Private Trajectory Intersection Testing: Is Garbled Circuit Better than Custom Protocols?

In this paper, two protocols are presented for private intersection detection of moving objects’ trajectories. Assuming that the movement trajectory an object can be described by a time-dependent polynomial function, problem finding points is simplified to common roots corresponding polynomials. Thereafter, GrObner Basis used design novel secure protocol Another also designed based on distance computation trajectories’ curves. Moreover, we present complexity analysis testing objects, which Basis. Then, compare its garbled circuit-based Euclidean Distance Computation l points. We prove security our proposed protocol, Keywords: Private Trajectory Intersection Testing, Basis, Computation, Complexity , Garbled Circuit,