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PAC Privacy: Automatic Privacy Measurement and Control of Data Processing

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Advances in Cryptology – CRYPTO 2023 (CRYPTO 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14082))

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Abstract

We propose and study a new privacy definition, termed Probably Approximately Correct (PAC) Privacy. PAC Privacy characterizes the information-theoretic hardness to recover sensitive data given arbitrary information disclosure/leakage during/after any processing. Unlike the classic cryptographic definition and Differential Privacy (DP), which consider the adversarial (input-independent) worst case, PAC Privacy is a simulatable metric that quantifies the instance-based impossibility of inference. A fully automatic analysis and proof generation framework is proposed: security parameters can be produced with arbitrarily high confidence via Monte-Carlo simulation for any black-box data processing oracle. This appealing automation property enables analysis of complicated data processing, where the worst-case proof in the classic privacy regime could be loose or even intractable. Moreover, we show that the produced PAC Privacy guarantees enjoy simple composition bounds and the automatic analysis framework can be implemented in an online fashion to analyze the composite PAC Privacy loss even under correlated randomness. On the utility side, the magnitude of (necessary) perturbation required in PAC Privacy is not lower bounded by \({\varTheta }(\sqrt{d})\) for a d-dimensional release but could be O(1) for many practical data processing tasks, which is in contrast to the input-independent worst-case information-theoretic lower bound. Example applications of PAC Privacy are included with comparisons to existing works.

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Notes

  1. 1.

    Here, we say \(X_0\) and \(X'_0\) are adjacent if they only differ in one datapoint, i.e., their Hamming distance is 1.

  2. 2.

    https://www.mathworks.com/help/stats/sample-data-sets.html.

  3. 3.

    In Theorem 9, we restrict the noise distribution to be Gaussian. We leave a generic lower bound for arbitrary noise distribution as an open problem.

  4. 4.

    If each entry of X is independently generated, and \(\mathcal {M}\) satisfies \(\xi \)-Concentrated Differential Privacy (CDP), then \(\textsf{MI}(X; \mathcal {M}(X)) \le n\xi \) [13].

  5. 5.

    An upper bound on individual sensitivity of Empirical Risk Minimization is only known for strongly-convex optimization [17] with an additional Lipschitz assumption and the loss function needs to be a sum of individual losses on each sample.

  6. 6.

    Besides MI, there are many other efficient side-channel attacks based on different statistical tests such as Pearson correlation [12].

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Acknowledgements

We gratefully acknowledge the support of DSTA Singapore, Cisco Systems, Capital One, and a MathWorks fellowship. We also thank the anonymous reviewers for their helpful comments.

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  1. MIT, Cambridge, USA

    Hanshen Xiao & Srinivas Devadas

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  1. Hanshen Xiao
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Correspondence to Hanshen Xiao .

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    Helena Handschuh

  2. Brown University, Providence, RI, USA

    Anna Lysyanskaya

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Xiao, H., Devadas, S. (2023). PAC Privacy: Automatic Privacy Measurement and Control of Data Processing. In: Handschuh, H., Lysyanskaya, A. (eds) Advances in Cryptology – CRYPTO 2023. CRYPTO 2023. Lecture Notes in Computer Science, vol 14082. Springer, Cham. https://doi.org/10.1007/978-3-031-38545-2_20

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