On the Distance Identifying Set Meta-Problem and Applications to the Complexity of Identifying Problems on Graphs

Numerous problems consisting in identifying vertices in graphs using distances are useful in domains such as network verification and graph isomorphism. Unifying them into a meta-problem may be of main interest. We introduce here a promising solution named Distance Identifying Set. The model contains Identifying Code (IC), Locating Dominating Set (LD) and their generalizations $r$-IC and $r$-LD where the closed neighborhood is considered up to distance $r$. It also contains Metric Dimension (MD) and its refinement $r$-MD in which the distance between two vertices is considered as infinite if the real distance exceeds $r$. Note that while IC = 1-IC and LD = 1-LD, we have MD = $\infty$-MD; we say that MD is not local In this article, we prove computational lower bounds for several problems included in Distance Identifying Set by providing generic reductions from (Planar) Hitting Set to the meta-problem. We mainly focus on two families of problem from the meta-problem: the first one, called bipartite gifted local, contains $r$-IC, $r$-LD and $r$-MD for each positive integer $r$ while the second one, called 1-layered, contains LD, MD and $r$-MD for each positive integer $r$. We have: - the 1-layered problems are NP-hard even in bipartite apex graphs, - the bipartite gifted local problems are NP-hard even in bipartite planar graphs, - assuming ETH, all these problems cannot be solved in $2^{o(\sqrt{n})}$ when restricted to bipartite planar or apex graph, respectively, and they cannot be solved in $2^{o(n)}$ on bipartite graphs, - even restricted to bipartite graphs, they do not admit parameterized algorithms in $2^{O(k)}.n^{O(1)}$ except if W[0] = W[2]. Here $k$ is the solution size of a relevant identifying set. In particular, Metric Dimension cannot be solved in $2^{o(n)}$ under ETH, answering a question of Hartung in 2013

Hard Mathematical Problems in Cryptography and Coding Theory

In this thesis, we are concerned with certain interesting computationally hard problems and the complexities of their associated algorithms. All of these problems share a common feature in that they all arise from, or have applications to, cryptography, or the theory of error correcting codes. Each chapter in the thesis is based on a stand-alone paper which attacks a particular hard problem. The problems and the techniques employed in attacking them are described in detail. The first problem concerns integer factorization: given a positive integer $N$. the problem is to find the unique prime factors of $N$. This problem, which was historically of only academic interest to number theorists, has in recent decades assumed a central importance in public-key cryptography. We propose a method for factorizing a given integer using a graph-theoretic algorithm employing Binary Decision Diagrams (BDD). The second problem that we consider is related to the classification of certain naturally arising classes of error correcting codes, called self-dual additive codes over the finite field of four elements, $GF(4)$. We address the problem of classifying self-dual additive codes, determining their weight enumerators, and computing their minimum distance. There is a natural relation between self-dual additive codes over $GF(4)$ and graphs via isotropic systems. Utilizing the properties of the corresponding graphs, and again employing Binary Decision Diagrams (BDD) to compute the weight enumerators, we can obtain a theoretical speed up of the previously developed algorithm for the classification of these codes. The third problem that we investigate deals with one of the central issues in cryptography, which has historical origins in the theory of geometry of numbers, namely the shortest vector problem in lattices. One method which is used both in theory and practice to solve the shortest vector problem is by enumeration algorithms. Lattice enumeration is an exhaustive search whose goal is to find the shortest vector given a lattice basis as input. In our work, we focus on speeding up the lattice enumeration algorithm, and we propose two new ideas to this end. The shortest vector in a lattice can be written as ${\bf s} = v_1{\bf b}_1+v_2{\bf b}_2+\ldots+v_n{\bf b}_n$. where $v_i \in \mathbb{Z}$ are integer coefficients and ${\bf b}_i$ are the lattice basis vectors. We propose an enumeration algorithm, called hybrid enumeration, which is a greedy approach for computing a short interval of possible integer values for the coefficients $v_i$ of a shortest lattice vector. Second, we provide an algorithm for estimating the signs $+$ or $-$ of the coefficients $v_1,v_2,\ldots,v_n$ of a shortest vector ${\bf s}=\sum_{i=1}^{n} v_i{\bf b}_i$. Both of these algorithms results in a reduction in the number of nodes in the search tree. Finally, the fourth problem that we deal with arises in the arithmetic of the class groups of imaginary quadratic fields. We follow the results of Soleng and Gillibert pertaining to the class numbers of some sequence of imaginary quadratic fields arising in the arithmetic of elliptic and hyperelliptic curves and compute a bound on the effective estimates for the orders of class groups of a family of imaginary quadratic number fields. That is, suppose $f(n)$ is a sequence of positive numbers tending to infinity. Given any positive real number $L$. an effective estimate is to find the smallest positive integer $N = N(L)$ depending on $L$ such that $f(n) > L$ for all $n > N$. In other words, given a constant $M > 0$. we find a value $N$ such that the order of the ideal class $I_n$ in the ring $R_n$ (provided by the homomorphism in Soleng's paper) is greater than $M$ for any $n>N$. In summary, in this thesis we attack some hard problems in computer science arising from arithmetic, geometry of numbers, and coding theory, which have applications in the mathematical foundations of cryptography and error correcting codes

Enhancing End User Security - Attacks & Solutions

End user computing environments, e.g. web browsers and PC operating systems, are the target of a large number of attacks, both online and offline. The nature of these attacks varies from simple online attacks, such as user tracking using cookies, to more sophisticated attacks on security protocols and cryptographic algorithms. Other methods of attack exist that target end user applications that utilise and interact with cryptographic functions provided by the PC operating system. After providing a general introduction to the security techniques and protocols used in this thesis, a review of possible threats to end user computing environments is given, followed by a discussion of the countermeasures needed to combat these threats. The contributions of this thesis include three new approaches for enhancing the security of end user systems, together with an analysis and a prototype implementation of an end user security enhancement tool. The following paragraphs summarise the three main contributions of this thesis. Digitally signing a digital document is a straightforward procedure; however, when the digital document contains dynamic content, the digital signature may remain valid but the viewed document may not be the same as the document when viewed by the signer. A new solution is proposed to solve the problem; the main idea behind the solution is to make the application aware of the sensitive cryptographic function being requested. In order to verify a digital signature computed on a document or any other object (e.g. an executable), access to the public key corresponding to the private key used to sign the document is required. Normally, the public part of the key is made available in a digital 'certificate', which is made up of the public key of the signer, the name of the signer, and other data, all signed using the private signing key of a trusted third party known as a Certification Authority (CA). To verify such a certificate, and thereby obtain a trusted copy of the document signer's public key, a trusted copy of the CA's public key is required. If a malicious party can insert a fake CA public key into the list of CA public keys stored in a PC, then this party could potentially do considerable harm to that PC, since this malicious party could then forge signatures apparently created by other entities. A method of achieving such an attack without attracting the user's attention is presented in this thesis. Countermeasures that can be deployed to prevent the insertion of a fake root public key are discussed. A suggested solution that can be used to detect and remove such fake keys is presented, and a prototype implementation of this solution is described. SSL/TLS supports mutual authentication, i.e. both server and client authentication, using public key certificates. However, this optional feature of SSL/TLS is not widely used because most end users do not have a certified public key. Certain attacks rely on this fact, such as web spoofing and phishing attacks. A method for supporting client-side SSL authentication using trusted computing platforms is proposed. The proposed approach makes a class of phishing attacks ineffective; moreover, the proposed method can also be used to protect against other online attacks

New York Law School Magazine, Vol. 28, No. 2

Features: From the Courtroom to the Classroom: The Racial Justice Project Defends the Right to Education Staying Afloat in a Downward Economy: Lessons From Sonnenschein Nath & Rosenthal LLP New York Law School Achieves Record Bar Pass Ratehttps://digitalcommons.nyls.edu/alum_mag/1010/thumbnail.jp

New York Law School Magazine, Vol. 28, No. 2

Features: From the Courtroom to the Classroom: The Racial Justice Project Defends the Right to Education Staying Afloat in a Downward Economy: Lessons From Sonnenschein Nath & Rosenthal LLP New York Law School Achieves Record Bar Pass Ratehttps://digitalcommons.nyls.edu/alum_mag/1010/thumbnail.jp

Reducing the risk of e-mail phishing in the state of Qatar through an effective awareness framework

In recent years, cyber crime has focused intensely on people to bypass existing sophisticated security controls; phishing is one of the most common forms of such attack. This research highlights the problem of e-mail phishing. A lot of previous research demonstrated the danger of phishing and its considerable consequences. Since users behaviour is unpredictable, there is no reliable technological protective solution (e.g. spam filters, anti-viruses) to diminish the risk arising from inappropriate user decisions. Therefore, this research attempts to reduce the risk of e-mail phishing through awareness and education. It underlines the problem of e-mail phishing in the State of Qatar, one of world s fastest developing countries and seeks to provide a solution to enhance people s awareness of e-mail phishing by developing an effective awareness and educational framework. The framework consists of valuable recommendations for the Qatar government, citizens and organisations responsible for ensuring information security along with an educational agenda to train them how to identify and avoid phishing attempts. The educational agenda supports users in making better trust decisions to avoid phishing that could complement any technical solutions. It comprises a collection of training methods: conceptual, embedded, e-learning and learning programmes which include a television show and a learning session with a variety of teaching components such as a game, quizzes, posters, cartoons and a presentation. The components were tested by trial in two Qatari schools and evaluated by experts and a representative sample of Qatari citizens. Furthermore, the research proves the existence and extent of the e-mail phishing problem in Qatar in comparison with the UK where people were found to be less vulnerable and more aware. It was discovered that Qatar is an attractive place for phishers and that a lack of awareness and e-law made Qatar more vulnerable to the phishing. The research identifies the factors which make Qatari citizens susceptible to e-mail phishing attacks such as cultural, country-specific factors, interests and beliefs, religion effect and personal characteristics and this identified the need for enhancing Qatari s level of awareness on phishing threat. Since literature on phishing in Qatar is sparse, empirical and non-empirical studies involved a variety of surveys, interviews and experiments. The research successfully achieved its aim and objectives and is now being considered by the Qatari Government

Updating the Lambda modes of a nuclear power reactor

[EN] Starting from a steady state configuration of a nuclear power reactor some situations arise in which the reactor configuration is perturbed. The Lambda modes are eigenfunctions associated with a given configuration of the reactor, which have successfully been used to describe unstable events in BWRs. To compute several eigenvalues and its corresponding eigenfunctions for a nuclear reactor is quite expensive from the computational point of view. Krylov subspace methods are efficient methods to compute the dominant Lambda modes associated with a given configuration of the reactor, but if the Lambda modes have to be computed for different perturbed configurations of the reactor more efficient methods can be used. In this paper, different methods for the updating Lambda modes problem will be proposed and compared by computing the dominant Lambda modes of different configurations associated with a Boron injection transient in a typical BWR reactor. (C) 2010 Elsevier Ltd. All rights reserved.This work has been partially supported by the Spanish Ministerio de Educacion y Ciencia under projects ENE2008-02669 and MTM2007-64477-AR07, the Generalitat Valenciana under project ACOMP/2009/058, and the Universidad Politecnica de Valencia under project PAID-05-09-4285.González Pintor, S.; Ginestar Peiro, D.; Verdú Martín, GJ. (2011). Updating the Lambda modes of a nuclear power reactor. Mathematical and Computer Modelling. 54(7):1796-1801. https://doi.org/10.1016/j.mcm.2010.12.013S1796180154