相关论文: Hard Instances of the Constrained Discrete Logarit…
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…
We present a differentially private learner for halfspaces over a finite grid $G$ in $\mathbb{R}^d$ with sample complexity $\approx d^{2.5}\cdot 2^{\log^*|G|}$, which improves the state-of-the-art result of [Beimel et al., COLT 2019] by a…
The recently developed dynamic discretization discovery (DDD) is a powerful method that allows many time-dependent problems to become more tractable. While DDD has been applied to a variety of problems, one particular challenge has been to…
We study the problem of quantization of discrete probability distributions, arising in universal coding, as well as other applications. We show, that in many situations this problem can be reduced to the covering problem for the unit…
We give an exposition of the hidden subgroup problem for dihedral groups from the point of view of the standard hidden subgroup quantum algorithm for finite groups. In particular, we recall the obstructions for strong Fourier sampling to…
We study the problem of differentially private optimization with linear constraints when the right-hand-side of the constraints depends on private data. This type of problem appears in many applications, especially resource allocation.…
We construct three public key knapsack cryptosystems. Standard knapsack cryptosystems hide easy instances of the knapsack problem and have been broken. The systems considered in the article face this problem: They hide a random (possibly…
The problem $\textrm{PosSLP}$ involves determining whether an integer computed by a given straight-line program is positive. This problem has attracted considerable attention within the field of computational complexity as it provides a…
The exact composition of mechanisms for which two differential privacy (DP) constraints hold simultaneously is studied. The resulting privacy region admits an exact representation as a mixture over compositions of mechanisms of…
In this paper we study extensively the discrete logarithm problem in the group of non-singular circulant matrices. The emphasis of this study was to find the exact parameters for the group of circulant matrices for a secure implementation.…
A succinct histogram captures frequent items and their frequencies across clients and has become increasingly important for large-scale, privacy-sensitive machine learning applications. To develop a rigorous framework to guarantee privacy…
Fingerprinting arguments, first introduced by Bun, Ullman, and Vadhan (STOC 2014), are the most widely used method for establishing lower bounds on the sample complexity or error of approximately differentially private (DP) algorithms.…
Despite intense interest and considerable effort, the current generation of neural networks suffers a significant loss of accuracy under most practically relevant privacy training regimes. One particularly challenging class of neural…
Differentially private (DP) machine learning has recently become popular. The privacy loss of DP algorithms is commonly reported using $(\varepsilon,\delta)$-DP. In this paper, we propose a numerical accountant for evaluating the privacy…
Consider the following problem: given a metric space, some of whose points are "clients", open a set of at most $k$ facilities to minimize the average distance from the clients to these facilities. This is just the well-studied $k$-median…
Finding a shortest path in a graph is one of the most classic problems in algorithmic and graph theory. While we dispose of quite efficient algorithms for this ordinary problem (like the Dijkstra or Bellman-Ford algorithms), some slight…
Metric Differential Privacy (mDP) extends the concept of Differential Privacy (DP) to serve as a new paradigm of data perturbation. It is designed to protect secret data represented in general metric space, such as text data encoded as word…
Let $X$ be a finite set in $Z^d$. We consider the problem of optimizing linear function $f(x) = c^T x$ on $X$, where $c\in Z^d$ is an input vector. We call it a problem $X$. A problem $X$ is related with linear program $\max\limits_{x \in…
We consider an application to the discrete log problem using completely regular semigroups which may provide a more secure symmetric cryptosystem than the classic system based on groups. In particular we describe a scheme that would appear…
An instance of Max CSP is a finite collection of constraints on a set of variables, and the goal is to assign values to the variables that maximises the number of satisfied constraints. Max CSP captures many well-known problems (such as Max…