Searcharxiv⌕ Search

arXiv subjects

Salil Vadhan

Publications and source records attributed to Salil Vadhan.

At least 37 records · Page 2Linked to original sources

Black-Box Training Data Identification in GANs via Detector Networks

Since their inception Generative Adversarial Networks (GANs) have been popular generative models across images, audio, video, and tabular data. In this paper we study whether given access to a trained GAN, as well as fresh samples from the underlying distribution, if it is possible for an attacker to efficiently identify if a given point is a member of the GAN's training data. This is of interest for both reasons related to copyright, where a user may want to determine if their copyrighted data has been used to train a GAN, and in the study of data privacy, where the ability to detect training set membership is known as a membership inference attack. Unlike the majority of prior work this paper investigates the privacy implications of using GANs in black-box settings, where the attack only has access to samples from the generator, rather than access to the discriminator as well. We introduce a suite of membership inference attacks against GANs in the black-box setting and evaluate our attacks on image GANs trained on the CIFAR10 dataset and tabular GANs trained on genomic data. Our most successful attack, called The Detector, involve training a second network to score samples based on their likelihood of being generated by the GAN, as opposed to a fresh sample from the distribution. We prove under a simple model of the generator that the detector is an approximately optimal membership inference attack. Across a wide range of tabular and image datasets, attacks, and GAN architectures, we find that adversaries can orchestrate non-trivial privacy attacks when provided with access to samples from the generator. At the same time, the attack success achievable against GANs still appears to be lower compared to other generative and discriminative models; this leaves the intriguing open question of whether GANs are in fact more private, or if it is a matter of developing stronger attacks.

cs.LG↗

Singular Value Approximation and Sparsifying Random Walks on Directed Graphs

In this paper, we introduce a new, spectral notion of approximation between directed graphs, which we call singular value (SV) approximation. SV-approximation is stronger than previous notions of spectral approximation considered in the literature, including spectral approximation of Laplacians for undirected graphs (Spielman Teng STOC 2004), standard approximation for directed graphs (Cohen et. al. STOC 2017), and unit-circle approximation for directed graphs (Ahmadinejad et. al. FOCS 2020). Further, SV approximation enjoys several useful properties not possessed by previous notions of approximation, e.g., it is preserved under products of random-walk matrices and bounded matrices. We provide a nearly linear-time algorithm for SV-sparsifying (and hence UC-sparsifying) Eulerian directed graphs, as well as $\ell$-step random walks on such graphs, for any $\ell\leq \text{poly}(n)$. Combined with the Eulerian scaling algorithms of (Cohen et. al. FOCS 2018), given an arbitrary (not necessarily Eulerian) directed graph and a set $S$ of vertices, we can approximate the stationary probability mass of the $(S,S^c)$ cut in an $\ell$-step random walk to within a multiplicative error of $1/\text{polylog}(n)$ and an additive error of $1/\text{poly}(n)$ in nearly linear time. As a starting point for these results, we provide a simple black-box reduction from SV-sparsifying Eulerian directed graphs to SV-sparsifying undirected graphs; such a directed-to-undirected reduction was not known for previous notions of spectral approximation.

cs.DS↗

On the works of Avi Wigderson

This is an overview of some of the works of Avi Wigderson, 2021 Abel prize laureate. Wigderson's contributions span many fields of computer science and mathematics. In this survey we focus on four subfields: cryptography, pseudorandomness, computational complexity lower bounds, and the theory of optimization over symmetric manifolds. Even within those fields, we are not able to mention all of Wigderson's results, let alone cover them in full detail. However, we attempt to give a broad view of each field, as well as describe how Wigderson's papers have answered central questions, made key definitions, forged unexpected connections, or otherwise made lasting changes to our ways of thinking in that field.

cs.CC↗

Concurrent Composition Theorems for Differential Privacy

We study the concurrent composition properties of interactive differentially private mechanisms, whereby an adversary can arbitrarily interleave its queries to the different mechanisms. We prove that all composition theorems for non-interactive differentially private mechanisms extend to the concurrent composition of interactive differentially private mechanisms, whenever differential privacy is measured using the hypothesis testing framework of $f$-DP, which captures standard $(\eps,δ)$-DP as a special case. We prove the concurrent composition theorem by showing that every interactive $f$-DP mechanism can be simulated by interactive post-processing of a non-interactive $f$-DP mechanism. In concurrent and independent work, Lyu~\cite{lyu2022composition} proves a similar result to ours for $(\eps,δ)$-DP, as well as a concurrent composition theorem for Rényi DP. We also provide a simple proof of Lyu's concurrent composition theorem for Rényi DP. Lyu leaves the general case of $f$-DP as an open problem, which we solve in this paper.

cs.DS↗

Don't Look at the Data! How Differential Privacy Reconfigures the Practices of Data Science

Across academia, government, and industry, data stewards are facing increasing pressure to make datasets more openly accessible for researchers while also protecting the privacy of data subjects. Differential privacy (DP) is one promising way to offer privacy along with open access, but further inquiry is needed into the tensions between DP and data science. In this study, we conduct interviews with 19 data practitioners who are non-experts in DP as they use a DP data analysis prototype to release privacy-preserving statistics about sensitive data, in order to understand perceptions, challenges, and opportunities around using DP. We find that while DP is promising for providing wider access to sensitive datasets, it also introduces challenges into every stage of the data science workflow. We identify ethics and governance questions that arise when socializing data scientists around new privacy constraints and offer suggestions to better integrate DP and data science.

cs.HC↗

Canonical Noise Distributions and Private Hypothesis Tests

$f$-DP has recently been proposed as a generalization of differential privacy allowing a lossless analysis of composition, post-processing, and privacy amplification via subsampling. In the setting of $f$-DP, we propose the concept of a canonical noise distribution (CND), the first mechanism designed for an arbitrary $f$-DP guarantee. The notion of CND captures whether an additive privacy mechanism perfectly matches the privacy guarantee of a given $f$. We prove that a CND always exists, and give a construction that produces a CND for any $f$. We show that private hypothesis tests are intimately related to CNDs, allowing for the release of private $p$-values at no additional privacy cost as well as the construction of uniformly most powerful (UMP) tests for binary data, within the general $f$-DP framework. We apply our techniques to the problem of difference of proportions testing, and construct a UMP unbiased (UMPU) "semi-private" test which upper bounds the performance of any $f$-DP test. Using this as a benchmark we propose a private test, based on the inversion of characteristic functions, which allows for optimal inference for the two population parameters and is nearly as powerful as the semi-private UMPU. When specialized to the case of $(ε,0)$-DP, we show empirically that our proposed test is more powerful than any $(ε/\sqrt 2)$-DP test and has more accurate type I errors than the classic normal approximation test.

cs.CR↗

Widespread Underestimation of Sensitivity in Differentially Private Libraries and How to Fix It

We identify a new class of vulnerabilities in implementations of differential privacy. Specifically, they arise when computing basic statistics such as sums, thanks to discrepancies between the implemented arithmetic using finite data types (namely, ints or floats) and idealized arithmetic over the reals or integers. These discrepancies cause the sensitivity of the implemented statistics (i.e., how much one individual's data can affect the result) to be much larger than the sensitivity we expect. Consequently, essentially all differential privacy libraries fail to introduce enough noise to meet the requirements of differential privacy, and we show that this may be exploited in realistic attacks that can extract individual-level information from private query systems. In addition to presenting these vulnerabilities, we also provide a number of solutions, which modify or constrain the way in which the sum is implemented in order to recover the idealized or near-idealized bounds on sensitivity.

cs.CR↗

Hypothesis Testing for Differentially Private Linear Regression

In this work, we design differentially private hypothesis tests for the following problems in the general linear model: testing a linear relationship and testing for the presence of mixtures. The majority of our hypothesis tests are based on differentially private versions of the $F$-statistic for the general linear model framework, which are uniformly most powerful unbiased in the non-private setting. We also present other tests for these problems, one of which is based on the differentially private nonparametric tests of Couch, Kazan, Shi, Bray, and Groce (CCS 2019), which is especially suited for the small dataset regime. We show that the differentially private $F$-statistic converges to the asymptotic distribution of its non-private counterpart. As a corollary, the statistical power of the differentially private $F$-statistic converges to the statistical power of the non-private $F$-statistic. Through a suite of Monte Carlo based experiments, we show that our tests achieve desired significance levels and have a high power that approaches the power of the non-private tests as we increase sample sizes or the privacy-loss parameter. We also show when our tests outperform existing methods in the literature.

math.ST↗

High-precision Estimation of Random Walks in Small Space

We provide a deterministic $\tilde{O}(\log N)$-space algorithm for estimating random walk probabilities on undirected graphs, and more generally Eulerian directed graphs, to within inverse polynomial additive error ($ε=1/\mathrm{poly}(N)$) where $N$ is the length of the input. Previously, this problem was known to be solvable by a randomized algorithm using space $O(\log N)$ (following Aleliunas et al., FOCS 79) and by a deterministic algorithm using space $O(\log^{3/2} N)$ (Saks and Zhou, FOCS 95 and JCSS 99), both of which held for arbitrary directed graphs but had not been improved even for undirected graphs. We also give improvements on the space complexity of both of these previous algorithms for non-Eulerian directed graphs when the error is negligible ($ε=1/N^{ω(1)}$), generalizing what Hoza and Zuckerman (FOCS 18) recently showed for the special case of distinguishing whether a random walk probability is $0$ or greater than $ε$. We achieve these results by giving new reductions between powering Eulerian random-walk matrices and inverting Eulerian Laplacian matrices, providing a new notion of spectral approximation for Eulerian graphs that is preserved under powering, and giving the first deterministic $\tilde{O}(\log N)$-space algorithm for inverting Eulerian Laplacian matrices. The latter algorithm builds on the work of Murtagh et al. (FOCS 17) that gave a deterministic $\tilde{O}(\log N)$-space algorithm for inverting undirected Laplacian matrices, and the work of Cohen et al. (FOCS 19) that gave a randomized $\tilde{O}(N)$-time algorithm for inverting Eulerian Laplacian matrices. A running theme throughout these contributions is an analysis of "cycle-lifted graphs", where we take a graph and "lift" it to a new graph whose adjacency matrix is the tensor product of the original adjacency matrix and a directed cycle (or variants of one).

cs.CC↗

Deterministic Approximation of Random Walks via Queries in Graphs of Unbounded Size

Consider the following computational problem: given a regular digraph $G=(V,E)$, two vertices $u,v \in V$, and a walk length $t\in \mathbb{N}$, estimate the probability that a random walk of length $t$ from $u$ ends at $v$ to within $\pm \varepsilon.$ A randomized algorithm can solve this problem by carrying out $O(1/\varepsilon^2)$ random walks of length $t$ from $u$ and outputting the fraction that end at $v$. In this paper, we study deterministic algorithms for this problem that are also restricted to carrying out walks of length $t$ from $u$ and seeing which ones end at $v$. Specifically, if $G$ is $d$-regular, the algorithm is given oracle access to a function $f : [d]^t\to \{0,1\}$ where $f(x)$ is $1$ if the walk from $u$ specified by the edge labels in $x$ ends at $v$. We assume that G is consistently labelled, meaning that the edges of label $i$ for each $i\in [d]$ form a permutation on $V$. We show that there exists a deterministic algorithm that makes $\text{poly}(dt/\varepsilon)$ nonadaptive queries to $f$, regardless of the number of vertices in the graph $G$. Crucially, and in contrast to the randomized algorithm, our algorithm does not simply output the average value of its queries. Indeed, Hoza, Pyne, and Vadhan (ITCS 2021) showed that any deterministic algorithm of the latter form that works for graphs of unbounded size must have query complexity at least $\exp(\tildeΩ(\log(t)\log(1/\varepsilon)))$.

cs.CC↗

Concurrent Composition of Differential Privacy

We initiate a study of the composition properties of interactive differentially private mechanisms. An interactive differentially private mechanism is an algorithm that allows an analyst to adaptively ask queries about a sensitive dataset, with the property that an adversarial analyst's view of the interaction is approximately the same regardless of whether or not any individual's data is in the dataset. Previous studies of composition of differential privacy have focused on non-interactive algorithms, but interactive mechanisms are needed to capture many of the intended applications of differential privacy and a number of the important differentially private primitives. We focus on concurrent composition, where an adversary can arbitrarily interleave its queries to several differentially private mechanisms, which may be feasible when differentially private query systems are deployed in practice. We prove that when the interactive mechanisms being composed are pure differentially private, their concurrent composition achieves privacy parameters (with respect to pure or approximate differential privacy) that match the (optimal) composition theorem for noninteractive differential privacy. We also prove a composition theorem for interactive mechanisms that satisfy approximate differential privacy. That bound is weaker than even the basic (suboptimal) composition theorem for noninteractive differential privacy, and we leave closing the gap as a direction for future research, along with understanding concurrent composition for other variants of differential privacy.

cs.CR↗

Inaccessible Entropy I: Inaccessible Entropy Generators and Statistically Hiding Commitments from One-Way Functions

We put forth a new computational notion of entropy, measuring the (in)feasibility of sampling high-entropy strings that are consistent with a given generator. Specifically, the i'th output block of a generator G has accessible entropy at most k if the following holds: when conditioning on its prior coin tosses, no polynomial-time strategy $\widetilde{G}$ can generate valid output for G's i'th output block with entropy greater than k. A generator has inaccessible entropy if the total accessible entropy (summed over the blocks) is noticeably smaller than the real entropy of G's output. As an application of the above notion, we improve upon the result of Haitner, Nguyen, Ong, Reingold, and Vadhan [Sicomp '09], presenting a much simpler and more efficient construction of statistically hiding commitment schemes from arbitrary one-way functions.

cs.CR↗

Privacy Odometers and Filters: Pay-as-you-Go Composition

In this paper we initiate the study of adaptive composition in differential privacy when the length of the composition, and the privacy parameters themselves can be chosen adaptively, as a function of the outcome of previously run analyses. This case is much more delicate than the setting covered by existing composition theorems, in which the algorithms themselves can be chosen adaptively, but the privacy parameters must be fixed up front. Indeed, it isn't even clear how to define differential privacy in the adaptive parameter setting. We proceed by defining two objects which cover the two main use cases of composition theorems. A privacy filter is a stopping time rule that allows an analyst to halt a computation before his pre-specified privacy budget is exceeded. A privacy odometer allows the analyst to track realized privacy loss as he goes, without needing to pre-specify a privacy budget. We show that unlike the case in which privacy parameters are fixed, in the adaptive parameter setting, these two use cases are distinct. We show that there exist privacy filters with bounds comparable (up to constants) with existing privacy composition theorems. We also give a privacy odometer that nearly matches non-adaptive private composition theorems, but is sometimes worse by a small asymptotic factor. Moreover, we show that this is inherent, and that any valid privacy odometer in the adaptive parameter setting must lose this factor, which shows a formal separation between the filter and odometer use-cases.

cs.CR↗

Inaccessible Entropy II: IE Functions and Universal One-Way Hashing

This paper uses a variant of the notion of \emph{inaccessible entropy} (Haitner, Reingold, Vadhan and Wee, STOC 2009), to give an alternative construction and proof for the fundamental result, first proved by Rompel (STOC 1990), that \emph{Universal One-Way Hash Functions (UOWHFs)} can be based on any one-way functions. We observe that a small tweak of any one-way function $f$ is already a weak form of a UOWHF: consider the function $F(x,i)$ that returns the $i$-bit-long prefix of $f(x)$. If $F$ were a UOWHF then given a random $x$ and $i$ it would be hard to come up with $x'\neq x$ such that $F(x,i)=F(x',i)$. While this may not be the case, we show (rather easily) that it is hard to sample $x'$ with almost full entropy among all the possible such values of $x'$. The rest of our construction simply amplifies and exploits this basic property.Combined with other recent work, the construction of three fundamental cryptographic primitives (Pseudorandom Generators, Statistically Hiding Commitments and UOWHFs) out of one-way functions is now to a large extent unified. In particular, all three constructions rely on and manipulate computational notions of entropy in similar ways. Pseudorandom Generators rely on the well-established notion of pseudoentropy, whereas Statistically Hiding Commitments and UOWHFs rely on the newer notion of inaccessible entropy.

cs.CR↗

Differentially Private Simple Linear Regression

Economics and social science research often require analyzing datasets of sensitive personal information at fine granularity, with models fit to small subsets of the data. Unfortunately, such fine-grained analysis can easily reveal sensitive individual information. We study algorithms for simple linear regression that satisfy differential privacy, a constraint which guarantees that an algorithm's output reveals little about any individual input data record, even to an attacker with arbitrary side information about the dataset. We consider the design of differentially private algorithms for simple linear regression for small datasets, with tens to hundreds of datapoints, which is a particularly challenging regime for differential privacy. Focusing on a particular application to small-area analysis in economics research, we study the performance of a spectrum of algorithms we adapt to the setting. We identify key factors that affect their performance, showing through a range of experiments that algorithms based on robust estimators (in particular, the Theil-Sen estimator) perform well on the smallest datasets, but that other more standard algorithms do better as the dataset size increases.

cs.LG↗

Spectral Sparsification via Bounded-Independence Sampling

We give a deterministic, nearly logarithmic-space algorithm for mild spectral sparsification of undirected graphs. Given a weighted, undirected graph $G$ on $n$ vertices described by a binary string of length $N$, an integer $k\leq \log n$, and an error parameter $ε> 0$, our algorithm runs in space $\tilde{O}(k\log (N\cdot w_{\mathrm{max}}/w_{\mathrm{min}}))$ where $w_{\mathrm{max}}$ and $w_{\mathrm{min}}$ are the maximum and minimum edge weights in $G$, and produces a weighted graph $H$ with $\tilde{O}(n^{1+2/k}/ε^2)$ edges that spectrally approximates $G$, in the sense of Spielmen and Teng [ST04], up to an error of $ε$. Our algorithm is based on a new bounded-independence analysis of Spielman and Srivastava's effective resistance based edge sampling algorithm [SS08] and uses results from recent work on space-bounded Laplacian solvers [MRSV17]. In particular, we demonstrate an inherent tradeoff (via upper and lower bounds) between the amount of (bounded) independence used in the edge sampling algorithm, denoted by $k$ above, and the resulting sparsity that can be achieved.

cs.DS↗

Deterministic Approximation of Random Walks in Small Space

We give a deterministic, nearly logarithmic-space algorithm that given an undirected graph $G$, a positive integer $r$, and a set $S$ of vertices, approximates the conductance of $S$ in the $r$-step random walk on $G$ to within a factor of $1+ε$, where $ε>0$ is an arbitrarily small constant. More generally, our algorithm computes an $ε$-spectral approximation to the normalized Laplacian of the $r$-step walk. Our algorithm combines the derandomized square graph operation (Rozenman and Vadhan, 2005), which we recently used for solving Laplacian systems in nearly logarithmic space (Murtagh, Reingold, Sidford, and Vadhan, 2017), with ideas from (Cheng, Cheng, Liu, Peng, and Teng, 2015), which gave an algorithm that is time-efficient (while ours is space-efficient) and randomized (while ours is deterministic) for the case of even $r$ (while ours works for all $r$). Along the way, we provide some new results that generalize technical machinery and yield improvements over previous work. First, we obtain a nearly linear-time randomized algorithm for computing a spectral approximation to the normalized Laplacian for odd $r$. Second, we define and analyze a generalization of the derandomized square for irregular graphs and for sparsifying the product of two distinct graphs. As part of this generalization, we also give a strongly explicit construction of expander graphs of every size.

cs.CC↗

Unifying computational entropies via Kullback-Leibler divergence

We introduce hardness in relative entropy, a new notion of hardness for search problems which on the one hand is satisfied by all one-way functions and on the other hand implies both next-block pseudoentropy and inaccessible entropy, two forms of computational entropy used in recent constructions of pseudorandom generators and statistically hiding commitment schemes, respectively. Thus, hardness in relative entropy unifies the latter two notions of computational entropy and sheds light on the apparent "duality" between them. Additionally, it yields a more modular and illuminating proof that one-way functions imply next-block inaccessible entropy, similar in structure to the proof that one-way functions imply next-block pseudoentropy (Vadhan and Zheng, STOC '12).

cs.CR↗