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Three-party quantum private computation of cardinalities of set intersection and union based on GHZ states

Authors
  • Zhang, Cai1
  • Long, Yinxiang2
  • Sun, Zhiwei3
  • Li, Qin4
  • Huang, Qiong1
  • 1 South China Agricultural University, Guangzhou, 510642, China , Guangzhou (China)
  • 2 Guangdong Technical College of Water Resources and Electric Engineering, Guangzhou, 510925, China , Guangzhou (China)
  • 3 Shenzhen PolyTechnic, Shenzhen, 518055, China , Shenzhen (China)
  • 4 Xiangtan University, Xiangtan, 411105, China , Xiangtan (China)
Type
Published Article
Journal
Scientific Reports
Publisher
Springer Nature
Publication Date
Dec 17, 2020
Volume
10
Issue
1
Identifiers
DOI: 10.1038/s41598-020-77579-w
Source
Springer Nature
License
Green

Abstract

Private Set Intersection Cardinality (PSI-CA) and Private Set Union Cardinality (PSU-CA) are two cryptographic primitives whereby two or more parties are able to obtain the cardinalities of the intersection and the union of their respective private sets, and the privacy of their sets is preserved. In this paper, we propose a three-party protocol to finish these tasks by using quantum resources, where every two, as well as three, parties can obtain the cardinalities of the intersection and the union of their private sets with the help of a semi-honest third party (TP). In our protocol, GHZ states play a role in encoding private information that will be used by TP to compute the cardinalities. We show that the presented protocol is secure against well-known quantum attacks. In addition, we analyze the influence of six typical kinds of Markovian noise on our protocol.

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