TY - EJOU
AU - Liu, Wenjie
AU - Xu, Yong
AU - Yang, James C. N.
AU - Yu, Wenbin
AU - Chi, Lianhua
TI - Privacy-Preserving Quantum Two-Party Geometric Intersection
T2 - Computers, Materials \& Continua
PY - 2019
VL - 60
IS - 3
SN - 1546-2226
AB - 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} =(a_{0},a_{1},…,a_{M-1}) (S_{B} =(b_{0},b_{1},…,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.
KW - Privacy-preserving computational geometry
KW - quantum two-party geometric intersection
KW - oracle
KW - quantum counting
DO - 10.32604/cmc.2019.03551