The Three-Party Semi-Quantum Key Agreement Protocol Based on Logical $\chi $-States

doi:10.3969/j.issn.1671-1122.2025.01.003

Abstract

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

CLC Number:

TP309

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.

Figures/Tables 7

References 26

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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%