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Advanced Probabilistic Couplings for Differential Privacy

Gilles Barthe, Noémie Fong, Marco Gaboardi, Benjamin Grégoire, Justin Hsu, Pierre-Yves Strub
2016 Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security - CCS'16  
We implement our logic in EasyCrypt, and formally verify privacy. We also introduce a novel coupling technique called optimal subset coupling that may be of independent interest.  ...  We address these limitations with a new formalism extending apRHL, a relational program logic that has been used for proving differential privacy of non-interactive algorithms, and incorporating aHL, a  ...  on accuracy, privacy from advanced composition, and privacy for interactive algorithm.  ... 
doi:10.1145/2976749.2978391 dblp:conf/ccs/BartheFGGHS16 fatcat:4ge6fousn5frrkcicmszlniboa

Proving Differential Privacy via Probabilistic Couplings [article]

Gilles Barthe, Marco Gaboardi, Benjamin Grégoire, Justin Hsu, Pierre-Yves Strub
2017 arXiv   accepted
Our methods are based on the observation that differential privacy has deep connections with a generalization of probabilistic couplings, an established mathematical tool for reasoning about stochastic  ...  In this paper, we develop compositional methods for formally verifying differential privacy for algorithms whose analysis goes beyond the composition theorem.  ...  Acknowledgments We warmly thank Aaron Roth for challenging us with the problem of verifying Sparse Vector.  ... 
arXiv:1601.05047v4 fatcat:ebuijcjdzvbalcbqephgryxoyy

Differential Privacy at Risk: Bridging Randomness and Privacy Budget

Ashish Dandekar, Debabrota Basu, Stéphane Bressan
2021 Proceedings on Privacy Enhancing Technologies  
We instantiate the probabilistic calibration for the Laplace mechanism by providing analytical results.Secondly, we propose a cost model that bridges the gap between the privacy level and the compensation  ...  We quantitatively show that composition using the cost optimal privacy at risk provides stronger privacy guarantee than the classical advanced composition.  ...  We thank Pierre Senellart for his help in reviewing derivations of privacy at risk for the Laplace mechanism.  ... 
doi:10.2478/popets-2021-0005 fatcat:vuubbbuzrfbijd2ajfnzrxb2bu

Synthesizing coupling proofs of differential privacy

Aws Albarghouthi, Justin Hsu
2017 Proceedings of the ACM on Programming Languages  
Differential privacy has emerged as a promising probabilistic formulation of privacy, generating intense interest within academia and industry.  ...  We present a push-button, automated technique for verifying ε-differential privacy of sophisticated randomized algorithms.  ...  ACKNOWLEDGMENTS We thank Gilles Barthe, Marco Gaboardi, Zachary Kinkaid, Danfeng Zhang, and the anonymous reviewers for stimulating discussions and useful comments on earlier drafts of this work.  ... 
doi:10.1145/3158146 dblp:journals/pacmpl/AlbarghouthiH18 fatcat:c3od4wpcbvhgfgaotao7crk5jm

Differential Privacy at Risk: Bridging Randomness and Privacy Budget [article]

Ashish Dandekar, Debabrota Basu, Stephane Bressan
2020 arXiv   pre-print
We provide a composition theorem that leverages privacy at risk. We instantiate the probabilistic calibration for the Laplace mechanism by providing analytical results.  ...  We quantitatively show that composition using the cost optimal privacy at risk provides stronger privacy guarantee than the classical advanced composition.  ...  Acknowledgements We want convey a special thanks to Pierre Senellart at DI,École Normale Supérieure, Paris for his careful reading of our drafts and thoughtful interventions.  ... 
arXiv:2003.00973v2 fatcat:gdt3xf6ho5bgrjvsy5p5x7vssq

Probabilistic Couplings for Probabilistic Reasoning [article]

Justin Hsu
2017 arXiv   pre-print
Finally, we propose several more sophisticated constructions for approximate couplings: a principle for showing accuracy-dependent privacy, a generalization of the advanced composition theorem, and an  ...  proof of privacy for Sparse Vector in apRHL.  ...  Applying the advanced composition theorem of differential privacy (Theorem 4.1.5), h n (−, a) : → Distr(A) is ( * , δ * )-differentially private for every a ∈ A.  ... 
arXiv:1710.09951v2 fatcat:emqjytis65go3l6nuzy2ivw52y

Probabilistic Counters for Privacy Preserving Data Aggregation [article]

Dominik Bojko, Krzysztof Grining, Marek Klonowski
2022 arXiv   pre-print
We use standard, rigid differential privacy notion.  ...  Probabilistic counters are well known tools often used for space-efficient set cardinality estimation. In this paper we investigate probabilistic counters from the perspective of preserving privacy.  ...  There is a possibility to provide analogous differential privacy properties for other probabilistic counters.  ... 
arXiv:2003.11446v2 fatcat:x6eazya2wvbadoyxhoygbbryl4

Probabilistic Relational Reasoning via Metrics [article]

Arthur Azevedo de Amorim, Marco Gaboardi, Justin Hsu, Shin-ya Katsumata
2019 arXiv   pre-print
We show how to extend Fuzz to capture more general relational properties of probabilistic programs, with approximate, or (ϵ, δ)-differential privacy serving as a leading example.  ...  privacy.  ...  [7] develops a program logic for reasoning about a probabilistic notion of sensitivity based on couplings and the Kantorovich metric. Barthe et al.  ... 
arXiv:1807.05091v3 fatcat:rl7rwnqeb5a77h2a3mg3fylvpa

Privacy: Theory meets Practice on the Map

Ashwin Machanavajjhala, Daniel Kifer, John Abowd, Johannes Gehrke, Lars Vilhuber
2008 2008 IEEE 24th International Conference on Data Engineering  
Instead, we generate synthetic data that statistically mimic the original data while providing privacy guarantees. We use these synthetic data as a surrogate for the original data.  ...  The target application for this work is a mapping program that shows the commuting patterns of the population of the United States. The source data for this application were collected by the U.S.  ...  Hence, a dataset satisfies ( , δ)-probabilistic differential privacy if each partition of the dataset satisfies ( , δ)probabilistic differential privacy.  ... 
doi:10.1109/icde.2008.4497436 dblp:conf/icde/MachanavajjhalaKAGV08 fatcat:neqxrlbfs5di3czfak3qyzizya

Privacy Amplification by Subsampling: Tight Analyses via Couplings and Divergences [article]

Borja Balle and Gilles Barthe and Marco Gaboardi
2018 arXiv   pre-print
Differential privacy comes equipped with multiple analytical tools for the design of private data analyses.  ...  Furthermore, it introduces new tools, including advanced joint convexity and privacy profiles, which might be of independent interest.  ...  In particular, the proof of advanced joint convexity uses ideas from probabilistic couplings, and more specifically the maximal coupling construction (see Theorem 2 and its proof for more details).  ... 
arXiv:1807.01647v2 fatcat:cx5ov4b5ifgc3mif7p77w6uvaq

Automated Methods for Checking Differential Privacy [article]

Gilles Barthe, Rohit Chadha, Vishal Jagannath, A. Prasad Sistla and Mahesh Viswanathan
2019 arXiv   pre-print
We propose the first decision procedure for checking the differential privacy of a non-trivial class of probabilistic computations.  ...  Thanks to its mathematical definition, differential privacy is also a natural target for formal analysis. A broad line of work uses logical methods for proving privacy.  ...  Even though significant advances have been made in identifying proof principles to establish differential privacy [27, 19, 8, 6, 4, 30, 14, 1] and techniques have been proposed to find differential privacy  ... 
arXiv:1910.04137v1 fatcat:h2qddvpih5eylez7c2qv7zj2bq

Privacy Profiles and Amplification by Subsampling

Borja Balle, Gilles Barthe, Marco Gaboardi
2020 Journal of Privacy and Confidentiality  
argument, and introduces a new tool to analyse differential privacy for mixture distributions.  ...  \'e}nyi differential privacy.  ...  This research was initiated during the 2017 Probabilistic Programming Languages workshop hosted by McGill University's Bellairs Research Institute.  ... 
doi:10.29012/jpc.726 fatcat:mttoco5dnnbwrelglz7nkkkmnm

SoK: Differential Privacies [article]

Damien Desfontaines, Balázs Pejó
2020 arXiv   pre-print
Shortly after it was first introduced in 2006, differential privacy became the flagship data privacy definition.  ...  We list all data privacy definitions based on differential privacy, and partition them into seven categories, depending on which aspect of the original definition is modified.  ...  Acknowledgments The authors would like to thank Alex Kulesza, Esfandiar Mohammadi, David Basin, and the anonymous reviewers for their helpful comments.  ... 
arXiv:1906.01337v4 fatcat:dnkli276a5atll7xytbi23sjxq

Relational ⋆-Liftings for Differential Privacy

Gilles Barthe, Thomas Espitau, Justin Hsu, Tetsuya Sato, Pierre-Yves Strub
2018 Logical Methods in Computer Science  
Recent developments in formal verification have identified approximate liftings (also known as approximate couplings) as a clean, compositional abstraction for proving differential privacy.  ...  To capture the quantitative nature of differential privacy, these systems rely on a quantitative generalization of probabilistic couplings (see, e.g., (Lindvall, 2002; Thorisson, 2000; Villani, 2008) )  ...  Acknowledgments We thank the anonymous reviewers for their helpful suggestions.  ... 
doi:10.23638/lmcs-15(4:18)2019 fatcat:br7pgyikijce5obdwca6emnymq

Contextual Linear Types for Differential Privacy [article]

Matías Toro, David Darais, Chike Abuah, Joe Near, Damián Árquez, Federico Olmedo, Éric Tanter
2021 arXiv   pre-print
Since the seminal design of Fuzz, which is restricted to ϵ-differential privacy, a lot of effort has been made to support more advanced variants of differential privacy, like (ϵ,δ)-differential privacy  ...  recent differential privacy literature.  ...  Approximate couplings [13] are a probabilistic abstraction that witnesses differential privacy properties of programs and have been successfully exploited for verification purposes.  ... 
arXiv:2010.11342v2 fatcat:gwgcsvx2mzewlpui56256g4noa
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