Mastergradsoppgaver i matematikk

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Mastergradsoppgaver i matematikk

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• Matroids, demi-matroids and chains of linear codes

  Martin, James Aloysius (Master thesis; Mastergradsoppgave, 09-Dec-2010)

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  Abstract:	The central theme of this thesis is the study of matroids and related concepts such as linear codes and graphs. Demi-matroids, structures which arise from a relaxation of the definition of a matroid are explored along with related themes. Finally we examine the fact that some results in coding theory are essentially consequences of results for demi-matroids.
  URI:	http://hdl.handle.net/10037/2957

  File(s) in this item: 1

  thesis.pdf   (538.0Kb)
• Extensions of groups and modules

  Nermo, Catalina Nicole Vintilescu (Master thesis; Mastergradsoppgave, 2010)

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  Abstract:

  The main goal of this thesis is to build up detailed constructions and give complete proofs for the extension functors of modules and groups, which we define using cohomology functors. Further, we look at the relations that appear between these and short exact sequences of modules, respectively groups. We calculate also several concrete cohomology groups, and build extensions that are described by those cohomologies.

  URI:

  http://hdl.handle.net/10037/2642

  File(s) in this item: 1

  thesis.pdf   (674.4Kb)
• Kompleksiteten til noen kryptologisk viktige algoritmer

  Brattli, Tore (Master thesis; Mastergradsoppgave, 04-Apr-1990)

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  Abstract:

  Denne hovedfagsoppgaven har som mål å sammenligne teoretisk og praktisk kompleksitet til algoritmer som har stor kryptologisk betydning. Et av målene er å avsløre den skjulte konstanten bak O-notasjonen, slik at algoritmene kan sammenlignes på et reelt grunnlag. I tillegg er det sett på sammenheng mellom sikkerhet, størrelsen på tall, asymptotisk og praktisk kompleksitet. Spesielt algoritmer som inngår i kryptering / dekryptering er forsøkt analysert i dybden. Algoritmer som er av mindre betydning er kun analysert med tanke på den asymptotiske kompleksiteten, mens andre algoritmer kun er beskrevet. De viktigste algoritmene er programmert i C, og kjørt på en datamaskin for å bedre kunne sammenligne dem. Spesielt gjelder det multiplikasjon, der 7-8 algoritmer er analysert og 3 av dem programmert. Programmering av langtallsaritmetikk er forøvrig noe av det som har krevd mest tid. Totalt gir oppgaven gir en brukbar oversikt over mer enn 30 tallteoretiske algoritmer som har betydning innen moderne kryptologi.

  URI:

  http://hdl.handle.net/10037/2341

  File(s) in this item: 1

  thesis.pdf   (10.69Mb)
• Distributing a private key generator in Ad hoc Networks

  Stenberg, Eystein Måløy (Master thesis; Mastergradsoppgave, 15-May-2009)

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  Abstract:

  A Mobile Ad hoc Network (MANET) is a wireless network that does not rely on a fixed infrastructure. These characteristics make algorithms that route network traffic particularly vulnerable to attack. Mechanisms used to protect against such attacks often depend on cryptographic keys. Since the nodes in a MANET have limited resources, designing methods for cryptographic key management is particularly challenging. Because the network infrastructure is unstable, assuming that authorities used in key management are implemented using any single node is not realistic. Threshold cryptography can be used to distribute an authority, such that it is implemented by multiple nodes. This makes the authority more robust against network failures and harder to compromise. However, the bandwidth limitations in a MANET result in that public key distribution becomes very challenging. Identity-based cryptography (IBC), where any identity may serve as a public key, makes public keys and their certificates superfluous. The authority issuing private keys corresponding to an identity is called a Private Key Generator (PKG). This thesis considers the issue of distributing a PKG to the nodes in a MANET. It gives a description of a generic distributed PKG, including a definition of security. An example of a distributed PKG is also given. This distributed PKG is compatible with some of the most prevalent IBC systems. It is shown that the security properties of the base IBC systems are preserved when this distributed PKG is used instead of the original one. Threshold cryptography and identity-based cryptography are found to result in very efficient key management systems, compared to other methods. It is however important to consider which security properties a distributed authority has, especially with respect to any leakage of information on the authority's secret key. However, the main challenge in connection with key management in a MANET is to authenticate nodes without requiring preestablished trust.

  URI:

  http://hdl.handle.net/10037/2074

  File(s) in this item: 1

  thesis.pdf   (755.9Kb)
• Light induced forces on dielectric nanospheres

  Lundamo, Trine (Master thesis; Mastergradsoppgave, 15-Feb-2008)

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  Abstract:	Waves that are reflected and refracted by material bodies also transfer momentum to these bodies. This means that the wave field induces a force on the bodies, and multiple reflections between bodies induce forces between them. Light is an electromagnetic wave phenomenon, and the waves carry energy and momentum. Hence, any object that is scattering and refracting light is also acted upon by a light induced force. This force is a tiny force and is usually ignored, but if the objects are small enough the force induced by the light field would dominate all other forces. Due to this it is possible to manipulate small objects using light from a laser. This thesis is based on an experiment on optical binding of two dielectric spheres, where the spheres were small enough to make the force induced by the light field the dominating force. In the experiment bistability and hysteresis in the equilibrium separations of the optically bound dielectric spheres were observed in one dimension. In this thesis the experiment will be modeled with a simplified setup, and the goal is to see if it is possible to find bistability in two dimensions also. Numerical approximations are used to calculate the wave field, and from this the force on the objects can be found.
  Description:	Appendix A to D have been removed from the published pdf at the request of the author.
  URI:	http://hdl.handle.net/10037/1395

  File(s) in this item: 1

  thesis.pdf   (7.947Mb)

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