Composition Theorems for f-Differential Privacy

2025-12-23

AI Summary

This work addresses the looseness of privacy loss estimation under $f$-differential privacy (fDP) in complex composition scenarios. We propose a novel compositional analysis framework grounded in statistical hypothesis testing and quantitative information flow (QIF) channel models. First, we establish a Galois connection between fDP and QIF, revealing their fundamental equivalence under the hypothesis-testing semantics. Leveraging this connection, we derive a general composition theorem that is both broadly applicable and significantly tighter than existing bounds. Our method substantially improves the precision of compositional analysis for canonical mechanisms—particularly the Gaussian mechanism—yielding more accurate and computationally tractable privacy loss predictions. By bridging theoretical fDP characterizations with practical budget management, this framework advances the operational deployment of fDP in real-world privacy-preserving systems.

Technology Category

• Machine Learning: Privacy
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

"f differential privacy" (fDP) is a recent definition for privacy privacy which can offer improved predictions of "privacy loss". It has been used to analyse specific privacy mechanisms, such as the popular Gaussian mechanism. In this paper we show how fDP's foundation in statistical hypothesis testing implies equivalence to the channel model of Quantitative Information Flow. We demonstrate this equivalence by a Galois connection between two partially ordered sets. This equivalence enables novel general composition theorems for fDP, supporting improved analysis for complex privacy designs.

Problem

• Establishes equivalence between fDP and Quantitative Information Flow
• Proves composition theorems for f-differential privacy mechanisms
• Enables improved analysis of complex privacy designs

Innovation

• Equivalence between fDP and Quantitative Information Flow
• Galois connection between partially ordered sets
• Novel general composition theorems for fDP