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Register a new userDifferential Privacy on Finite Computers
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Added by
Victor Balcer
Publication date
2017
fields
Informatics Engineering
and research's language is
English
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We consider the problem of designing and analyzing differentially private algorithms that can be implemented on {em discrete} models of computation in {em strict} polynomial time, motivated by known attacks on floating point implementations of real-arithmetic differentially private algorithms (Mironov, CCS 2012) and the potential for timing attacks on expected polynomial-time algorithms. As a case study, we examine the basic problem of approximating the histogram of a categorical dataset over a possibly large data universe $mathcal{X}$. The classic Laplace Mechanism (Dwork, McSherry, Nissim, Smith, TCC 2006 and J. Privacy & Confidentiality 2017) does not satisfy our requirements, as it is based on real arithmetic, and natural discrete analogues, such as the Geometric Mechanism (Ghosh, Roughgarden, Sundarajan, STOC 2009 and SICOMP 2012), take time at least linear in $|mathcal{X}|$, which can be exponential in the bit length of the input. In this paper, we provide strict polynomial-time discrete algorithms for approximate histograms whose simultaneous accuracy (the maximum error over all bins) matches that of the Laplace Mechanism up to constant factors, while retaining the same (pure) differential privacy guarantee. One of our algorithms produces a sparse histogram as output. Its per-bin accuracy (the error on individual bins) is worse than that of the Laplace Mechanism by a factor of $log|mathcal{X}|$, but we prove a lower bound showing that this is necessary for any algorithm that produces a sparse histogram. A second algorithm avoids this lower bound, and matches the per-bin accuracy of the Laplace Mechanism, by producing a compact and efficiently computable representation of a dense histogram, it is based on an $(n+1)$-wise independent implementation of an appropriately clamped version of the Discrete Geometric Mechanism.
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We give a fast algorithm to optimally compose privacy guarantees of differentially private (DP) algorithms to arbitrary accuracy. Our method is based on the notion of privacy loss random variables to quantify the privacy loss of DP algorithms. The running time and memory needed for our algorithm to approximate the privacy curve of a DP algorithm composed with itself $k$ times is $tilde{O}(sqrt{k})$. This improves over the best prior method by Koskela et al. (2020) which requires $tilde{Omega}(k^{1.5})$ running time. We demonstrate the utility of our algorithm by accurately computing the privacy loss of DP-SGD algorithm of Abadi et al. (2016) and showing that our algorithm speeds up the privacy computations by a few orders of magnitude compared to prior work, while maintaining similar accuracy.
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In recent years, concerns about location privacy are increasing with the spread of location-based services (LBSs). Many methods to protect location privacy have been proposed in the past decades. Especially, perturbation methods based on Geo-Indistinguishability (Geo-I), which randomly perturb a true location to a pseudolocation, are getting attention due to its strong privacy guarantee inherited from differential privacy. However, Geo-I is based on the Euclidean plane even though many LBSs are based on road networks (e.g. ride-sharing services). This causes unnecessary noise and thus an insufficient tradeoff between utility and privacy for LBSs on road networks. To address this issue, we propose a new privacy notion, Geo-Graph-Indistinguishability (GG-I), for locations on a road network to achieve a better tradeoff. We propose Graph-Exponential Mechanism (GEM), which satisfies GG-I. Moreover, we formalize the optimization problem to find the optimal GEM in terms of the tradeoff. However, the computational complexity of a naive method to find the optimal solution is prohibitive, so we propose a greedy algorithm to find an approximate solution in an acceptable amount of time. Finally, our experiments show that our proposed mechanism outperforms a Geo-Is mechanism with respect to the tradeoff.
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