIANG Xiyuan. The Three-Party Semi-Quantum Key Agreement Protocol Based on Logical $\chi $-States[J]. Netinfo Security, 2025, 25(1): 27-35.

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情况	Bob	Charlie	Alice
a	CTRL	CTRL	操作1
b	CTRL	SIFT	操作2
c	SIFT	CTRL	操作3
d	SIFT	SIFT	操作4

Bell态	协议中得到的$S_{B}^{\text{**}}$	$S_{B}^{\text{**}}$	${{k}_{b}}$	协议中得到的$S_{C}^{\text{**}}$	$S_{C}^{\text{**}}$	${{k}_{c}}$
$\left\| {{\phi }^{-}} \right\rangle $	$\left\| 1 \right\rangle $	$\left\| 0 \right\rangle $	1	$\left\| 1 \right\rangle $	$\left\| 1 \right\rangle $	0
$\left\| {{\psi }^{+}} \right\rangle $	$\left\| 1 \right\rangle $	$\left\| 1 \right\rangle $	0	$\left\| 0 \right\rangle $	$\left\| 1 \right\rangle $	1
$\left\| {{\psi }^{-}} \right\rangle $	$\left\| 0 \right\rangle $	$\left\| 0 \right\rangle $	0	$\left\| 1 \right\rangle $	$\left\| 0 \right\rangle $	1
$\left\| {{\psi }^{+}} \right\rangle $	$\left\| 1 \right\rangle $	$\left\| 0 \right\rangle $	1	$\left\| 0 \right\rangle $	$\left\| 0 \right\rangle $	0

${{S}_{\text{A1}}}$	$S_{\text{C}}^{\text{ *}}$	${{k}_{\text{c}}}$	$S_{\text{B}}^{\text{ *}}$	${{S}_{\text{A2}}}$	${{k}_{\text{b}}}$
$\left\| 0 \right\rangle $	$\left\| 0 \right\rangle $	0	$\left\| 1 \right\rangle $	$\left\| 0 \right\rangle $	1
$\left\| 1 \right\rangle $	$\left\| 0 \right\rangle $	1	$\left\| 1 \right\rangle $	$\left\| 1 \right\rangle $	0
$\left\| 1 \right\rangle $	$\left\| 1 \right\rangle $	0	$\left\| 1 \right\rangle $	$\left\| 1 \right\rangle $	0
$\left\| 0 \right\rangle $	$\left\| 0 \right\rangle $	0	$\left\| 0 \right\rangle $	$\left\| 1 \right\rangle $	1

协议	量子资源	量子参与方必要量子操作	参与人数与经典方参与人数比值	量子比特效率
文献[23]协议	Cluster states	SPM+BM+FPOM	3/2	2.08%
文献[24]协议	GHZ states	SPM+BM+TPOM	3/2	2.63%
文献[25]协议	Cluster states	SPM+BM+FPOM	4/3	1.60%
本文协议	$\chi $states	SPM+BM	3/2	2.63%