Fakultät für Informatik und Mathematik
Refine
Year of publication
- 2015 (11) (remove)
Document Type
- Doctoral Thesis (11)
Has Fulltext
- yes (11)
Is part of the Bibliography
- no (11)
Keywords
- Computersicherheit (2)
- (generalized) border bases (1)
- (lokale) Bildmerkmale (1)
- Abfrageverarbeitung (1)
- Approximation (1)
- Bildverarbeitung (1)
- C <Programmiersprache> (1)
- Caching (1)
- Cloud Computing (1)
- Compliance-System (1)
Institute
Als sich in der ersten Hälfte des 19. Jahrhunderts zunehmend mehr bedeutende Mathematiker mit der Suche nach Invarianten beschäftigten, konnte natürlich noch niemand vorhersehen, dass die Invariantentheorie mit Beginn des Computerzeitalters in der Bildverarbeitung bzw. dem Rechnersehen ein äußerst fruchtbares Anwendungsgebiet finden wird. In dieser Arbeit wird eine neue Anwendungsmöglichkeit der Invariantentheorie in der Bildverarbeitung vorgestellt. Dazu werden lokale Bildmerkmale betrachtet. Dabei handelt es sich um die Koordinaten einer Polynomfunktion bzgl. einer geeigneten Orthonormalbasis von P_n(R^2,R), die die zeitintegrierte Sensorinputfunktion auf lokalen Pixelfenstern bestmöglich approximiert. Diese Bildmerkmale werden in vielen Anwendungen eingesetzt, um Objekte in Bildern zu erkennen und zu lokalisieren. Beispiele hierfür sind die Detektion von Werkstücken an einem Fließband oder die Verfolgung von Fahrbahnmarkierungen in Fahrerassistenzsystemen. Modellieren lässt sich die Suche nach einem Muster in einem Suchbild als Paar von Stereobildern, auf denen lokal die affin-lineare Gruppe AGL(R) operiert. Will man also feststellen, ob zwei lokale Pixelfenster in etwa Bilder eines bestimmten dreidimensionalen Oberflächenausschnitts sind, ist zu klären, ob die Bildausschnitte durch eine Operation der Gruppe AGL(R) näherungsweise ineinander übergeführt werden können. Je nach Anwendung genügt es bereits, passende Untergruppen G von AGL(R) zu betrachten. Dank der lokalen Approximation durch Polynomfunktionen induziert die Operation einer Untergruppe G eine Operation auf dem reellen Vektorraum P_n(R^2,R). Damit lässt sich das Korrespondenzproblem auf die Frage reduzieren, ob es eine Transformation T in G gibt so, dass p ungefähr mit der Komposition von q und T für die zugehörigen Approximationspolynome p,q in P_n(R^2,R) gilt. Mit anderen Worten, es ist zu klären, ob sich p und q näherungsweise in einer G-Bahn befinden, eine typische Fragestellung der Invariantentheorie. Da nur lokale Bildausschnitte betrachtet werden, genügt es weiter, Untergruppen G von GL_2(R) zu betrachten. Dann erhält man sofort auch die Antwort für das semidirekte Produkt von R^2 mit G. Besonders interessant für Anwendungen ist hierbei die spezielle orthogonale Gruppe G=SO_2(R) und damit insgesamt die eigentliche Euklidische Gruppe. Für diese Gruppe und spezielle Pixelfenster ist das Korrespondenzproblem bereits gelöst. In dieser Arbeit wird das Problem in eben dieser Konstellation ebenfalls gelöst, allerdings auf elegante Weise mit Methoden der Invariantentheorie. Der Ansatz, der hier vorgestellt wird, ist aber nicht auf diese Gruppe und spezielle Pixelfenster begrenzt, sondern leicht auf weitere Fälle erweiterbar. Dazu ist insbesondere zu klären, wie sich sogenannte fundamentale Invarianten von lokalen Bildmerkmalen, also letztendlich Invarianten von Polynomfunktionen, berechnen lassen, d.h. Erzeugendensysteme der entsprechenden Invariantenringe. Mit deren Hilfe lässt sich die Zugehörigkeit einer Polynomfunktion zur Bahn einer anderen Funktion auf einfache Weise untersuchen.
Neben der Vorstellung des Verfahrens zur Korrespondenzfindung und der dafür notwendigen Theorie werden in dieser Arbeit Erzeugendensysteme von Invariantenringen untersucht, die besonders "schöne" Eigenschaften besitzen. Diese schönen Erzeugendensysteme von Unteralgebren werden, analog zu Gröbner-Basen als Erzeugendensysteme von Idealen, SAGBI-Basen genannt ("Subalgebra Analogs to Gröbner Bases for Ideals"). SAGBI-Basen werden hier insbesondere aus algorithmischer Sicht behandelt, d.h. die Berechnung von SAGBI-Basen steht im Vordergrund. Dazu werden verschiedene Algorithmen erarbeitet, deren Korrektheit bewiesen und implementiert. Daraus resultiert ein Software-Paket zu SAGBI-Basen für das Computeralgebrasystem ApCoCoA, dessen Funktionalität in diesem Umfang in keinem Computeralgebrasystem zu finden sein wird. Im Zuge der Umsetzung der einzelnen Algorithmen konnte außerdem die Theorie der SAGBI-Basen an zahlreichen Stellen erweitert werden.
IT outsourcing to clouds bears new challenges to the technical implementation of legally compliant clouds. On the one hand, outsourcing companies have to comply with legal requirements. On the other hand, cloud providers have to support their customers in achieving compliance with these legal requirements when processing data in the cloud. Consequently, the questions arise when IT outsourcing to clouds is lawful, which legal requirements apply to data processing in clouds, and how cloud providers can support their customers on achieving legal compliance.
In this thesis, answers to these questions are given by performing a legal analysis identifying the legal requirements and a technical analysis identifying how legal requirements can be addressed in the context of cloud computing. Further, an information flow analysis is done, resulting in a system theoretical model that is able to describe information flow control in clouds based on the security classification of virtual resources and hardware resources. In a proof-of-concept implementation which is based on the OpenStack open-source cloud platform, it is shown that information flow control can be implemented as a part of cloud management and that legal compliance can be monitored and reported based on the actual assignment of virtual resources to hardware resources. Thereby, cloud providers are able to provide cloud customers with cloud resources, which are automatically assigned to hardware resources that comply with the legal requirements of the cloud customers. This consequently empowers cloud customers to utilise cloud resources according to their legal requirements and to keep control of managing the legal compliance of their data processing in clouds.
This doctoral thesis is devoted to generalize border bases to the module setting and to apply them in various ways.
First, we generalize the theory of border bases to finitely generated modules over a polynomial ring. We characterize these generalized border bases and show that we can compute them. As an application, we are able to characterize subideal border bases in various new ways and give a new algorithm for their computation. Moreover, we prove Schreyer's Theorem for border bases of submodules of free modules of finite rank over a polynomial ring.
In the second part of this thesis, we study the effect of homogenization to border bases of zero-dimensional ideals. This yields the new concept of projective border bases of homogeneous one-dimensional ideals. We show that there is a one-to-one correspondence between projective border bases and zero-dimensional closed subschemes of weighted projective spaces that have no point on the hyperplane at infinity. Applying that correspondence, we can characterize uniform zero-dimensional closed subschemes of weighted projective spaces that have a rational support over the base field in various ways. Finally, we introduce projective border basis schemes as specific subschemes of border basis schemes. We show that these projective border basis schemes parametrize all zero-dimensional closed subschemes of a weighted projective space whose defining ideals possess a projective border basis. Assuming that the base field is algebraically closed, we are able to prove that the set of all closed points of a projective border basis scheme that correspond to a uniform subscheme is a constructive set with respect to the Zariski topology.
This thesis attempts to investigate the Noether, Dedekind, and Kähler differents for a 0-dimensional scheme X in the projective n-space P^n_K over an arbitrary field K. In particular, we focus on studying the relations between the algebraic structure of these differents and geometric properties of the scheme X.
In Chapter 1 we give an outline to the problems this thesis is concerned with, a brief literature review for each problem, and the main results regarding these problems. Chapter 2 contains background results that we will need in the subsequent chapters. We introduce the concept of maximal p_j-subschemes of a 0-dimensional scheme X and give some descriptions of them and their Hilbert functions. Furthermore, we generalize the notion of a separator of a subscheme of X of degree deg(X)-1 to a set of separators of a maximal p_j-subscheme of X. In Chapter 3 we explore the Noether, Dedekind, and Kähler differents for 0-dimensional schemes X. First we define these differents for X, and take a look at how to compute these differents and examine their relations. Then we give an answer to the question "What are the Hilbert functions of these differents?" in some cases.
In Chapter 4 we use the differents to investigate the Cayley-Bacharach property of 0-dimensional schemes over an arbitrary field K. The principal results of this chapter are characterizations of CB-schemes and of arithmetically Gorenstein schemes in terms of their Dedekind differents and a criterion for a 0-dimensional smooth scheme to be a complete intersection. We also generalize some results such as Dedekind's formula and the characterization of the Cayley-Bacharach property by using Liaison theory. In addition, several propositions on the uniformities are proven. In Chapter 5 we are interested in studying the Noether, Dedekind, and Kähler differents for finite special classes of schemes and finding out some applications of these differents. First, we investigate these differents for reduced 0-dimensional almost complete intersections X in P^n_K over a perfect field K. Then we investigate the relationships between these differents and the i-th Fitting ideals of the module of Kähler differentials of the homogeneous coordinate ring of X. Finally, we look more closely at the Hilbert functions and the regularity indices of these differents for fat point schemes.
This doctoral thesis is dedicated to the analysis and the design of
symmetric cryptographic algorithms.
In the first part of the dissertation, we deal with fault-based attacks
on cryptographic circuits which belong to the field of active implementation
attacks and aim to retrieve secret keys stored on such chips. Our main focus
lies on the cryptanalytic aspects of those attacks. In particular, we target
block ciphers with a lightweight and (often) non-bijective key schedule where
the derived subkeys are (almost) independent from each other. An attacker who is
able to reconstruct one of the subkeys is thus not necessarily able to directly
retrieve other subkeys or even the secret master key by simply reversing the key
schedule. We introduce a framework based on differential fault analysis that
allows to attack block ciphers with an arbitrary number of independent subkeys
and which rely on a substitution-permutation network. These methods are then
applied to the lightweight block ciphers LED and PRINCE and we show in both
cases how to recover the secret master key requiring only a small number of
fault injections. Moreover, we investigate approaches that utilize algebraic
instead of differential techniques for the fault analysis and discuss advantages
and drawbacks. At the end of the first part of the dissertation, we explore
fault-based attacks on the block cipher Bel-T which also has a lightweight key
schedule but is not based on a substitution-permutation network but instead on
the so-called Lai-Massey scheme. The framework mentioned above is thus not
usable against Bel-T. Nevertheless, we also present techniques for the case of
Bel-T that enable full recovery of the secret key in a very efficient way using
differential fault analysis.
In the second part of the thesis, we focus on authenticated encryption
schemes. While regular ciphers only protect privacy of processed data,
authenticated encryption schemes also secure its authenticity and integrity.
Many of these ciphers are additionally able to protect authenticity and
integrity of so-called associated data. This type of data is transmitted
unencrypted but nevertheless must be protected from being tampered with during
transmission. Authenticated encryption is nowadays the standard technique to
protect in-transit data. However, most of the currently deployed schemes have
deficits and there are many leverage points for improvements. With NORX we
introduce a novel authenticated encryption scheme supporting associated data.
This algorithm was designed with high security, efficiency in both hardware and
software, simplicity, and robustness against side-channel attacks in mind. Next
to its specification, we present special features, security goals,
implementation details, extensive performance measurements and discuss
advantages over currently deployed standards. Finally, we describe our
preliminary security analysis where we investigate differential and rotational
properties of NORX. Noteworthy are in particular the newly developed
techniques for differential cryptanalysis of NORX which exploit the power of
SAT- and SMT-solvers and have the potential to be easily adaptable to other
encryption schemes as well.
The aim of this dissertation is to investigate Kaehler differential algebras and their Hilbert functions for 0-dimensional schemes in P^n. First we give relations between Kaehler differential 1-forms of fat point schemes and another fat point schemes. Then we determine the Hilbert polynomial and give a sharp bound for the regularity index of the module of Kaehler differential m-forms, for 0<m<n+2. Next, we examine the Kaehler differential algebras for fat point schemes whose supports lie on non-singular conics in P^2. Finally, we prove the Segre bounds for equimultiple fat point schemes in P^4, this result allows us to determine the regularity index of the module of Kaehler differential 1-forms, and a sharp bound for the regularity index of the module of Kaehler differential m-forms, for 1<m<6.
This thesis is divided into two parts. The first part is devoted to the curvature estimation of piecewise smooth curves using variation diminishing splines. The variation diminishing property combined with the ability to reconstruct linear functions leads to a convexity preserving approximation that is crucial if additional sign changes in the curvature estimation have to be avoided. To this end, we will first establish the foundations of variation diminishing transforms and introduce the Bernstein and the Schoenberg operator on the space of continuous functions and its generalization to the Lp-spaces. In order to be able to detect C2-singularities in piecewise smooth curves, we establish lower estimates for the approximation error in terms of the second order modulus of smoothness for Schoenberg’s variation diminishing operator. Afterwards, we consider smooth curve approximations using only finitely many samples of the curve, where the approximation, its first, and its second derivative converge uniformly to its corresponding part of the curve to be approximated. In this case, we can show that the estimated curvature converges uniformly to the real curvature if the number of samples goes to infinity. Based on the lower estimates that relates the decay rate of the approximation error with smoothness we propose a multi-scale algorithm to estimate the curvature and to detect C2-singularities. We numerically evaluate our algorithm and compare it to others to show that our algorithm achieves competitive accuracy while our curvature estimations are significantly faster to compute.
The second part deals with generalizations of the established lower estimates for the Schoenberg operator. We will show that such estimates can be obtained for linear operators on a general Banach function space with smooth range provided that the iterates of the operator converge uniformly and a semi-norm defined on the range of the operator annihilates the fixed points of the operator. To this end, we will prove by spectral properties that the iterates of every positive finite-rank operator converge uniformly. As highlight of this thesis, we show a constructive way using a Gramian matrix where the dual fixed points operate on the fixed points of an operator to derive the limit of the iterates for an arbitrary quasi-compact operator defined on a general Banach space.
Most major airports collect recordings of the position of aircrafts at specific times. Those data typically requires extensive smoothing and corrections before it can be used for later analysis. Conventional smoothing approaches fail to model the movement physically correct, i.e. do not take standstills of aircrafts into account.
In this thesis we develop a method to detect standstills, employ robust smoothing splines for data fitting, add adequate boundary conditions for the detected standstill periods (i.e. force the function to be constant and to entry- and exit-direction for the standstills to be identical) and give an algorithm to solve those approximation problems efficiently.
In the progress we give an explicit proof for the convergence of the IRLS algorithm proposed by Huber to solve M-type estimates for non-linear approximation problems. Furthermore we derive a blueprint for a method to solve separable, quadratic least squares problems with very few quadratic variables.
Top-k Semantic Caching
(2015)
The subject of this thesis is the intelligent caching of top-k queries in an environment with high latency and low throughput. In such an environment, caching can be used to reduce network traffic and improve response time. Slow database connections of mobile devices and to databases, which have been offshored, are practical use cases.
A semantic cache is a query-based cache that caches query results and maintains their semantic description. It reuses partial matches of previous query results. Each query that is processed by the semantic cache is split into two disjoint parts: one that can be completely answered with tuples of the cache probe query, and another that requires tuples to be transferred from the server (remainder query).
Existing semantic caches do not support top-k queries, i.e., ordered and limited queries. In this thesis, we present an innovative semantic cache that naturally supports top-k queries. The support of top-k queries in a semantic cache has considerable effects on cache elements, operations on cache elements -- like creation, difference, intersection, and union -- and query answering. Hence, we introduce new techniques for cache management and query processing. They enable the semantic cache to become a true top-k semantic cache.
In addition, we have developed a new algorithm that can estimate the lower bounds of query results of sorted queries using multidimensional histograms. Using this algorithm, our top-k semantic cache is able to pipeline partial query results of top-k queries. Thereby, query execution performance can be significantly increased.
We have implemented a prototype of a top-k semantic cache called IQCache (Intelligent Query Cache). An extensive and thorough evaluation with various benchmarks using our prototype demonstrates the applicability and performance of top-k semantic caching in practice. The experiments prove that the top-k semantic cache invariably outperforms simple hash-based caching strategies and scales very well.
The world wide web today serves as a distributed application platform. Its origins, however, go back to a simple delivery network for static hypertexts. The legacy from these days can still be observed in the communication protocol used by increasingly sophisticated clients and applications. This thesis identifies the actual security requirements of modern web applications and shows that HTTP does not fit them: user and application authentication, message integrity and confidentiality, control-flow integrity, and application-to-application authorization. We explore the other protocols in the web stack and work out why they can not fill the gap. Our analysis shows that the underlying problem is the connectionless property of HTTP. However, history shows that a fresh start with web communication is far from realistic. As a consequence, we come up with approaches that contribute to meet the identified requirements.
We first present impersonation attack vectors that begin before the actual user authentication, i.e. when secure web interaction and authentication seem to be unnecessary. Session fixation attacks exploit a responsibility mismatch between the web developer and the used web application framework. We describe and compare three countermeasures on different implementation levels: on the source code level, on the framework level, and on the network level as a reverse proxy.
Then, we explain how the authentication credentials that are transmitted for the user login, i.e. the password, and for session tracking, i.e. the session cookie, can be complemented by browser-stored and user-based secrets respectively. This way, an attacker can not hijack user accounts only by phishing the user's password because an additional browser-based secret is required for login. Also, the class of well-known session hijacking attacks is mitigated because a secret only known by the user must be provided in order to perform critical actions.
In the next step, we explore alternative approaches to static authentication credentials. Our approach implements a trusted UI and a mutually authenticated session using signatures as a means to authenticate requests. This way, it establishes a trusted path between the user and the web application without exchanging reusable authentication credentials. As a downside, this approach requires support on the client side and on the server side in order to provide maximum protection. Another approach avoids client-side support but can not implement a trusted UI and is thus susceptible to phishing and clickjacking attacks.
Our approaches described so far increase the security level of all web communication at all time. This is why we investigate adaptive security policies that fit the actual risk instead of permanently restricting all kinds of communication including non-critical requests. We develop a smart browser extension that detects when the user is authenticated on a website meaning that she can be impersonated because all requests carry her identity proof. Uncritical communication, however, is released from restrictions to enable all intended web features.
Finally, we focus on attacks targeting a web application's control-flow integrity. We explain them thoroughly, check whether current web application frameworks provide means for protection, and implement two approaches to protect web applications: The first approach is an extension for a web application framework and provides protection based on its configuration by checking all requests for policy conformity. The second approach generates its own policies ad hoc based on the observed web traffic and assuming that regular users only click on links and buttons and fill forms but do not craft requests to protected resources.