Reconstructing with Less: Leakage Abuse Attacks in Two-Dimensions

Access and search pattern leakage from range queries are detrimental to the security of encrypted databases, as evidenced by a large body of work on efficient attacks that reconstruct one-dimensional databases. Recently, the first attack from 2D range queries showed that higher-dimensional databases are also in danger. This attack requires complete information for reconstruction. In this paper, we develop reconstructions that require less information. We present an order reconstruction attack that only depends on access pattern leakage, and empirically show that the order allows the attacker to infer the geometry of the underlying data. Notably, this attack also achieves full database reconstruction when the 1D horizontal and vertical projections of the points are dense. We also give an approximate database reconstruction attack that is distribution-agnostic and works with any subset of the possible search pattern, given the order of the database. Finally, we show how knowledge of auxiliary information such as the centroid of a related dataset allows to improve the reconstruction. We support our results with formal analysis and experiments on real-world databases and queries drawn from various distributions

Reasoning about Regular Properties: A Comparative Study

Several new algorithms for deciding emptiness of Boolean combinations of regular languages and of languages of alternating automata (AFA) have been proposed recently, especially in the context of analysing regular expressions and in string constraint solving. The new algorithms demonstrated a significant potential, but they have never been systematically compared, neither among each other nor with the state-of-the art implementations of existing (non)deterministic automata-based methods. In this paper, we provide the first such comparison as well as an overview of the existing algorithms and their implementations. We collect a diverse benchmark mostly originating in or related to practical problems from string constraint solving, analysing LTL properties, and regular model checking, and evaluate collected implementations on it. The results reveal the best tools and hint on what the best algorithms and implementation techniques are. Roughly, although some advanced algorithms are fast, such as antichain algorithms and reductions to IC3/PDR, they are not as overwhelmingly dominant as sometimes presented and there is no clear winner. The simplest NFA-based technology may be actually the best choice, depending on the problem source and implementation style. Our findings should be highly relevant for development of these techniques as well as for related fields such as string constraint solving

Rainbow Ramsey problems for the Boolean lattice

We address the following rainbow Ramsey problem: For posets $P,Q$ what is the smallest number $n$ such that any coloring of the elements of the Boolean lattice $B_n$ either admits a monochromatic copy of $P$ or a rainbow copy of $Q$. We consider both weak and strong (non-induced and induced) versions of this problem. We also investigate related problems on (partial) $k$-colorings of $B_n$ that do not admit rainbow antichains of size $k$

Problem of Time in Quantum Gravity

The Problem of Time occurs because the `time' of GR and of ordinary Quantum Theory are mutually incompatible notions. This is problematic in trying to replace these two branches of physics with a single framework in situations in which the conditions of both apply, e.g. in black holes or in the very early universe. Emphasis in this Review is on the Problem of Time being multi-faceted and on the nature of each of the eight principal facets. Namely, the Frozen Formalism Problem, Configurational Relationalism Problem (formerly Sandwich Problem), Foliation Dependence Problem, Constraint Closure Problem (formerly Functional Evolution Problem), Multiple Choice Problem, Global Problem of Time, Problem of Beables (alias Problem of Observables) and Spacetime Reconstruction/Replacement Problem. Strategizing in this Review is not just centred about the Frozen Formalism Problem facet, but rather about each of the eight facets. Particular emphasis is placed upon A) relationalism as an underpinning of the facets and as a selector of particular strategies (especially a modification of Barbour relationalism, though also with some consideration of Rovelli relationalism). B) Classifying approaches by the full ordering in which they embrace constrain, quantize, find time/history and find observables, rather than only by partial orderings such as "Dirac-quantize". C) Foliation (in)dependence and Spacetime Reconstruction for a wide range of physical theories, strategizing centred about the Problem of Beables, the Patching Approach to the Global Problem of Time, and the role of the question-types considered in physics. D) The Halliwell- and Gambini-Porto-Pullin-type combined Strategies in the context of semiclassical quantum cosmology.Comment: Invited Review: 26 pages including 2 Figures. This v2 has a number of minor improvements and correction

Large Graph Analysis in the GMine System

Current applications have produced graphs on the order of hundreds of thousands of nodes and millions of edges. To take advantage of such graphs, one must be able to find patterns, outliers and communities. These tasks are better performed in an interactive environment, where human expertise can guide the process. For large graphs, though, there are some challenges: the excessive processing requirements are prohibitive, and drawing hundred-thousand nodes results in cluttered images hard to comprehend. To cope with these problems, we propose an innovative framework suited for any kind of tree-like graph visual design. GMine integrates (a) a representation for graphs organized as hierarchies of partitions - the concepts of SuperGraph and Graph-Tree; and (b) a graph summarization methodology - CEPS. Our graph representation deals with the problem of tracing the connection aspects of a graph hierarchy with sub linear complexity, allowing one to grasp the neighborhood of a single node or of a group of nodes in a single click. As a proof of concept, the visual environment of GMine is instantiated as a system in which large graphs can be investigated globally and locally

On colorings of the Boolean lattice avoiding a rainbow copy of a poset

Let F(n,k) (f(n,k)) denote the maximum possible size of the smallest color class in a (partial) k-coloring of the Boolean lattice Bn that does not admit a rainbow antichain of size k. The value of F(n,3) and f(n,2) has been recently determined exactly. We prove that for any fixed k if n is large enough, then F(n,k),f(n,k)=2(1∕2+o(1))n holds. We also introduce the general functions for any poset P and integer c≥|P|: let F(n,c,P) (f(n,c,P)) denote the maximum possible size of the smallest color class in a (partial) c-coloring of the Boolean lattice Bn that does not admit a rainbow copy of P. We consider the first instances of this general problem. © 201

Co-Design of Autonomous Systems: From Hardware Selection to Control Synthesis

Designing cyber-physical systems is a complex task which requires insights at multiple abstraction levels. The choices of single components are deeply interconnected and need to be jointly studied. In this work, we consider the problem of co-designing the control algorithm as well as the platform around it. In particular, we leverage a monotone theory of co-design to formalize variations of the LQG control problem as monotone feasibility relations. We then show how this enables the embedding of control co-design problems in the higher level co-design problem of a robotic platform. We illustrate the properties of our formalization by analyzing the co-design of an autonomous drone performing search-and-rescue tasks and show how, given a set of desired robot behaviors, we can compute Pareto efficient design solutions.Comment: 8 pages, 6 figures, to appear in the proceedings of the 20th European Control Conference (ECC21

Minimising the total number of subsets and supersets

Let $\mathcal{F}$ be a family of subsets of a ground set $\{1,\ldots,n\}$ with $|\mathcal{F}|=m$, and let $\mathcal{F}^{\updownarrow}$ denote the family of all subsets of $\{1,\ldots,n\}$ that are subsets or supersets of sets in $\mathcal{F}$. Here we determine the minimum value that $|\mathcal{F}^{\updownarrow}|$ can attain as a function of $n$ and $m$. This can be thought of as a `two-sided' Kruskal-Katona style result. It also gives a solution to the isoperimetric problem on the graph whose vertices are the subsets of $\{1,\ldots,n\}$ and in which two vertices are adjacent if one is a subset of the other. This graph is a supergraph of the $n$-dimensional hypercube and we note some similarities between our results and Harper's theorem, which solves the isoperimetric problem for hypercubes. In particular, analogously to Harper's theorem, we show there is a total ordering of the subsets of $\{1,\ldots,n\}$ such that, for each initial segment $\mathcal{F}$ of this ordering, $\mathcal{F}^{\updownarrow}$ has the minimum possible size. Our results also answer a question that arises naturally out of work of Gerbner et al. on cross-Sperner families and allow us to strengthen one of their main results.Comment: 21 pages, 1 figur