Privately Evaluating Region Overlaps with Applications to Collaborative Sensor Output Validation.

Advances in computer vision have made it possible to accurately map objects as regions in 3-dimensional space using LIDAR point clouds. These systems are key building blocks of several emerging technologies including autonomous vehicles. Comparing and validating the output of sensors at different vantage points observing the same scenery can enable these systems to detect faults, identify common obstacles, and improve decision making. However sharing sensor outputs among mutually untrusting parties can leak unwanted information, e.g., model parameters or relative location of the sensors. This work initiates the study of cryptographic protocols that enable two parties observing regions (or objects) in an arbitrary-dimension Euclidean space to privately detect if the regions overlap and approximate the volume of the overlapping region. The protocols rely only on cheap symmetric-key primitives and feature reasonable communication costs and compute times. As applications, the protocols have been benchmarked on data generated from the CARLA autonomous driving simulator and the ScanNet 3D image dataset; they outperform a 2PC garbled-circuit baseline in communication volume and compute time. For instance it takes roughly 0.5 seconds to approximate the volume of the overlapping region of two 3D boxes with low error probability.