Zero-Knowledge Location Privacy via Accurate Floating-Point SNARKs (2404.14983v2)

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

• The paper introduces ZKLP, a method that secures location proofs using IEEE 754-compliant floating-point SNARK circuits.
• The approach optimizes FP32 operations to just 64 constraints each, significantly improving computational efficiency.
• Evaluated on peer-to-peer proximity tests, the method processes about 470 validations per second, proving its scalability.

Zero-Knowledge Location Privacy via Accurate Floating-Point SNARKs

This paper introduces Zero-Knowledge Location Privacy (ZKLP), a privacy-preserving approach that enables users to demonstrate their presence within specified geographical regions without disclosing their exact location. This is achieved by utilizing a novel set of circuits for zero-knowledge proofs (ZKPs) that adhere to the IEEE 754 standard for floating-point arithmetic.

Key Contributions

The primary contributions of this paper are twofold: the introduction of ZKLP and the development of efficient floating-point SNARK circuits. ZKLP leverages the advancements in ZKPs to tackle privacy issues arising from location-based services. The proposed method provides customizable granularity, allowing users to obfuscate their exact location data depending on the application, thus preserving both utility and privacy.

Key innovations in floating-point arithmetic include the optimization of basic operations such as addition, subtraction, multiplication, division, and square root extraction, ensuring full compliance with IEEE 754. The authors also eliminate the need for costly trigonometric operations traditionally required in geospatial computations, employing optimization techniques that substitute these functions with equivalent mathematical expressions and leverage precomputed values.

Numerical Results and Practical Implementations

The efficiency of the constructed circuits is highlighted by their amortized cost. For FP32 operations, the constraints per operation were reduced to 64 constraints for large-scale executions, significantly lower than other contemporary approaches. These efficiencies enable ZKLP to be practical for real-world applications. The paper evaluates the practicability of ZKLP through a peer-to-peer proximity testing use case, showcasing the ability to evaluate proximity to approximately 470 peers per second with Groth16 as the SNARK protocol.

Moreover, both single and double precision floating-point circuits are successfully implemented and tested against the Berkeley TestFloat library to ensure compliance, passing all test cases owing to their rigorous adherence to IEEE 754.

Implications and Future Research Directions

The implications of this research are substantial, providing a groundwork for securely integrating ZKP into location-based services that require both authenticity and privacy. By demonstrating the practicality and scalability of their approach, the authors set a precedent for adopting ZKLP in varied applications, such as contact tracing and personalized location-based services, without compromising user privacy.

Future work could focus on expanding ZKLP's applicability by bridging the gap between obtaining authentic location data and generating proofs in an atomic manner, potentially leveraging recent advancements in secure multi-party computation and blockchain oracle systems. Additionally, the paper outlines the potential integration of ZKLP with systems like Apple's ``Find My'' network or authenticated GNSS, offering significant prospects for further exploration and implementation of ZKLP in securing geolocation data across diverse platforms.