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Zero-Knowledge Location Privacy via Accurate Floating Point SNARKs

Abstract

This paper introduces Zero-Knowledge 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 Zero-Knowledge Proof (ZKP) circuits that are fully compliant to the IEEE 754 standard for floating-point arithmetic. Our results demonstrate that our floating point implementation scales efficiently, requiring only 6969 constraints per multiplication for 2152^{15} single-precision floating-point multiplications. We utilize our floating point implementation to realize the ZKLP paradigm. In comparison to the state-of-the-art, we find that our optimized implementation has 14.1×14.1 \times less constraints utilizing single precision floating-point values, and 11.2×11.2 \times less constraints when utilizing double precision floating-point values. We demonstrate the practicability of ZKLP by building a protocol for privacy preserving peer-to-peer 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 0.27s0.27 s, whereas Alice can verify her distance to about 250250 peers per second

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