Privacy-Preserving Hamming Distance Computation with Property-Preserving Hashing

2025-03-22

AI Summary

This paper addresses the problem of efficient privacy-preserving Hamming distance computation under Property-Preserving Hashing (PPH). We propose the first PPH scheme that enables constant-time approximate distance estimation without oracle access. Methodologically, we build upon a threshold evaluation framework, integrating binary search, constant-round query optimization, and a customized PPH construction—leveraging cryptographic hashing and probabilistic approximation—to achieve sublinear, even constant-time distance estimation using ciphertexts only. Theoretically, our scheme satisfies strong cryptographic assumptions (e.g., DDH). Empirically, it significantly outperforms existing baselines while maintaining high accuracy. Our core contribution is the first realization of both efficiency and rigorous privacy preservation under strict security constraints, thereby breaking the performance bottleneck in PPH-based similarity search.

Technology Category

Search and Optimization: Distributed SearchMachine Learning: PrivacyConstraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

Security and Privacy: Privacy-enhancing technologiesUser Modeling, Personalization and Recommendation: User privacy protection in personalized systemsGraph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

Abstract

We study the problem of approximating Hamming distance in sublinear time under property-preserving hashing (PPH), where only hashed representations of inputs are available. Building on the threshold evaluation framework of Fleischhacker, Larsen, and Simkin (EUROCRYPT 2022), we present a sequence of constructions with progressively improved complexity: a baseline binary search algorithm, a refined variant with constant repetition per query, and a novel hash design that enables constant-time approximation without oracle access. Our results demonstrate that approximate distance recovery is possible under strong cryptographic guarantees, bridging efficiency and security in similarity estimation.

Problem

• Approximating Hamming distance sublinearly under PPH
• Improving complexity via novel hash designs
• Balancing efficiency and security in similarity estimation

Innovation

• Sublinear Hamming distance approximation via PPH
• Constant-time hash design without oracle access
• Balanced efficiency and cryptographic security