691 |
Classical Authenticated Key Exchange and Quantum CryptographyStebila, Douglas January 2009 (has links)
Cryptography plays an integral role in secure communication and is usually the strongest link in the chain of security. Yet security problems abound in electronic communication: spyware, phishing, denial of service, and side-channel attacks are still major concerns. The main goal in this thesis is to consider how cryptographic techniques can be extended to offer greater defence against these non-traditional security threats.
In the first part of this thesis, we consider problems in classical cryptography. We introduce multi-factor password-authenticated key exchange which allows secure authentication and key agreement based on multiple short secrets, such as a long-term password and a one-time response; it can provide an enhanced level of assurance in higher security scenarios because a multi-factor protocol is designed to remain secure even if all but one of the factors has been compromised due to attacks such as phishing or spyware. Next, we consider the integration of denial of service countermeasures with key exchange protocols: by introducing a formal model for denial of service resilience that complements the extended Canetti-Krawczyk model for secure key agreement, we cover a wide range of existing denial of service attacks and prevent them by carefully using client puzzles. Additionally, we look at how side-channel attacks affect certain types of formulae used in elliptic curve cryptography, and demonstrate that information leaked during field operations such as addition, subtraction, and multiplication can be exploited by an attacker.
In the second part of this thesis, we examine cryptography in the quantum setting. We argue that quantum key distribution will have an important role to play in future information security infrastructures and will operate best when integrated with the powerful public key infrastructures that are used today. Finally, we present a new look at quantum money and describe a quantum coin scheme where the coins are not easily counterfeited, are locally verifiable, and can be transferred to another party.
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692 |
The Linkage Problem for Group-labelled GraphsHuynh, Tony January 2009 (has links)
This thesis aims to extend some of the results of the Graph Minors Project of Robertson and Seymour to "group-labelled graphs". Let $\Gamma$ be a group. A $\Gamma$-labelled graph is an oriented graph with its edges labelled from $\Gamma$, and is thus a generalization of a signed graph.
Our primary result is a generalization of the main result from Graph Minors XIII. For any finite abelian group $\Gamma$, and any fixed $\Gamma$-labelled graph $H$, we present a polynomial-time algorithm that determines if an input $\Gamma$-labelled graph $G$ has an $H$-minor. The correctness of our algorithm relies on much of the machinery developed throughout the graph minors papers. We therefore hope it can serve as a reasonable introduction to the subject.
Remarkably, Robertson and Seymour also prove that for any sequence $G_1, G_2, \dots$ of graphs, there exist indices $i<j$ such that $G_i$ is isomorphic to a minor of $G_j$. Geelen, Gerards and Whittle recently announced a proof of the analogous result for $\Gamma$-labelled graphs, for $\Gamma$ finite abelian. Together with the main result of this thesis, this implies that membership in any minor closed class of $\Gamma$-labelled graphs can be decided in polynomial-time. This also has some implications for well-quasi-ordering certain classes of matroids, which we discuss.
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693 |
Path Tableaux and the Combinatorics of the Immanant FunctionTessier, Rebecca January 2013 (has links)
Immanants are a generalization of the well-studied determinant and permanent. Although the combinatorial interpretations for the determinant and permanent have been studied in excess, there remain few combinatorial interpretations for the immanant.
The main objective of this thesis is to consider the immanant, and its possible combinatorial interpretations, in terms of recursive structures on the character. This thesis presents a comprehensive view of previous interpretations of immanants. Furthermore, it discusses algebraic techniques that may be used to investigate further into the combinatorial aspects of the immanant.
We consider the Temperley-Lieb algebra and the class of immanants over the elements of this algebra. Combinatorial tools including the Temperley-Lieb algebra and Kauffman diagrams will be used in a number of interpretations. In particular, we extend some results for the permanent and determinant based on the $R$-weighted planar network construction, where $R$ is a convenient ring, by Clearman, Shelton, and Skandera. This thesis also presents some cases in which this construction cannot be extended. Finally, we present some extensions to combinatorial interpretations on certain classes of tableaux, as well as certain classes of matrices.
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694 |
On Excluded Minors for Even Cut MatroidsPivotto, Irene January 2006 (has links)
In this thesis we will present two main theorems that can be used to study
minor minimal non even cut matroids.
Given any signed graph we can associate an even cut matroid. However, given
an even cut matroid, there are in general, several signed graphs which
represent that matroid. This is in contrast to, for instance graphic (or
cographic) matroids, where all graphs corresponding to a particular
graphic matroid are essentially equivalent. To tackle the multiple
non equivalent representations of even cut matroids we use the concept of
Stabilizer first introduced by Wittle. Namely, we show the following:
given a "substantial" signed graph, which represents a matroid N that is a
minor of a matroid M, then if the signed graph extends to a signed graph
which represents M then it does so uniquely. Thus the representations of the
small matroid determine the representations of the larger matroid containing
it. This allows us to consider each representation of an even cut matroid
essentially independently.
Consider a small even cut matroid N that is a minor of a matroid M that is
not an even cut matroid. We would like to prove that there exists a
matroid N' which contains N and is contained in M such that the size of N'
is small and such that N' is not an even cut matroid (this would imply in
particular that there are only finitely many minimally non even cut
matroids containing N). Clearly, none of the representations of N extends to
M. We will show that (under certain technical conditions) starting from a
fixed representation of N, there exists a matroid N' which contains N
and is contained in M such that the size of N' is small and such that the
representation of N does not extend to N'.
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695 |
Welch Bounds and Quantum State TomographyBelovs, Aleksandrs January 2008 (has links)
In this thesis we investigate complete systems of MUBs and SIC-POVMs. These are highly
symmetric sets of vectors in Hilbert space, interesting because of their applications in quantum
tomography, quantum cryptography and other areas. It is known that these objects
form complex projective 2-designs, that is, they satisfy Welch bounds for k = 2 with equality.
Using this fact, we derive a necessary and sufficient condition for a set of vectors to be
a complete system of MUBs or a SIC-POVM. This condition uses the orthonormality of a
specific set of vectors.
Then we define homogeneous systems, as a special case of systems of vectors for which
the condition takes an especially elegant form. We show how known results and some new
results naturally follow from this construction.
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696 |
Classical Authenticated Key Exchange and Quantum CryptographyStebila, Douglas January 2009 (has links)
Cryptography plays an integral role in secure communication and is usually the strongest link in the chain of security. Yet security problems abound in electronic communication: spyware, phishing, denial of service, and side-channel attacks are still major concerns. The main goal in this thesis is to consider how cryptographic techniques can be extended to offer greater defence against these non-traditional security threats.
In the first part of this thesis, we consider problems in classical cryptography. We introduce multi-factor password-authenticated key exchange which allows secure authentication and key agreement based on multiple short secrets, such as a long-term password and a one-time response; it can provide an enhanced level of assurance in higher security scenarios because a multi-factor protocol is designed to remain secure even if all but one of the factors has been compromised due to attacks such as phishing or spyware. Next, we consider the integration of denial of service countermeasures with key exchange protocols: by introducing a formal model for denial of service resilience that complements the extended Canetti-Krawczyk model for secure key agreement, we cover a wide range of existing denial of service attacks and prevent them by carefully using client puzzles. Additionally, we look at how side-channel attacks affect certain types of formulae used in elliptic curve cryptography, and demonstrate that information leaked during field operations such as addition, subtraction, and multiplication can be exploited by an attacker.
In the second part of this thesis, we examine cryptography in the quantum setting. We argue that quantum key distribution will have an important role to play in future information security infrastructures and will operate best when integrated with the powerful public key infrastructures that are used today. Finally, we present a new look at quantum money and describe a quantum coin scheme where the coins are not easily counterfeited, are locally verifiable, and can be transferred to another party.
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697 |
The Linkage Problem for Group-labelled GraphsHuynh, Tony January 2009 (has links)
This thesis aims to extend some of the results of the Graph Minors Project of Robertson and Seymour to "group-labelled graphs". Let $\Gamma$ be a group. A $\Gamma$-labelled graph is an oriented graph with its edges labelled from $\Gamma$, and is thus a generalization of a signed graph.
Our primary result is a generalization of the main result from Graph Minors XIII. For any finite abelian group $\Gamma$, and any fixed $\Gamma$-labelled graph $H$, we present a polynomial-time algorithm that determines if an input $\Gamma$-labelled graph $G$ has an $H$-minor. The correctness of our algorithm relies on much of the machinery developed throughout the graph minors papers. We therefore hope it can serve as a reasonable introduction to the subject.
Remarkably, Robertson and Seymour also prove that for any sequence $G_1, G_2, \dots$ of graphs, there exist indices $i<j$ such that $G_i$ is isomorphic to a minor of $G_j$. Geelen, Gerards and Whittle recently announced a proof of the analogous result for $\Gamma$-labelled graphs, for $\Gamma$ finite abelian. Together with the main result of this thesis, this implies that membership in any minor closed class of $\Gamma$-labelled graphs can be decided in polynomial-time. This also has some implications for well-quasi-ordering certain classes of matroids, which we discuss.
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698 |
Two Affine Scaling Methods for Solving Optimization Problems Regularized with an L1-normLi, Zhirong January 2010 (has links)
In finance, the implied volatility surface is plotted against strike price and time to maturity.
The shape of this volatility surface can be identified by fitting the model to what is actually
observed in the market. The metric that is used to measure the discrepancy between the
model and the market is usually defined by a mean squares of error of the model prices to the
market prices. A regularization term can be added to this error metric to make the solution
possess some desired properties. The discrepancy that we want to minimize is usually a highly
nonlinear function of a set of model parameters with the regularization term. Typically
monotonic decreasing algorithm is adopted to solve this minimization problem. Steepest
descent or Newton type algorithms are two iterative methods but they are local, i.e., they
use derivative information around the current iterate to find the next iterate. In order to
ensure convergence, line search and trust region methods are two widely used globalization
techniques.
Motivated by the simplicity of Barzilai-Borwein method and the convergence properties
brought by globalization techniques, we propose a new Scaled Gradient (SG) method for
minimizing a differentiable function plus an L1-norm. This non-monotone iterative method
only requires gradient information and safeguarded Barzilai-Borwein steplength is used in
each iteration. An adaptive line search with the Armijo-type condition check is performed in
each iteration to ensure convergence. Coleman, Li and Wang proposed another trust region
approach in solving the same problem. We give a theoretical proof of the convergence of
their algorithm. The objective of this thesis is to numerically investigate the performance
of the SG method and establish global and local convergence properties of Coleman, Li and
Wang’s trust region method proposed in [26]. Some future research directions are also given
at the end of this thesis.
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699 |
Optimization of Laminated Dies ManufacturingAhari, Hossein January 2011 (has links)
Due to the increasing competition from developing countries, companies are struggling to reduce their manufacturing costs. In the field of tool manufacturing, manufacturers are under pressure to produce new products as quickly as possible at minimum cost with high accuracy. Laminated tooling, where parts are manufactured layer by layer, is a promising technology to reduce production costs. Laminated tooling is based on taking sheets of metal and stacking them to produce the final product after cutting each layer profile using laser cutting or other techniques. It is also a powerful tool to make complex tools with conformal cooling channels. In conventional injection moulds and casting dies the cooling channels are drilled in straight paths whereas the cavity has a complex profile. In these cases the cooling system may not be sufficiently effective resulting in a longer cooling time and loss of productivity. Furthermore, conventional cooling channels are limited to circular cross sections, while conformal cooling channels could follow any curved path with variable and non circular cross sections.
One of the issues in laminated tooling is the surface jaggedness. The surface jaggedness depends on the layers' thicknesses and surface geometry. If the sheets are thin, the surface quality is improved, but the cost of layer profile cutting is increased. On the other hand, increasing the layers' thicknesses reduces the lamination process cost, but it increases the post processing cost. One solution is having variable thicknesses for the layers and optimally finding the set of layer thicknesses to achieve the minimum surface jaggedness and the number of layers at the same time. In practice, the choice of layers thicknesses depends on the availability of commercial sheet metals. One solution to reduce the number of layers without compromising the surface jaggedness is to use a non-uniform lamination technique in which the layers' thicknesses are changed according to the surface geometry. Another factor in the final surface quality is the lamination direction which can be used to reduce the number of laminations. Optimization by considering lamination direction can be done assuming one or multiple directions.
In this thesis, an optimization method to minimize the surface jaggedness and the number of layers in laminated tooling is presented. In this optimization, the layers' thicknesses are selected from a set of available sheet metals. Also, the lamination direction as one of the optimization parameters is studied. A modified version of genetic algorithm is created for the optimization purpose in this research. The proposed method is presented as an optimization package which is applicable to any injection mould, hydroforming or sheet metal forming tool to create an optimized laminated prototype based on the actual model.
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700 |
Exponentially Dense MatroidsNelson, Peter January 2011 (has links)
This thesis deals with questions relating to the maximum density of rank-n matroids in a minor-closed class.
Consider a minor-closed class M of matroids that does not contain a given rank-2 uniform matroid. The growth rate function is defined by h_M(n) = max(|N| : N ∈ M simple, r(N) ≤ n).
The Growth Rate Theorem, due to Geelen, Kabell, Kung, and Whittle, shows that the growth rate function is either linear, quadratic, or exponential in n. In the case of exponentially dense classes, we conjecture that, for sufficiently large n,
h_M(n) = (q^(n+k) − 1)/(q-1) − c, where q is a prime power, and k and c are non-negative integers depending only on M. We show that this holds for several interesting classes, including the class of all matroids with no U_{2,t}-minor.
We also consider more general minor-closed classes that exclude an arbitrary uniform matroid. Here the growth rate, as defined above, can be infinite. We define a more suitable notion of density, and prove a growth rate theorem for this more general notion, dividing minor-closed classes into those that are at most polynomially dense, and those that are exponentially dense.
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