@Article{cmc.2019.03551,
AUTHOR = {Wenjie  Liu, Yong  Xu, James C. N.  Yang, Wenbin  Yu, Lianhua  Chi},
TITLE = {Privacy-Preserving Quantum Two-Party Geometric Intersection},
JOURNAL = {Computers, Materials \& Continua},
VOLUME = {60},
YEAR = {2019},
NUMBER = {3},
PAGES = {1237--1250},
URL = {http://www.techscience.com/cmc/v60n3/23091},
ISSN = {1546-2226},
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 <i>G<sub>A</sub> (G<sub>B</sub>)</i> as the set of numbered grids <i>S<sub>A</sub> (S<sub>B</sub>)</i>, an efficient privacy-preserving quantum two-party geometric intersection (PQGI) protocol is proposed. In the protocol, the oracle operation <i>O<sub>A</sub> (O<sub>B</sub>)</i> is firstly utilized to encode the private elements of <i>S<sub>A</sub> =(a<sub>0</sub>,a<sub>1</sub>,…,a<sub>M-1</sub>) (S<sub>B</sub> =(b<sub>0</sub>,b<sub>1</sub>,…,b<sub>N-1</sub>))</i> into the quantum states, and then the oracle operation <i>O<sub>f</sub></i> is applied to obtain a new quantum state which includes the XOR results between each element of <i>S<sub>A</sub></i> and <i>S<sub>B</sub></i>. Finally, the quantum counting is introduced to get the amount (<i>t</i>) of the states |<i>a<sub>i</sub>⊕b<sub>j</sub></i>| equaling to |0|, and the intersection result can be obtained by judging <i>t >0</i> or not. Compared with classical PGI protocols, our proposed protocol not only has higher security, but also holds lower communication complexity.},
DOI = {10.32604/cmc.2019.03551}
}