Preserving privacy of spatial distances using randomized geometric surface calculations

This paper introduces and evaluates a novel method for privacy-preserving distance computations. The method is based on randomized geometric surface calculations and replaces coordinates with contextual variables representing information about the coordinates or the distances between coordinates. The method is presented with an accompanying step-by-step workflow. Its applicability is demonstrated with real-world spatial data sets from Germany and the Netherlands that contain information about hospital and school locations. Open data was used to enable reproducibility. The method's utility is evaluated in detail using correlations, the relative root mean squared error (RRMSE), a Monte Carlo simulation, and the Wasserstein distance. The results show that the method yields high correlations, provides reasonably accurate results as an RRMSE of about 20% is achieved, converges fast, and preserves the spatial distribution of the true coordinates.