Spatial Discretization for Fine-Grain Zone Checks with STARKs

TL;DR

This paper introduces a distance-aware grid encoding method for point-in-polygon tests in zero-knowledge proofs, significantly improving accuracy with moderate proof cost, enabling efficient privacy-preserving spatial verification.

Contribution

It proposes a novel distance-aware encoding approach for spatial zones in zero-knowledge proofs, enhancing accuracy over Boolean grid methods.

Findings

Distance-aware encoding achieves up to 60% accuracy gain.

Moderate proof overhead of approximately 1.4x.

Effective for coarse grid spatial checks.

Abstract

Many location-based services rely on a point-in-polygon test (PiP), checking whether a point or a trajectory lies inside a geographic zone. Since geometric operations are expensive in zero-knowledge proofs, privately performing the PiP test is challenging. In this paper, we answer the research questions of how different ways of encoding zones affect accuracy and proof cost by exploiting gridbased lookup tables under a fixed STARK execution model. Beyond a Boolean grid-based baseline that marks cells as in- or outside, we explore a distance-aware encoding approach that stores how far each cell is from a zone boundary and uses interpolation to reason within a cell. Our experiments on real-world data demonstrate that the proposed distance-aware approach achieves higher accuracy on coarse grids (max. 60%p accuracy gain) with only a moderate verification overhead (approximately 1.4x), making zone encoding the key lever for efficient zero-knowledge spatial checks.