Optimizing Implementations of Boolean Functions

Symmetric cryptography primitives are constructed by iterative applications of linear and nonlinear layers. Constructing efficient circuits for these layers, even for the linear one, is challenging. In 1997, Paar proposed a heuristic to minimize the number of XORs (modulo 2 addition) necessary to implement linear layers. In this study, we slightly modify Paar’s heuristics to find implementations for nonlinear Boolean functions, in particular to homogeneous Boolean functions. Additionally, we show how this heuristic can be used to construct circuits for generic Boolean functions with small number of AND gates, by exploiting affine equivalence relations

Succinct Data Structures for Chordal Graphs

We study the problem of approximate shortest path queries in chordal graphs and give a n log n + o(n log n) bit data structure to answer the approximate distance query to within an additive constant of 1 in O(1) time. We study the problem of succinctly storing a static chordal graph to answer adjacency, degree, neighbourhood and shortest path queries. Let G be a chordal graph with n vertices. We design a data structure using the information theoretic minimal n^2/4 + o(n^2) bits of space to support the queries: - whether two vertices u,v are adjacent in time f(n) for any f(n) in omega(1). - the degree of a vertex in O(1) time. - the vertices adjacent to u in (f(n))^2 time per neighbour - the length of the shortest path from u to v in O(nf(n)) tim

Decidability and Complexity of Tree Share Formulas

Fractional share models are used to reason about how multiple actors share ownership of resources. We examine the decidability and complexity of reasoning over the "tree share" model of Dockins et al. using first-order logic, or fragments thereof. We pinpoint a connection between the basic operations on trees union, intersection, and complement and countable atomless Boolean algebras, allowing us to obtain decidability with the precise complexity of both first-order and existential theories over the tree share model with the aforementioned operations. We establish a connection between the multiplication operation on trees and the theory of word equations, allowing us to derive the decidability of its existential theory and the undecidability of its full first-order theory. We prove that the full first-order theory over the model with both the Boolean operations and the restricted multiplication operation (with constants on the right hand side) is decidable via an embedding to tree-automatic structures

Governance of Dual-Use Technologies: Theory and Practice

The term dual-use characterizes technologies that can have both military and civilian applications. What is the state of current efforts to control the spread of these powerful technologies—nuclear, biological, cyber—that can simultaneously advance social and economic well-being and also be harnessed for hostile purposes? What have previous efforts to govern, for example, nuclear and biological weapons taught us about the potential for the control of these dual-use technologies? What are the implications for governance when the range of actors who could cause harm with these technologies include not just national governments but also non-state actors like terrorists? These are some of the questions addressed by Governance of Dual-Use Technologies: Theory and Practice, the new publication released today by the Global Nuclear Future Initiative of the American Academy of Arts and Sciences. The publication's editor is Elisa D. Harris, Senior Research Scholar, Center for International Security Studies, University of Maryland School of Public Affairs. Governance of Dual-Use Technologies examines the similarities and differences between the strategies used for the control of nuclear technologies and those proposed for biotechnology and information technology. The publication makes clear the challenges concomitant with dual-use governance. For example, general agreement exists internationally on the need to restrict access to technologies enabling the development of nuclear weapons. However, no similar consensus exists in the bio and information technology domains. The publication also explores the limitations of military measures like deterrence, defense, and reprisal in preventing globally available biological and information technologies from being misused. Some of the other questions explored by the publication include: What types of governance measures for these dual-use technologies have already been adopted? What objectives have those measures sought to achieve? How have the technical characteristics of the technology affected governance prospects? What have been the primary obstacles to effective governance, and what gaps exist in the current governance regime? Are further governance measures feasible? In addition to a preface from Global Nuclear Future Initiative Co-Director Robert Rosner (University of Chicago) and an introduction and conclusion from Elisa Harris, Governance of Dual-Use Technologiesincludes:On the Regulation of Dual-Use Nuclear Technology by James M. Acton (Carnegie Endowment for International Peace)Dual-Use Threats: The Case of Biotechnology by Elisa D. Harris (University of Maryland)Governance of Information Technology and Cyber Weapons by Herbert Lin (Stanford University

Kernelization of Cycle Packing with Relaxed Disjointness Constraints

A key result in the field of kernelization, a subfield of parameterized complexity, states that the classic Disjoint Cycle Packing problem, i.e. finding k vertex disjoint cycles in a given graph G, admits no polynomial kernel unless NP subseteq coNP/poly. However, very little is known about this problem beyond the aforementioned kernelization lower bound (within the parameterized complexity framework). In the hope of clarifying the picture and better understanding the types of "constraints" that separate "kernelizable" from "non-kernelizable" variants of Disjoint Cycle Packing, we investigate two relaxations of the problem. The first variant, which we call Almost Disjoint Cycle Packing, introduces a "global" relaxation parameter t. That is, given a graph G and integers k and t, the goal is to find at least k distinct cycles such that every vertex of G appears in at most t of the cycles. The second variant, Pairwise Disjoint Cycle Packing, introduces a "local" relaxation parameter and we seek at least k distinct cycles such that every two cycles intersect in at most t vertices. While the Pairwise Disjoint Cycle Packing problem admits a polynomial kernel for all t >= 1, the kernelization complexity of Almost Disjoint Cycle Packing reveals an interesting spectrum of upper and lower bounds. In particular, for t = k/c, where c could be a function of k, we obtain a kernel of size O(2^{c^{2}}*k^{7+c}*log^3(k)) whenever c in o(sqrt(k))). Thus the kernel size varies from being sub-exponential when c in o(sqrt(k)), to quasipolynomial when c in o(log^l(k)), l in R_+, and polynomial when c in O(1). We complement these results for Almost Disjoint Cycle Packing by showing that the problem does not admit a polynomial kernel whenever t in O(k^{epsilon}), for any 0 <= epsilon < 1

Alternative parameterizations of Metric Dimension

A set of vertices $W$ in a graph $G$ is called resolving if for any two distinct $x,y\in V(G)$, there is $v\in W$ such that ${\rm dist}_G(v,x)\neq{\rm dist}_G(v,y)$, where ${\rm dist}_G(u,v)$ denotes the length of a shortest path between $u$ and $v$ in the graph $G$. The metric dimension ${\rm md}(G)$ of $G$ is the minimum cardinality of a resolving set. The Metric Dimension problem, i.e. deciding whether ${\rm md}(G)\le k$, is NP-complete even for interval graphs (Foucaud et al., 2017). We study Metric Dimension (for arbitrary graphs) from the lens of parameterized complexity. The problem parameterized by $k$ was proved to be $W[2]$-hard by Hartung and Nichterlein (2013) and we study the dual parameterization, i.e., the problem of whether ${\rm md}(G)\le n- k,$ where $n$ is the order of $G$. We prove that the dual parameterization admits (a) a kernel with at most $3k^4$ vertices and (b) an algorithm of runtime $O^*(4^{k+o(k)}).$ Hartung and Nichterlein (2013) also observed that Metric Dimension is fixed-parameter tractable when parameterized by the vertex cover number $vc(G)$ of the input graph. We complement this observation by showing that it does not admit a polynomial kernel even when parameterized by $vc(G) + k$. Our reduction also gives evidence for non-existence of polynomial Turing kernels

Cyber Threats and NATO 2030: Horizon Scanning and Analysis

The book includes 13 chapters that look ahead to how NATO can best address the cyber threats, as well as opportunities and challenges from emerging and disruptive technologies in the cyber domain over the next decade. The present volume addresses these conceptual and practical requirements and contributes constructively to the NATO 2030 discussions. The book is arranged in five short parts...All the chapters in this book have undergone double-blind peer review by at least two external experts.https://scholarworks.wm.edu/asbook/1038/thumbnail.jp

International Summerschool Computer Science 2014: Proceedings of Summerschool 7.7. - 13.7.2014

Proceedings of International Summerschool Computer Science 201