E-payment protocol scheme based on quantum entanglement measurement theory

doi:10.3969/j.issn.1000-5641.2024.03.015

Abstract

Abstract:

An electronic payment protocol based on basic quantum mechanics is proposed. Some current loopholes in the classic payment systems pose security risks. The proposed scheme utilizes the correlations existing between entangled particles at the quantum level to implement the steps of signing, purchasing, and paying, whereby the validity of a signature is verified via quantum one-way functions and quantum SWAP test circuits. Payment information is transmitted through redundant particles in channel detection, thereby saving costs. Experimental results show that the proposed scheme has unconditional security as guaranteed by the basic principles of quantum mechanics and meets the basic requirements of payment systems.

Key words: quantum payment protocol, quantum entanglement, quantum signature, unconditional security

CLC Number:

O413.2

Minhao ZHU, Lei MA. E-payment protocol scheme based on quantum entanglement measurement theory[J]. Journal of East China Normal University(Natural Science), 2024, 2024(3): 136-146.

Figures/Tables 9

Table 1

Correlation of GHZ particles"

光子$ \rm{A} $的测量结果	光子$ \rm{B} $的测量结果	光子$ \rm{T} $的量子态
${\left\| { + x} \right\rangle _{\rm{A}}} $	${\left\| { + x} \right\rangle _{\rm{B}}} $	${\left\| { + x} \right\rangle _{\rm{T}}} $
${\left\| { + x} \right\rangle _{\rm{A}}} $	${\left\| { - x} \right\rangle _{\rm{B}}} $	${\left\| { - x} \right\rangle _{\rm{T}}} $
${\left\| { + x} \right\rangle _{\rm{A}}} $	${\left\| { + y} \right\rangle _{\rm{B}}} $	${\left\| { - y} \right\rangle _{\rm{T}}} $
${\left\| { + x} \right\rangle _{\rm{A}}} $	${\left\| { - y} \right\rangle _{\rm{B}}} $	${\left\| { + y} \right\rangle _{\rm{T}}} $
${\left\| { - x} \right\rangle _{\rm{A}}} $	${\left\| { + x} \right\rangle _{\rm{B}}} $	${\left\| { - x} \right\rangle _{\rm{T}}} $
${\left\| { - x} \right\rangle _{\rm{A}}} $	${\left\| { - x} \right\rangle _{\rm{B}}} $	${\left\| { + x} \right\rangle _{\rm{T}}} $
${\left\| { - x} \right\rangle _{\rm{A}}} $	${\left\| { + y} \right\rangle _{\rm{B}}} $	${\left\| { + y} \right\rangle _{\rm{T}}} $
${\left\| { - x} \right\rangle _{\rm{A}}} $	${\left\| { - y} \right\rangle _{\rm{B}}} $	${\left\| { - y} \right\rangle _{\rm{T}}} $
${\left\| { + y} \right\rangle _{\rm{A}}} $	${\left\| { + x} \right\rangle _{\rm{B}}} $	${\left\| { - y} \right\rangle _{\rm{T}}} $
${\left\| { + y} \right\rangle _{\rm{A}}} $	${\left\| { - x} \right\rangle _{\rm{B}}} $	${\left\| { + y} \right\rangle _{\rm{T}}} $
${\left\| { + y} \right\rangle _{\rm{A}}} $	${\left\| { + y} \right\rangle _{\rm{B}}} $	${\left\| { - x} \right\rangle _{\rm{T}}} $
${\left\| { + y} \right\rangle _{\rm{A}}} $	${\left\| { - y} \right\rangle _{\rm{B}}} $	${\left\| { + x} \right\rangle _{\rm{T}}} $
${\left\| { - y} \right\rangle _{\rm{A}}} $	${\left\| { + x} \right\rangle _{\rm{B}}} $	${\left\| { + y} \right\rangle _{\rm{T}}} $
${\left\| { - y} \right\rangle _{\rm{A}}} $	${\left\| { - x} \right\rangle _{\rm{B}}} $	${\left\| { - y} \right\rangle _{\rm{T}}} $
${\left\| { - y} \right\rangle _{\rm{A}}} $	${\left\| { + y} \right\rangle _{\rm{B}}} $	${\left\| { + x} \right\rangle _{\rm{T}}} $
${\left\| { - y} \right\rangle _{\rm{A}}} $	${\left\| { - y} \right\rangle _{\rm{B}}} $	${\left\| { - x} \right\rangle _{\rm{T}}} $

Table 1

Fig.1

Table 2

Table 3

Table 4

Table 5

Table 6

Table 7

Table 8

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光子$ \rm{A} $的测量结果	光子$ \rm{B} $的测量结果	光子$ \rm{T} $的量子态
${\left\| { + x} \right\rangle _{\rm{A}}} $	${\left\| { + x} \right\rangle _{\rm{B}}} $	${\left\| { + x} \right\rangle _{\rm{T}}} $
${\left\| { + x} \right\rangle _{\rm{A}}} $	${\left\| { - x} \right\rangle _{\rm{B}}} $	${\left\| { - x} \right\rangle _{\rm{T}}} $
${\left\| { + x} \right\rangle _{\rm{A}}} $	${\left\| { + y} \right\rangle _{\rm{B}}} $	${\left\| { - y} \right\rangle _{\rm{T}}} $
${\left\| { + x} \right\rangle _{\rm{A}}} $	${\left\| { - y} \right\rangle _{\rm{B}}} $	${\left\| { + y} \right\rangle _{\rm{T}}} $
${\left\| { - x} \right\rangle _{\rm{A}}} $	${\left\| { + x} \right\rangle _{\rm{B}}} $	${\left\| { - x} \right\rangle _{\rm{T}}} $
${\left\| { - x} \right\rangle _{\rm{A}}} $	${\left\| { - x} \right\rangle _{\rm{B}}} $	${\left\| { + x} \right\rangle _{\rm{T}}} $
${\left\| { - x} \right\rangle _{\rm{A}}} $	${\left\| { + y} \right\rangle _{\rm{B}}} $	${\left\| { + y} \right\rangle _{\rm{T}}} $
${\left\| { - x} \right\rangle _{\rm{A}}} $	${\left\| { - y} \right\rangle _{\rm{B}}} $	${\left\| { - y} \right\rangle _{\rm{T}}} $
${\left\| { + y} \right\rangle _{\rm{A}}} $	${\left\| { + x} \right\rangle _{\rm{B}}} $	${\left\| { - y} \right\rangle _{\rm{T}}} $
${\left\| { + y} \right\rangle _{\rm{A}}} $	${\left\| { - x} \right\rangle _{\rm{B}}} $	${\left\| { + y} \right\rangle _{\rm{T}}} $
${\left\| { + y} \right\rangle _{\rm{A}}} $	${\left\| { + y} \right\rangle _{\rm{B}}} $	${\left\| { - x} \right\rangle _{\rm{T}}} $
${\left\| { + y} \right\rangle _{\rm{A}}} $	${\left\| { - y} \right\rangle _{\rm{B}}} $	${\left\| { + x} \right\rangle _{\rm{T}}} $
${\left\| { - y} \right\rangle _{\rm{A}}} $	${\left\| { + x} \right\rangle _{\rm{B}}} $	${\left\| { + y} \right\rangle _{\rm{T}}} $
${\left\| { - y} \right\rangle _{\rm{A}}} $	${\left\| { - x} \right\rangle _{\rm{B}}} $	${\left\| { - y} \right\rangle _{\rm{T}}} $
${\left\| { - y} \right\rangle _{\rm{A}}} $	${\left\| { + y} \right\rangle _{\rm{B}}} $	${\left\| { + x} \right\rangle _{\rm{T}}} $
${\left\| { - y} \right\rangle _{\rm{A}}} $	${\left\| { - y} \right\rangle _{\rm{B}}} $	${\left\| { - x} \right\rangle _{\rm{T}}} $

密钥	持有方
K_test	Alice, Charlie
K_AT	Alice,Trent
K_CT1	Charlie, Trent
K_CT2	Charlie, Trent
K_AB	Alice, Bob

量子序列	发送方	接收方	内容形式	作用
${\rm{Seq}}{\psi _{\rm{A}}}$	Alice	Alice	GHZ态	签名
${\rm{Seq}}{\psi _{\rm{C}}}$	Alice	Charlie	GHZ态	传递购买信息
${\rm{Seq}}{\psi _{\rm{T}}}$	Alice	Trent	GHZ态	传递购买信息
${\rm{Seq}}{P_{\rm{A}}}$	Alice	Alice	EPR对	传递支付信息
${\rm{Seq}}{P_{\rm{B}}}$	Alice	Bob	EPR对	传递支付信息
${\rm{Seq}}{t_{\rm{A}}}$	Alice	Alice	EPR对	监听检测、传递支付信息
${\rm{Seq}}{t_{\rm{C}}}$	Alice	Charlie	EPR对	监听检测

Alice选用的测量基	Alice的测量结果	Charlie的测量结果
${B_z}$	$\left\| 0 \right\rangle $	$\left\| 1 \right\rangle $
${B_z}$	$\left\| 1 \right\rangle $	$\left\| 0 \right\rangle $
${B_x}$	$\dfrac{1}{{\sqrt 2 }}\left( {\left\| 0 \right\rangle + \left\| 1 \right\rangle } \right)$	$\dfrac{1}{{\sqrt 2 }}\left( { - \left\| 0 \right\rangle + \left\| 1 \right\rangle } \right)$
${B_x}$	$\dfrac{1}{{\sqrt 2 }}\left( {\left\| 0 \right\rangle - \left\| 1 \right\rangle } \right)$	$\dfrac{1}{{\sqrt 2 }}\left( {\left\| 0 \right\rangle + \left\| 1 \right\rangle } \right)$

购买信息经典比特	Alice选用测量基	测量后的量子态
00	${B_x}$	$\dfrac{1}{{\sqrt 2 }}(\left\| 0 \right\rangle + \left\| 1 \right\rangle )$或$\dfrac{1}{{\sqrt 2 }}(\left\| 0 \right\rangle - \left\| 1 \right\rangle )$
01	${B_x}$
10	${B_y}$	$\dfrac{1}{{\sqrt 2 }}(\left\| 0 \right\rangle + i\left\| 1 \right\rangle )$或$\dfrac{1}{{\sqrt 2 }}(\left\| 0 \right\rangle - i\left\| 1 \right\rangle )$
11	${B_y}$