This paper introduces ZeroKnowledge Location Privacy (ZKLP), enabling users to prove to third parties that they are within a specified geographical region while not disclosing their exact location. ZKLP supports varying levels of granularity, allowing for customization depending on the use case. To realize ZKLP, we introduce the first set of ZeroKnowledge Proof (ZKP) circuits that are fully compliant to the IEEE 754 standard for floatingpoint arithmetic. Our results demonstrate that our floating point implementation scales efficiently, requiring only 69 constraints per multiplication for 2 15 singleprecision floatingpoint multiplications. We utilize
our floating point implementation to realize the ZKLP paradigm. In comparison to the stateoftheart, we find that our optimized implementation has 14.1× less constraints utilizing single precision floatingpoint values, and 11.2× less constraints when utilizing double precision floatingpoint values. We demonstrate the practicability of ZKLP by building a protocol for privacy preserving peertopeer proximity testing — Alice can test if she is close to Bob by receiving a single message, without either party revealing any other information about their location. In such a configuration, Bob can create a proof of (non)proximity in 0.27 s, whereas Alice can verify her distance to about 250 peers per second.
https://arxiv.org/pdf/2404.14983