Privacy-Preserving Quantum Two-Party Geometric Intersection

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 GA ( GB ) as the set of numbered grids SA ( SB ), an efficient privacy-preserving quantum two-party geometric intersection (PQGI) protocol is proposed. In the protocol, the oracle operation OA ( OB ) is firstly utilized to encode the private elements of SA = (a0,a1,⋯,aM-1) ( SB = (b0,b1,⋯,bN-1) ) into the quantum states, and then the oracle operation Of is applied to obtain a new quantum state which includes the XOR results between each element of SA and SB. Finally, the quantum counting is introduced to get the amount ( t ) of the states |ai ⊕ bj > 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.