arXiv subjects

Kobbi Nissim

Publications and source records attributed to Kobbi Nissim.

At least 19 recordsLinked to original sources

arXiv2026

Machine Unlearning as Private Retroactive Algorithms

Machine unlearning typically aims to emulate retraining from scratch: upon a deletion request, the unlearning algorithm should produce an outcome that would have been obtained had the deleted point never been included. Recent work has shown that this emulation requirement carries no meaningful privacy semantics against an adversary who observes a sequence of releases. Machine unlearning is thus not a privacy question per se, but rather a data maintenance question, which is precisely the subject of retroactive algorithms. These are algorithms supporting modifications of past operations, guaranteeing that all subsequent answers reflect the revised history as if it had always been in force. We put forward a definition of private retroactive algorithms, combining the retroactivity requirement with differential privacy under continual observation. We present constructions achieving both privacy and retroactivity at no asymptotic cost over privacy alone for linear statistics, clustering, and histograms, alongside impossibility results.

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arXiv2026

Learning from Equivalence Queries, Revisited

Modern machine learning systems, such as generative models and recommendation systems, often evolve through a cycle of deployment, user interaction, and periodic model updates. This differs from standard supervised learning frameworks, which focus on loss or regret minimization over a fixed sequence of prediction tasks. Motivated by this setting, we revisit the classical model of learning from equivalence queries, introduced by Angluin (1988). In this model, a learner repeatedly proposes hypotheses and, when a deployed hypothesis is inadequate, receives a counterexample. Under fully adversarial counterexample generation, however, the model can be overly pessimistic. In addition, most prior work assumes a \emph{full-information} setting, where the learner also observes the correct label of the counterexample, an assumption that is not always natural. We address these issues by restricting the environment to a broad class of less adversarial counterexample generators, which we call \emph{symmetric}. Informally, such generators choose counterexamples based only on the symmetric difference between the hypothesis and the target. This class captures natural mechanisms such as random counterexamples (Angluin and Dohrn, 2017; Bhatia, 2021; Chase, Freitag, and Reyzin, 2024), as well as generators that return the simplest counterexample according to a prescribed complexity measure. Within this framework, we study learning from equivalence queries under both full-information and bandit feedback. We obtain tight bounds on the number of learning rounds in both settings and highlight directions for future work. Our analysis combines a game-theoretic view of symmetric adversaries with adaptive weighting methods and minimax arguments.

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arXiv2026

Protecting the Undeleted in Machine Unlearning

Machine unlearning aims to remove specific data points from a trained model, often striving to emulate "perfect retraining", i.e., producing the model that would have been obtained had the deleted data never been included. We demonstrate that this approach, and security definitions that enable it, carry significant privacy risks for the remaining (undeleted) data points. We present a reconstruction attack showing that for certain tasks, which can be computed securely without deletions, a mechanism adhering to perfect retraining allows an adversary controlling merely $ω(1)$ data points to reconstruct almost the entire dataset merely by issuing deletion requests. We survey existing definitions for machine unlearning, showing they are either susceptible to such attacks or too restrictive to support basic functionalities like exact summation. To address this problem, we propose a new security definition that specifically safeguards undeleted data against leakage caused by the deletion of other points. We show that our definition permits several essential functionalities, such as bulletin boards, summations, and statistical learning.

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arXiv2025

Bayesian Perspective on Memorization and Reconstruction

We introduce a new Bayesian perspective on the concept of data reconstruction, and leverage this viewpoint to propose a new security definition that, in certain settings, provably prevents reconstruction attacks. We use our paradigm to shed new light on one of the most notorious attacks in the privacy and memorization literature - fingerprinting code attacks (FPC). We argue that these attacks are really a form of membership inference attacks, rather than reconstruction attacks. Furthermore, we show that if the goal is solely to prevent reconstruction (but not membership inference), then in some cases the impossibility results derived from FPC no longer apply.

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arXiv2025

Differentially Private Quasi-Concave Optimization: Bypassing the Lower Bound and Application to Geometric Problems

We study the sample complexity of differentially private optimization of quasi-concave functions. For a fixed input domain $\mathcal{X}$, Cohen et al. (STOC 2023) proved that any generic private optimizer for low sensitive quasi-concave functions must have sample complexity $Ω(2^{\log^*|\mathcal{X}|})$. We show that the lower bound can be bypassed for a series of ``natural'' problems. We define a new class of \emph{approximated} quasi-concave functions, and present a generic differentially private optimizer for approximated quasi-concave functions with sample complexity $\tilde{O}(\log^*|\mathcal{X}|)$. As applications, we use our optimizer to privately select a center point of points in $d$ dimensions and \emph{probably approximately correct} (PAC) learn $d$-dimensional halfspaces. In previous works, Bun et al. (FOCS 2015) proved a lower bound of $Ω(\log^*|\mathcal{X}|)$ for both problems. Beimel et al. (COLT 2019) and Kaplan et al. (NeurIPS 2020) gave an upper bound of $\tilde{O}(d^{2.5}\cdot 2^{\log^*|\mathcal{X}|})$ for the two problems, respectively. We improve the dependency of the upper bounds on the cardinality of the domain by presenting a new upper bound of $\tilde{O}(d^{5.5}\cdot\log^*|\mathcal{X}|)$ for both problems. To the best of our understanding, this is the first work to reduce the sample complexity dependency on $|\mathcal{X}|$ for these two problems from exponential in $\log^* |\mathcal{X}|$ to $\log^* |\mathcal{X}|$.

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arXiv2024

Differentially Private Release and Learning of Threshold Functions

We prove new upper and lower bounds on the sample complexity of $(ε, δ)$ differentially private algorithms for releasing approximate answers to threshold functions. A threshold function $c_x$ over a totally ordered domain $X$ evaluates to $c_x(y) = 1$ if $y \le x$, and evaluates to $0$ otherwise. We give the first nontrivial lower bound for releasing thresholds with $(ε,δ)$ differential privacy, showing that the task is impossible over an infinite domain $X$, and moreover requires sample complexity $n \ge Ω(\log^*|X|)$, which grows with the size of the domain. Inspired by the techniques used to prove this lower bound, we give an algorithm for releasing thresholds with $n \le 2^{(1+ o(1))\log^*|X|}$ samples. This improves the previous best upper bound of $8^{(1 + o(1))\log^*|X|}$ (Beimel et al., RANDOM '13). Our sample complexity upper and lower bounds also apply to the tasks of learning distributions with respect to Kolmogorov distance and of properly PAC learning thresholds with differential privacy. The lower bound gives the first separation between the sample complexity of properly learning a concept class with $(ε,δ)$ differential privacy and learning without privacy. For properly learning thresholds in $\ell$ dimensions, this lower bound extends to $n \ge Ω(\ell \cdot \log^*|X|)$. To obtain our results, we give reductions in both directions from releasing and properly learning thresholds and the simpler interior point problem. Given a database $D$ of elements from $X$, the interior point problem asks for an element between the smallest and largest elements in $D$. We introduce new recursive constructions for bounding the sample complexity of the interior point problem, as well as further reductions and techniques for proving impossibility results for other basic problems in differential privacy.

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arXiv2024

Data Reconstruction: When You See It and When You Don't

We revisit the fundamental question of formally defining what constitutes a reconstruction attack. While often clear from the context, our exploration reveals that a precise definition is much more nuanced than it appears, to the extent that a single all-encompassing definition may not exist. Thus, we employ a different strategy and aim to "sandwich" the concept of reconstruction attacks by addressing two complementing questions: (i) What conditions guarantee that a given system is protected against such attacks? (ii) Under what circumstances does a given attack clearly indicate that a system is not protected? More specifically, * We introduce a new definitional paradigm -- Narcissus Resiliency -- to formulate a security definition for protection against reconstruction attacks. This paradigm has a self-referential nature that enables it to circumvent shortcomings of previously studied notions of security. Furthermore, as a side-effect, we demonstrate that Narcissus resiliency captures as special cases multiple well-studied concepts including differential privacy and other security notions of one-way functions and encryption schemes. * We formulate a link between reconstruction attacks and Kolmogorov complexity. This allows us to put forward a criterion for evaluating when such attacks are convincingly successful.

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arXiv2024

Credit Attribution and Stable Compression

Credit attribution is crucial across various fields. In academic research, proper citation acknowledges prior work and establishes original contributions. Similarly, in generative models, such as those trained on existing artworks or music, it is important to ensure that any generated content influenced by these works appropriately credits the original creators. We study credit attribution by machine learning algorithms. We propose new definitions--relaxations of Differential Privacy--that weaken the stability guarantees for a designated subset of $k$ datapoints. These $k$ datapoints can be used non-stably with permission from their owners, potentially in exchange for compensation. Meanwhile, the remaining datapoints are guaranteed to have no significant influence on the algorithm's output. Our framework extends well-studied notions of stability, including Differential Privacy ($k = 0$), differentially private learning with public data (where the $k$ public datapoints are fixed in advance), and stable sample compression (where the $k$ datapoints are selected adaptively by the algorithm). We examine the expressive power of these stability notions within the PAC learning framework, provide a comprehensive characterization of learnability for algorithms adhering to these principles, and propose directions and questions for future research.

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arXiv2024

Properties of Effective Information Anonymity Regulations

A firm seeks to analyze a dataset and to release the results. The dataset contains information about individual people, and the firm is subject to some regulation that forbids the release of the dataset itself. The regulation also imposes conditions on the release of the results. What properties should the regulation satisfy? We restrict our attention to regulations tailored to controlling the downstream effects of the release specifically on the individuals to whom the data relate. A particular example of interest is an anonymization rule, where a data protection regulation limiting the disclosure of personally identifiable information does not restrict the distribution of data that has been sufficiently anonymized. In this paper, we develop a set of technical requirements for anonymization rules and related regulations. The requirements are derived by situating within a simple abstract model of data processing a set of guiding general principles put forth in prior work. We describe an approach to evaluating such regulations using these requirements -- thus enabling the application of the general principles for the design of mechanisms. As an exemplar, we evaluate competing interpretations of regulatory requirements from the EU's General Data Protection Regulation.

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arXiv2023

Adaptive Data Analysis in a Balanced Adversarial Model

In adaptive data analysis, a mechanism gets $n$ i.i.d. samples from an unknown distribution $D$, and is required to provide accurate estimations to a sequence of adaptively chosen statistical queries with respect to $D$. Hardt and Ullman (FOCS 2014) and Steinke and Ullman (COLT 2015) showed that in general, it is computationally hard to answer more than $Θ(n^2)$ adaptive queries, assuming the existence of one-way functions. However, these negative results strongly rely on an adversarial model that significantly advantages the adversarial analyst over the mechanism, as the analyst, who chooses the adaptive queries, also chooses the underlying distribution $D$. This imbalance raises questions with respect to the applicability of the obtained hardness results -- an analyst who has complete knowledge of the underlying distribution $D$ would have little need, if at all, to issue statistical queries to a mechanism which only holds a finite number of samples from $D$. We consider more restricted adversaries, called \emph{balanced}, where each such adversary consists of two separated algorithms: The \emph{sampler} who is the entity that chooses the distribution and provides the samples to the mechanism, and the \emph{analyst} who chooses the adaptive queries, but has no prior knowledge of the underlying distribution (and hence has no a priori advantage with respect to the mechanism). We improve the quality of previous lower bounds by revisiting them using an efficient \emph{balanced} adversary, under standard public-key cryptography assumptions. We show that these stronger hardness assumptions are unavoidable in the sense that any computationally bounded \emph{balanced} adversary that has the structure of all known attacks, implies the existence of public-key cryptography.

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arXiv2023

Private Everlasting Prediction

A private learner is trained on a sample of labeled points and generates a hypothesis that can be used for predicting the labels of newly sampled points while protecting the privacy of the training set [Kasiviswannathan et al., FOCS 2008]. Research uncovered that private learners may need to exhibit significantly higher sample complexity than non-private learners as is the case with, e.g., learning of one-dimensional threshold functions [Bun et al., FOCS 2015, Alon et al., STOC 2019]. We explore prediction as an alternative to learning. Instead of putting forward a hypothesis, a predictor answers a stream of classification queries. Earlier work has considered a private prediction model with just a single classification query [Dwork and Feldman, COLT 2018]. We observe that when answering a stream of queries, a predictor must modify the hypothesis it uses over time, and, furthermore, that it must use the queries for this modification, hence introducing potential privacy risks with respect to the queries themselves. We introduce private everlasting prediction taking into account the privacy of both the training set and the (adaptively chosen) queries made to the predictor. We then present a generic construction of private everlasting predictors in the PAC model. The sample complexity of the initial training sample in our construction is quadratic (up to polylog factors) in the VC dimension of the concept class. Our construction allows prediction for all concept classes with finite VC dimension, and in particular threshold functions with constant size initial training sample, even when considered over infinite domains, whereas it is known that the sample complexity of privately learning threshold functions must grow as a function of the domain size and hence is impossible for infinite domains.

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arXiv2023

On Differentially Private Online Predictions

In this work we introduce an interactive variant of joint differential privacy towards handling online processes in which existing privacy definitions seem too restrictive. We study basic properties of this definition and demonstrate that it satisfies (suitable variants) of group privacy, composition, and post processing. We then study the cost of interactive joint privacy in the basic setting of online classification. We show that any (possibly non-private) learning rule can be effectively transformed to a private learning rule with only a polynomial overhead in the mistake bound. This demonstrates a stark difference with more restrictive notions of privacy such as the one studied by Golowich and Livni (2021), where only a double exponential overhead on the mistake bound is known (via an information theoretic upper bound).

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arXiv2022

Private Summation in the Multi-Message Shuffle Model

The shuffle model of differential privacy (Erlingsson et al. SODA 2019; Cheu et al. EUROCRYPT 2019) and its close relative encode-shuffle-analyze (Bittau et al. SOSP 2017) provide a fertile middle ground between the well-known local and central models. Similarly to the local model, the shuffle model assumes an untrusted data collector who receives privatized messages from users, but in this case a secure shuffler is used to transmit messages from users to the collector in a way that hides which messages came from which user. An interesting feature of the shuffle model is that increasing the amount of messages sent by each user can lead to protocols with accuracies comparable to the ones achievable in the central model. In particular, for the problem of privately computing the sum of $n$ bounded real values held by $n$ different users, Cheu et al. showed that $O(\sqrt{n})$ messages per user suffice to achieve $O(1)$ error (the optimal rate in the central model), while Balle et al. (CRYPTO 2019) recently showed that a single message per user leads to $Θ(n^{1/3})$ MSE (mean squared error), a rate strictly in-between what is achievable in the local and central models. This paper introduces two new protocols for summation in the shuffle model with improved accuracy and communication trade-offs. Our first contribution is a recursive construction based on the protocol from Balle et al. mentioned above, providing $\mathrm{poly}(\log \log n)$ error with $O(\log \log n)$ messages per user. The second contribution is a protocol with $O(1)$ error and $O(1)$ messages per user based on a novel analysis of the reduction from secure summation to shuffling introduced by Ishai et al. (FOCS 2006) (the original reduction required $O(\log n)$ messages per user).

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arXiv2021

Dynamic Algorithms Against an Adaptive Adversary: Generic Constructions and Lower Bounds

A dynamic algorithm against an adaptive adversary is required to be correct when the adversary chooses the next update after seeing the previous outputs of the algorithm. We obtain faster dynamic algorithms against an adaptive adversary and separation results between what is achievable in the oblivious vs. adaptive settings. To get these results we exploit techniques from differential privacy, cryptography, and adaptive data analysis. We give a general reduction transforming a dynamic algorithm against an oblivious adversary to a dynamic algorithm robust against an adaptive adversary. This reduction maintains several copies of the oblivious algorithm and uses differential privacy to protect their random bits. Using this reduction we obtain dynamic algorithms against an adaptive adversary with improved update and query times for global minimum cut, all pairs distances, and all pairs effective resistance. We further improve our update and query times by showing how to maintain a sparsifier over an expander decomposition that can be refreshed fast. This fast refresh enables it to be robust against what we call a blinking adversary that can observe the output of the algorithm only following refreshes. We believe that these techniques will prove useful for additional problems. On the flip side, we specify dynamic problems that, assuming a random oracle, every dynamic algorithm that solves them against an adaptive adversary must be polynomially slower than a rather straightforward dynamic algorithm that solves them against an oblivious adversary. We first show a separation result for a search problem and then show a separation result for an estimation problem. In the latter case our separation result draws from lower bounds in adaptive data analysis.

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arXiv2021

$\mathcal{E}\text{psolute}$: Efficiently Querying Databases While Providing Differential Privacy

As organizations struggle with processing vast amounts of information, outsourcing sensitive data to third parties becomes a necessity. To protect the data, various cryptographic techniques are used in outsourced database systems to ensure data privacy, while allowing efficient querying. A rich collection of attacks on such systems has emerged. Even with strong cryptography, just communication volume or access pattern is enough for an adversary to succeed. In this work we present a model for differentially private outsourced database system and a concrete construction, $\mathcal{E}\text{psolute}$, that provably conceals the aforementioned leakages, while remaining efficient and scalable. In our solution, differential privacy is preserved at the record level even against an untrusted server that controls data and queries. $\mathcal{E}\text{psolute}$ combines Oblivious RAM and differentially private sanitizers to create a generic and efficient construction. We go further and present a set of improvements to bring the solution to efficiency and practicality necessary for real-world adoption. We describe the way to parallelize the operations, minimize the amount of noise, and reduce the number of network requests, while preserving the privacy guarantees. We have run an extensive set of experiments, dozens of servers processing up to 10 million records, and compiled a detailed result analysis proving the efficiency and scalability of our solution. While providing strong security and privacy guarantees we are less than an order of magnitude slower than range query execution of a non-secure plain-text optimized RDBMS like MySQL and PostgreSQL.

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arXiv2021

Computational Two-Party Correlation: A Dichotomy for Key-Agreement Protocols

Let $π$ be an efficient two-party protocol that given security parameter $κ$, both parties output single bits $X_κ$ and $Y_κ$, respectively. We are interested in how $(X_κ,Y_κ)$ "appears" to an efficient adversary that only views the transcript $T_κ$. We make the following contributions: $\bullet$ We develop new tools to argue about this loose notion and show (modulo some caveats) that for every such protocol $π$, there exists an efficient simulator such that the following holds: on input $T_κ$, the simulator outputs a pair $(X'_κ,Y'_κ)$ such that $(X'_κ,Y'_κ,T_κ)$ is (somewhat) computationally indistinguishable from $(X_κ,Y_κ,T_κ)$. $\bullet$ We use these tools to prove the following dichotomy theorem: every such protocol $π$ is: - either uncorrelated -- it is (somewhat) indistinguishable from an efficient protocol whose parties interact to produce $T_κ$, but then choose their outputs independently from some product distribution (that is determined in poly-time from $T_κ$), - or, the protocol implies a key-agreement protocol (for infinitely many $κ$'s). Uncorrelated protocols are uninteresting from a cryptographic viewpoint, as the correlation between outputs is (computationally) trivial. Our dichotomy shows that every protocol is either completely uninteresting or implies key-agreement. $\bullet$ We use the above dichotomy to make progress on open problems on minimal cryptographic assumptions required for differentially private mechanisms for the XOR function. $\bullet$ A subsequent work of Haitner et al. uses the above dichotomy to makes progress on a longstanding open question regarding the complexity of fair two-party coin-flipping protocols.

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arXiv2021

The Sample Complexity of Distribution-Free Parity Learning in the Robust Shuffle Model

We provide a lowerbound on the sample complexity of distribution-free parity learning in the realizable case in the shuffle model of differential privacy. Namely, we show that the sample complexity of learning $d$-bit parity functions is $Ω(2^{d/2})$. Our result extends a recent similar lowerbound on the sample complexity of private agnostic learning of parity functions in the shuffle model by Cheu and Ullman. We also sketch a simple shuffle model protocol demonstrating that our results are tight up to $poly(d)$ factors.

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arXiv2021

Separating Adaptive Streaming from Oblivious Streaming

We present a streaming problem for which every adversarially-robust streaming algorithm must use polynomial space, while there exists a classical (oblivious) streaming algorithm that uses only polylogarithmic space. This is the first separation between oblivious streaming and adversarially-robust streaming, and resolves one of the central open questions in adversarial robust streaming.

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