Quantum auction protocol based on semi⁃quantum secure direct communication

YANG Han; FENG Yan; XIE Sijiang

doi:10.3969/j.issn.1007-5461.2024.01.012

Journals >Chinese Journal of Quantum Electronics >Volume 41 >Issue 1 >Page 125 > Article

Chinese Journal of Quantum Electronics
Vol. 41, Issue 1, 125 (2024)

Quantum auction protocol based on semi⁃quantum secure direct communication

YANG Han^1、*, FENG Yan^1、2, and XIE Sijiang^1、2

Author Affiliations

¹Cyberspace Security Department, Beijing Electronic Science and Technology Institute, Beijing 10070, China

²University of Science and Technology of China, Hefei 230026, China

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DOI: 10.3969/j.issn.1007-5461.2024.01.012 Cite this Article

Han YANG, Yan FENG, Sijiang XIE. Quantum auction protocol based on semi⁃quantum secure direct communication[J]. Chinese Journal of Quantum Electronics, 2024, 41(1): 125 Copy Citation Text

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The original Bell state	$M_{B_{i}}$	$M_{e_{i}}$	$s t r_{i}$	The original Bell state	$M_{B_{i}}$	$M_{e_{i}}$	$s t r_{i}$
$\|φ^{\pm}〉$	0	0	0	$\|ψ^{\pm}〉$	0	1	0
	0	1	1		0	0	1
	1	1	0		1	0	0
	1	0	1		1	1	1

Table 1. The process of obtaining secret information

s t r_{i}

Intercepting particles	Attacking particle	System mixed state after attack
${\|0〉}_{t}$	${\|0〉}_{e}$	$\|ϕ_{C N O T}〉 = {\|0〉}_{t} {\|0〉}_{e}$
${\|1〉}_{t}$		$\|ϕ_{C N O T}〉 = {\|1〉}_{t} {\|1〉}_{e}$
${\|+〉}_{t}$		$\|ϕ_{C N O T}〉 = \frac{{\|0〉}_{t} {\|0〉}_{e} + {\|1〉}_{t} {\|1〉}_{e}}{\sqrt[]{2}}$
${\|-〉}_{t}$		$\|ϕ_{C N O T}〉 = \frac{{\|0〉}_{t} {\|0〉}_{e} - {\|1〉}_{t} {\|1〉}_{e}}{\sqrt[]{2}}$

Table 2. Particle state before and after CNOT operation

Item	Information carrier	Quantum carryinginformation	Quotation encryption mode	Privacy	Literature
1	Bell state	Real quotation	None	Low	Reference [4]
2	GHZ state	Real quotation	None	Low	Reference [6]
3	Single particle	Encryption quotation	Linear encryption	Normal	Reference [20]
4	Bell state	Encryption quotation	Nonlinear encryption	High	This research

Table 3. Privacy comparison between quantum sealed auction protocols

Item	$c$	$q$	$b$	Efficiency $η$	Protocol
1	$l$	$21 l$	$2 l$	$4.35 %$	SQKD1 in reference [29]
2	$l$	$14 l$	$2 l$	$6.25 %$	SQKD2 in reference [29]
3	$l$	$13 l$	$0$	$7.69 %$	Protocol proposed by this research

Table 4. Communication efficiency comparison of semi⁃quantum secure direct communication

Item	Bidder's Quantumability	Auctioneer's Quantum ability	Efficiency $η$ ( $n$ : the number of bidders )	Literature
1	All	All	$η = 1 / n$ ( ignore decoy particles )	Reference [6]
2	All	All	$η = 1 / (n + 1)$ ( ignore decoy particles )	Reference [10]
3	All	All	$η = 20 %$ ( ignore decoy particles )	Reference [19]
4	All	Measure and reflect	$η = 7.69 %$	This research

Table 5. Communication efficiency comparison of several quantum auction protocols

Han YANG, Yan FENG, Sijiang XIE. Quantum auction protocol based on semi⁃quantum secure direct communication[J]. Chinese Journal of Quantum Electronics, 2024, 41(1): 125

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