Study Proposes Distance-Aware Grid Encoding to Boost Zero-Knowledge Spatial Checks

Global: Study Proposes Distance-Aware Grid Encoding to Boost Zero-Knowledge Spatial Checks

A new study released on December 30, 2025 by researchers Sungmin Lee, Kichang Lee, Gyeongmin Han and JeongGil Ko examines how spatial discretization techniques can improve the efficiency of fine‑grain zone checks performed with STARKs. The work was posted to the open‑access repository arXiv, making it globally accessible, and it addresses the challenge of privately verifying point‑in‑polygon (PiP) tests that are computationally intensive in zero‑knowledge proof systems.

Background

Location‑based services frequently need to determine whether a user’s coordinates or trajectory intersect a predefined geographic zone. Performing this point‑in‑polygon test inside a zero‑knowledge proof is costly because geometric operations translate into large arithmetic circuits, which increase both prover and verifier workloads.

Baseline Approach

The authors first evaluate a Boolean grid‑based baseline that partitions the space into cells and marks each cell as either inside or outside the target zone. This simple representation reduces the geometric problem to a lookup, but it can suffer from coarse granularity, leading to reduced accuracy when the grid cells are large.

Distance‑Aware Encoding

To overcome the limitations of the Boolean grid, the study introduces a distance‑aware encoding. Instead of a binary flag, each cell stores the distance to the nearest zone boundary. Interpolation within a cell allows the proof system to reason about points more precisely, effectively smoothing the transition between inside and outside regions.

Experimental Findings

Testing on real‑world geographic data, the distance‑aware method achieved a maximum accuracy improvement of 60%p over the Boolean baseline on coarse grids. Verification time increased modestly, with an overhead of approximately 1.4x compared to the baseline, indicating that the accuracy gains come at a manageable cost.

Implications

These results suggest that zone encoding is a pivotal lever for making zero‑knowledge spatial checks practical in privacy‑preserving location services. By balancing grid resolution with distance information, developers can obtain higher fidelity without prohibitive verification delays.

Future Directions

The authors propose extending the approach to adaptive grids and exploring integration with other zero‑knowledge proof systems beyond STARKs. Further research may also assess the trade‑offs in dynamic environments where zones evolve over time.

This report is based on information from arXiv, licensed under Academic Preprint / Open Access. Based on the abstract of the research paper. Full text available via ArXiv.