基于量子纠缠测量理论的电子支付协议设计

doi:10.3969/j.issn.1000-5641.2024.03.015

摘要/Abstract

摘要：

提出了一个基于量子力学基本理论的电子支付协议. 经典支付系统存在部分漏洞, 可能会带来安全隐患. 利用纠缠粒子之间的关联性, 实现签名、购买、支付等环节; 使用量子单向函数和量子交换测试线路, 验证签名的有效性; 通过信道检测中的冗余粒子传输支付信息, 节约成本. 该方案在量子力学基本原理的保证下, 具有无条件的安全性, 符合支付系统的基本要求.

关键词: 量子支付协议, 量子纠缠, 量子签名, 无条件安全

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

中图分类号:

O413.2

朱旻昊, 马雷. 基于量子纠缠测量理论的电子支付协议设计[J]. 华东师范大学学报（自然科学版）, 2024, 2024(3): 136-146.

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.

图/表 9

表1

GHZ粒子关联性"

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}}} $

表1

图1

表2

表3

表4

表5

表6

表7

表8

参考文献 19

1	CHAUM D. Blind signatures for untraceable payments [C]// Advances in Cryptology: Proceedings of Crypto 82. Boston, Springer, 1983: 199-203.
2	MOHANTY S, MAJHI B, DAS S, et al.. A secure electronic cash based on a certificateless group signcryption scheme. Mathematical and Computer Modelling, 2013, 58 (1/2): 186- 195.
3	MESHRAM C, IMOIZE A L, ALJAEDI A, et al.. An efficient electronic cash system based on certificateless group signcryption scheme using conformable chaotic maps. Sensors, 2021, 21 (21): 7039- 7039.
4	HATEFI Z, BAYAT M, ALAGHBAND M R, et al. A conditional privacy-preserving fair electronic payment scheme based on blockchain without trusted third party [J]. Journal of Ambient Intelligence and Humanized Computing, 2023, 14: 10089–10102.
5	SHOR P W.. Algorithms for quantum computation: Discrete logarithms and factoring. Artificial Ergy, 1994, 11 (5): 124- 134.
6	WOOTTERS W K, ZUREK W H.. A single quantum cannot be cloned. Nature, 1982, 299 (5886): 802- 803.
7	WEHNER S, WINTER A.. Entropic uncertainty relations—a survey. New Journal of Physics, 2010, 12 (2): 025009.
8	田原, 温晓军, 公延军, 等.. 应用量子盲签名和群签名的电子支付系统. 计算机工程与应用, 2011, 47 (19): 108- 112.
9	ZHOU R G, LI W, HUAN T T, et al.. An online banking system based on quantum cryptography communication. International Journal of Theoretical Physics, 2014, 53 (7): 2177- 2190.
10	ZHANG J Z, YANG Y Y, XIE S C, et al.. A third-party e-payment protocol based on quantum group blind signature. International Journal of Theoretical Physics, 2017, 56 (9): 2981- 2989.
11	NIU X F, ZHANG J Z, XIE S C, et al.. A third-party e-payment protocol based on quantum multi-proxy blind signature. International Journal of Theoretical Physics, 2018, 57 (8): 2563- 2573.
12	TILIWALIDI K, ZHANG J Z, XIE S C, et al.. A multi-bank e-payment protocol based on quantum proxy blind signature. International Journal of Theoretical Physics, 2019, 58 (10): 3510- 3520.
13	NIU X F, ZHANG J Z, XIE S C, et al.. A quantum multi-proxy blind signature scheme based on entangled four-qubit cluster state. Communications in Theoretical Physics, 2018, 70 (1): 43- 48.
14	JIANG D H, HU Q Z, LIANG X Q, et al.. A trusted third-party e-payment protocol based on locally indistinguishable orthogonal product states. International Journal of Theoretical Physics, 2020, 59, 1442- 1450.
15	GOU X L, SHI R H, GAO W, et al.. A novel quantum e-payment protocol based on blockchain. Quantum Information Processing, 2021, 20 (5): 192.
16	何业锋, 杨梦玫, 李智, 等.. 基于量子行走的电子支付协议. 光学学报, 2023, 43 (5): 0527001.
17	BUHRMAN H, CLEVE R, WATROUS J, et al.. Quantum fingerprinting. Physical Review Letters, 2001, 87 (16): 167902.
18	BENNETT C H, BRASSARD G.. Quantum cryptography: Public key distribution and coin tossing. Theoretical Computer Science, 2014, 560, 7- 11.
19	SHOR P W, PRESKILL J.. Simple proof of security of the BB84 quantum key distribution protocol. Physical Review Letters, 2000, 85 (2): 441- 444.

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	${B_y}$