arXiv subjects

Zeyu Ding

Publications and source records attributed to Zeyu Ding.

25 records · Page 2Linked to original sources

arXiv2020

Free Gap Estimates from the Exponential Mechanism, Sparse Vector, Noisy Max and Related Algorithms

Private selection algorithms, such as the Exponential Mechanism, Noisy Max and Sparse Vector, are used to select items (such as queries with large answers) from a set of candidates, while controlling privacy leakage in the underlying data. Such algorithms serve as building blocks for more complex differentially private algorithms. In this paper we show that these algorithms can release additional information related to the gaps between the selected items and the other candidates for free (i.e., at no additional privacy cost). This free gap information can improve the accuracy of certain follow-up counting queries by up to 66%. We obtain these results from a careful privacy analysis of these algorithms. Based on this analysis, we further propose novel hybrid algorithms that can dynamically save additional privacy budget.

cs.DB↗

arXiv2020

CheckDP: An Automated and Integrated Approach for Proving Differential Privacy or Finding Precise Counterexamples

We propose CheckDP, the first automated and integrated approach for proving or disproving claims that a mechanism is differentially private. CheckDP can find counterexamples for mechanisms with subtle bugs for which prior counterexample generators have failed. Furthermore, it was able to \emph{automatically} generate proofs for correct mechanisms for which no formal verification was reported before. CheckDP is built on static program analysis, allowing it to be more efficient and more precise in catching infrequent events than existing counterexample generators (which run mechanisms hundreds of thousands of times to estimate their output distribution). Moreover, its sound approach also allows automatic verification of correct mechanisms. When evaluated on standard benchmarks and newer privacy mechanisms, CheckDP generates proofs (for correct mechanisms) and counterexamples (for incorrect mechanisms) within 70 seconds without any false positives or false negatives.

cs.PL↗

arXiv2019

Canonical Barsotti-Tate Groups of Finite Level

Let $k$ be an algebraically closed field of characteristic $p>0$. Let $c,d\in \mathbb{N}$ be such that $h=c+d>0$. Let $H$ be a $p$-divisible group of codimension $c$ and dimension $d$ over $k$. For $m\in\mathbb{N}^\ast$ let $H[p^m]=\ker([p^m]:H\rightarrow H)$. It is a finite commutative group scheme over $k$ of $p$ power order, called a Barsotti-Tate group of level $m$. We study a particular type of $p$-divisible groups $H_π$, where $π$ is a permutation on the set $\{1,2,\dots,h\}$. Let $(M,φ_π)$ be the Dieudonné module of $H_π$. Each $H_π$ is uniquely determined by $H_π[p]$ and by the fact that there exists a maximal torus $T$ of $GL_M$ whose Lie algebra is normalized by $φ_π$ in a natural way. Moreover, if $H$ is a $p$-divisible group of codimension $c$ and dimension $d$ over $k$, then $H[p]\cong H_π[p]$ for some permutation $π$. We call these $H_π$ canonical lifts of Barsotti-Tate groups of level $1$. We obtain new formulas of combinatorial nature for the dimension of $\boldsymbol{Aut}(H_π[p^m])$ and for the number of connected components of $\boldsymbol{End}(H_π[p^m])$.

math.NT↗

arXiv2019

Free Gap Information from the Differentially Private Sparse Vector and Noisy Max Mechanisms

Noisy Max and Sparse Vector are selection algorithms for differential privacy and serve as building blocks for more complex algorithms. In this paper we show that both algorithms can release additional information for free (i.e., at no additional privacy cost). Noisy Max is used to return the approximate maximizer among a set of queries. We show that it can also release for free the noisy gap between the approximate maximizer and runner-up. This free information can improve the accuracy of certain subsequent counting queries by up to 50%. Sparse Vector is used to return a set of queries that are approximately larger than a fixed threshold. We show that it can adaptively control its privacy budget (use less budget for queries that are likely to be much larger than the threshold) in order to increase the amount of queries it can process. These results follow from a careful privacy analysis.

cs.LG↗

arXiv2019

Detecting Violations of Differential Privacy

The widespread acceptance of differential privacy has led to the publication of many sophisticated algorithms for protecting privacy. However, due to the subtle nature of this privacy definition, many such algorithms have bugs that make them violate their claimed privacy. In this paper, we consider the problem of producing counterexamples for such incorrect algorithms. The counterexamples are designed to be short and human-understandable so that the counterexample generator can be used in the development process -- a developer could quickly explore variations of an algorithm and investigate where they break down. Our approach is statistical in nature. It runs a candidate algorithm many times and uses statistical tests to try to detect violations of differential privacy. An evaluation on a variety of incorrect published algorithms validates the usefulness of our approach: it correctly rejects incorrect algorithms and provides counterexamples for them within a few seconds.

cs.CR↗

arXiv2019

Dimensions of automorphism group schemes of finite level truncations of $F$-cyclic $F$-crystals

Let $\mathcal{M}_π$ be an $F$-cyclic $F$-crystal $\mathcal{M}_π$ over an algebraically closed field defined by a permutation $π$ and a set of prescribed Hodge slopes. We prove combinatorial formulas for the dimension $γ_{\mathcal{M}_π}(m)$ of the automorphism group scheme of $\mathcal{M}_π$ at finite level $m$ and the number of connected components of the endomorphism group scheme of $\mathcal{M}_π$ at finite level $m$. As an application, we show that if $\mathcal{M}_π$ is a nonordinary Dieudonné module defined by a cycle $π$, then $γ_{\mathcal{M}_π}(m+1) - γ_{\mathcal{M}_π}(m) < γ_{\mathcal{M}_π}(m) - γ_{\mathcal{M}_π}(m-1)$ for all $1 \leq m \leq n_{\mathcal{M}_π}$, where $n_{\mathcal{M}_π}$ is the isomorphism number of $\mathcal{M}_π$.

math.NT↗

arXiv2019

Proving Differential Privacy with Shadow Execution

Recent work on formal verification of differential privacy shows a trend toward usability and expressiveness -- generating a correctness proof of sophisticated algorithm while minimizing the annotation burden on programmers. Sometimes, combining those two requires substantial changes to program logics: one recent paper is able to verify Report Noisy Max automatically, but it involves a complex verification system using customized program logics and verifiers. In this paper, we propose a new proof technique, called shadow execution, and embed it into a language called ShadowDP. ShadowDP uses shadow execution to generate proofs of differential privacy with very few programmer annotations and without relying on customized logics and verifiers. In addition to verifying Report Noisy Max, we show that it can verify a new variant of Sparse Vector that reports the gap between some noisy query answers and the noisy threshold. Moreover, ShadowDP reduces the complexity of verification: for all of the algorithms we have evaluated, type checking and verification in total takes at most 3 seconds, while prior work takes minutes on the same algorithms.

cs.PL↗