Open Access

ARTICLE

Privacy-Preserving Quantum Two-Party Geometric Intersection

Wenjie Liu^1,2,*, Yong Xu², James C. N. Yang³, Wenbin Yu^1,2, Lianhua Chi⁴

1 Jiangsu Engineering Center of Network Monitoring, Nanjing University of Information Science & Technology, Nanjing, 210044, China.
2 School of Computer and Software, Nanjing University of Information Science and Technology, Nanjing, 210044, China.
3 Department of Computer Science and Information Engineering, National Dong Hwa University, Hualien, 974, Taiwan.
4 Department of Computer Science and Information Technology, La Trobe University, VIC, 3086, Australia.

* Corresponding Author: Wenjie Liu. Email: .

Computers, Materials & Continua 2019, 60(3), 1237-1250. https://doi.org/10.32604/cmc.2019.03551

Abstract

Privacy-preserving computational geometry is the research area on the intersection of the domains of secure multi-party computation (SMC) and computational geometry. As an important field, the privacy-preserving geometric intersection (PGI) problem is when each of the multiple parties has a private geometric graph and seeks to determine whether their graphs intersect or not without revealing their private information. In this study, through representing Alice’s (Bob’s) private geometric graph G_A (G_B) as the set of numbered grids S_A (S_B), an efficient privacy-preserving quantum two-party geometric intersection (PQGI) protocol is proposed. In the protocol, the oracle operation O_A (O_B) is firstly utilized to encode the private elements of S_A =(a₀,a₁,…,a_M-1) (S_B =(b₀,b₁,…,b_N-1)) into the quantum states, and then the oracle operation O_f is applied to obtain a new quantum state which includes the XOR results between each element of S_A and S_B. Finally, the quantum counting is introduced to get the amount (t) of the states |a_i⊕b_j| equaling to |0|, and the intersection result can be obtained by judging t >0 or not. Compared with classical PGI protocols, our proposed protocol not only has higher security, but also holds lower communication complexity.

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Citations