Zero-Knowledge Location Privacy via Accurate Floating-Point SNARKs

TL;DR

This paper presents a novel zero-knowledge location privacy protocol using IEEE 754 compliant floating-point SNARKs, enabling efficient, privacy-preserving proximity testing with practical performance metrics.

Contribution

It introduces the first fully IEEE 754 compliant floating-point SNARK circuits and applies them to create an efficient zero-knowledge location privacy scheme.

Findings

Floating-point circuits require only 64 constraints per multiplication.

The optimized implementation reduces constraints by 15.9x for single precision.

Proximity proofs are generated in 0.26 seconds, with verification at 470 peers per second.

Abstract

We introduce 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 circuits amortize efficiently, requiring only $64$ constraints per multiplication for $2^{15}$ single-precision floating-point multiplications. We utilize our floating point implementation to realize the ZKLP paradigm. In comparison to a baseline, we find that our optimized implementation has $15.9 \times$ less constraints utilizing single precision floating-point values, and $12.2 \times$ 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 $0.26 s$, whereas Alice can verify her distance to about $470$ peers per second