Spatial Discretization for Fine-Grain Zone Checks with STARKs

Sungmin Lee, Kichang Lee, Gyeongmin Han, Jeonggil Ko

Keywords: Zero-Knowledge Proofs, STARK, Zone Checking, Spatial Discretization, Signed Distance Function

Abstract:

Many location-based services rely on a point-in-polygon test (\textit{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 \textit{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 grid-based 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 $1.4\times$), making zone encoding the key lever for efficient zero-knowledge spatial checks.

Email Sharing: We authorize the sharing of all author emails with Program Chairs.

Data Release: We authorize the release of our submission and author names to the public in the event of acceptance.

Submission Number: 7