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1. Duet: an expressive higher-order language and linear type system for statically enforcing differential privacy

   https://doi.org/10.1145/3360598  

   Near, Joseph P. ; Darais, David ; Abuah, Chike ; Stevens, Tim ; Gaddamadugu, Pranav ; Wang, Lun ; Somani, Neel ; Zhang, Mu ; Sharma, Nikhil ; Shan, Alex ; et al ( October 2019 , Proceedings of the ACM on Programming Languages)

   null (Ed.)

   During the past decade, differential privacy has become the gold standard for protecting the privacy of individuals. However, verifying that a particular program provides differential privacy often remains a manual task to be completed by an expert in the field. Language-based techniques have been proposed for fully automating proofs of differential privacy via type system design, however these results have lagged behind advances in differentially-private algorithms, leaving a noticeable gap in programs which can be automatically verified while also providing state-of-the-art bounds on privacy. We propose Duet, an expressive higher-order language, linear type system and tool for automatically verifying differential privacy of general-purpose higher-order programs. In addition to general purpose programming, Duet supports encoding machine learning algorithms such as stochastic gradient descent, as well as common auxiliary data analysis tasks such as clipping, normalization and hyperparameter tuning - each of which are particularly challenging to encode in a statically verified differential privacy framework. We present a core design of the Duet language and linear type system, and complete key proofs about privacy for well-typed programs. We then show how to extend Duet to support realistic machine learning applications and recent variants of differential privacy which result in improved accuracy for many practical differentially private algorithms. Finally, we implement several differentially private machine learning algorithms in Duet which have never before been automatically verified by a language-based tool, and we present experimental results which demonstrate the benefits of Duet's language design in terms of accuracy of trained machine learning models. 

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2. Synthesizing Tight Privacy and Accuracy Bounds via Weighted Model Counting

   Oakley, Lisa ; Holzen, Steven ; Oprea, Alina ( July 2024 , IEEE 37th Computer Security Foundations Symposium (CSF))

   Programmatically generating tight differential privacy (DP) bounds is a hard problem. Two core challenges are (1) finding expressive, compact, and efficient encodings of the distributions of DP algorithms, and (2) state space explosion stemming from the multiple quantifiers and relational properties of the DP definition. We address the first challenge by developing a method for tight privacy and accuracy bound synthesis using weighted model counting on binary decision diagrams, a state of the art technique from the artificial intelligence and automated reasoning communities for exactly computing probability distributions. We address the second challenge by developing a framework for leveraging inherent symmetries in DP algorithms. Our solution benefits from ongoing research in probabilistic programming languages, allowing us to succinctly and expressively represent different DP algorithms with approachable language syntax that can be used by non-experts. We provide a detailed case study of our solution on the binary randomized response algorithm. We also evaluate an implementation of our solution using the Dice probabilistic programming language for the randomized response and truncated geometric above threshold algorithms. We compare to prior work on exact DP verification using Markov chain probabilistic model checking and the decision procedure DiPC. Very few existing works consider mechanized analysis of accuracy guarantees for DP algorithms. We additionally provide a detailed analysis using our technique for finding tight accuracy bounds for DP algorithms 

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3. DuetSGX: Differential Privacy with Secure Hardware

   Nguyen, Phillip ; Silence, Alex ; Darais, David ; Near, Joseph P ( January 2020 , Workshop on Theory and Practice of Differential Privacy (TPDP))

   null (Ed.)

   Differential privacy offers a formal privacy guarantee for individuals, but many deployments of differentially private systems require a trusted third party (the data curator). We propose DuetSGX, a system that uses secure hardware (Intel’s SGX) to eliminate the need for a trusted data curator. Data owners submit encrypted data that can be decrypted only within a secure enclave running the DuetSGX system, ensuring that sensitive data is never available to the data curator. Analysts submit queries written in the Duet language, which is specifically designed for verifying that programs satisfy differential privacy; DuetSGX uses the Duet typechecker to verify that each query satisfies differential privacy before running it. DuetSGX therefore provides the benefits of local differential privacy and central differential privacy simultaneously: noise is only added to final results, and there is no trusted third party. We have implemented a proof-of-concept implementation of DuetSGX and we release it as open-source. 

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4. Gaussian Differential Privacy

   https://doi.org/10.1111/rssb.12454  

   Dong, Jinshuo ; Roth, Aaron ; Su, Weijie J. ( February 2022 , Journal of the Royal Statistical Society Series B: Statistical Methodology)

   In the past decade, differential privacy has seen remarkable success as a rigorous and practical formalization of data privacy. This privacy definition and its divergence based relaxations, however, have several acknowledged weaknesses, either in handling composition of private algorithms or in analysing important primitives like privacy amplification by subsampling. Inspired by the hypothesis testing formulation of privacy, this paper proposes a new relaxation of differential privacy, which we term ‘f-differential privacy’ (f-DP). This notion of privacy has a number of appealing properties and, in particular, avoids difficulties associated with divergence based relaxations. First, f-DP faithfully preserves the hypothesis testing interpretation of differential privacy, thereby making the privacy guarantees easily interpretable. In addition, f-DP allows for lossless reasoning about composition in an algebraic fashion. Moreover, we provide a powerful technique to import existing results proven for the original differential privacy definition to f-DP and, as an application of this technique, obtain a simple and easy-to-interpret theorem of privacy amplification by subsampling for f-DP. In addition to the above findings, we introduce a canonical single-parameter family of privacy notions within the f-DP class that is referred to as ‘Gaussian differential privacy’ (GDP), defined based on hypothesis testing of two shifted Gaussian distributions. GDP is the focal privacy definition among the family of f-DP guarantees due to a central limit theorem for differential privacy that we prove. More precisely, the privacy guarantees of any hypothesis testing based definition of privacy (including the original differential privacy definition) converges to GDP in the limit under composition. We also prove a Berry–Esseen style version of the central limit theorem, which gives a computationally inexpensive tool for tractably analysing the exact composition of private algorithms. Taken together, this collection of attractive properties render f-DP a mathematically coherent, analytically tractable and versatile framework for private data analysis. Finally, we demonstrate the use of the tools we develop by giving an improved analysis of the privacy guarantees of noisy stochastic gradient descent.

    

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5. Gaussian Differential Privacy

   Dong, Jinshuo ; Roth, Aaron ; Su, Weijie ( January 2021 , Journal of the Royal Statistical Society)

   Differential privacy has seen remarkable success as a rigorous and practical formalization of data privacy in the past decade. This privacy definition and its divergence based relaxations, however, have several acknowledged weaknesses, either in handling composition of private algorithms or in analyzing important primitives like privacy amplification by subsampling. Inspired by the hypothesis testing formulation of privacy, this paper proposes a new relaxation, which we term `f-differential privacy' (f-DP). This notion of privacy has a number of appealing properties and, in particular, avoids difficulties associated with divergence based relaxations. First, f-DP preserves the hypothesis testing interpretation. In addition, f-DP allows for lossless reasoning about composition in an algebraic fashion. Moreover, we provide a powerful technique to import existing results proven for original DP to f-DP and, as an application, obtain a simple subsampling theorem for f-DP. In addition to the above findings, we introduce a canonical single-parameter family of privacy notions within the f-DP class that is referred to as `Gaussian differential privacy' (GDP), defined based on testing two shifted Gaussians. GDP is focal among the f-DP class because of a central limit theorem we prove. More precisely, the privacy guarantees of \emph{any} hypothesis testing based definition of privacy (including original DP) converges to GDP in the limit under composition. The CLT also yields a computationally inexpensive tool for analyzing the exact composition of private algorithms. Taken together, this collection of attractive properties render f-DP a mathematically coherent, analytically tractable, and versatile framework for private data analysis. Finally, we demonstrate the use of the tools we develop by giving an improved privacy analysis of noisy stochastic gradient descent. 

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