Composition for Pufferfish Privacy

2026-02-02

AI Summary

This work addresses the lack of composability in Pufferfish privacy mechanisms under repeated invocation, which poses a risk of privacy leakage. We establish, for the first time, necessary and sufficient conditions under which Pufferfish mechanisms satisfy linear composability, and construct a formal bridge between Pufferfish and differential privacy that preserves semantic interpretability while enabling strong composability guarantees. Leveraging the $(a,b)$-influence curve framework, we systematically transform existing differential privacy algorithms into composable Pufferfish mechanisms. The resulting algorithms are successfully applied to Markov chain settings, demonstrating significant performance improvements over current approaches.

Technology Category

• Machine Learning: Privacy
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Security and Privacy: Data transparency and provenance
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Algorithmic accountability and transparency on the web

Abstract

When creating public data products out of confidential datasets, inferential/posterior-based privacy definitions, such as Pufferfish, provide compelling privacy semantics for data with correlations. However, such privacy definitions are rarely used in practice because they do not always compose. For example, it is possible to design algorithms for these privacy definitions that have no leakage when run once but reveal the entire dataset when run more than once. We prove necessary and sufficient conditions that must be added to ensure linear composition for Pufferfish mechanisms, hence avoiding such privacy collapse. These extra conditions turn out to be differential privacy-style inequalities, indicating that achieving both the interpretable semantics of Pufferfish for correlated data and composition benefits requires adopting differentially private mechanisms to Pufferfish. We show that such translation is possible through a concept called the $(a,b)$-influence curve, and many existing differentially private algorithms can be translated with our framework into a composable Pufferfish algorithm. We illustrate the benefit of our new framework by designing composable Pufferfish algorithms for Markov chains that significantly outperform prior work.

Problem

• Pufferfish Privacy
• Composition
• Correlated Data
• Privacy Collapse
• Differential Privacy

Innovation

• Pufferfish privacy
• composition
• differential privacy
• influence curve
• Markov chains