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

Cai Zhang,Qin Li,Yinxiang Long,Qiong Huang,Zhiwei Sun

doi:10.1038/s41598-020-77579-w

Cai Zhang, Qin Li + Show 3 more

Open Access

https://doi.org/10.1038/s41598-020-77579-w

Copy DOI

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.

Highlights

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
Private Set Intersection Cardinality (PSI-CA) and Private Set Union Cardinality (PSU-CA), which are two primitives in cryptography, involve two or more users who intend to obtain the cardinalities of the intersection and the union of their private sets through the minimum information disclosure of their sets[1,2,3]
By Shi et al.’s work, we are trying to design a three-party protocol to solve PSI-CA and PSU-CA problems, where every two and three parties can obtain the cardinalities of the intersection and the union of their respective private sets with the aid of a semi-honest third party (TP)

Summary

Introduction

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. By Shi et al.’s work, we are trying to design a three-party protocol to solve PSI-CA and PSU-CA problems, where every two and three parties can obtain the cardinalities of the intersection and the union of their respective private sets with the aid of a semi-honest third party (TP). Suppose that Alice, Bob and Charlie have private sets A = {a1, a2, .

Results

Conclusion