I would like to thank my parents for always believing in me. I would also like to thank my supervisors Richard Lindner and Johannes Buchmann for their useful comments and suggestions on how to improve the queality of the thesis. Not on last place I would like to thank Vadim Lyubashevsky and Luis Carlos Coronado Garcia for their kindness and readiness to answer my questions. Warranty I hereby warrant that the content of this thesis is the direct result of my own work and that any use made in it of published or unpublished material is fully and correctly referenced. I also warrant that the presented work has

den angegebenen Quellen und Hilfsmitteln angefertigt zu haben. Alle Stellen, die aus Quellen entnommen wurden, sind als solche kenntlich gemacht. Diese Arbeit hat in gleicher oder ähnlicher Form noch keiner Prüfungsbehörde vorgelegen. Darmstadt, den 26.06.2012 (T. Kilian) Contents

2010 to my wife, Joyce, and my family...- Résumé-

Implementational aspects of code-based cryptography

approaches for estimation in partial knowledge scenarios. The first is based on replacing the orthogonality principle by an oblique counterpart, and is proven to coincide with the method of instrumental variables from statistics, although developed in a different context. The second is based on a worst

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Abstract | This review provides an introduction to Sup-

Abstract Basic ideas of rough set theory were proposed by Zdzis law Pawlak [85, 86] in the early 1980’s. In the ensuing years, we have witnessed a systematic, world–wide growth of interest in rough sets and their applications. The main goal of rough set analysis is induction of approximations of con-cepts. This main goal is motivated by the basic fact, constituting also the main problem of KDD, that languages we may choose for knowledge description are incomplete. A fortiori, we have to describe concepts of interest (features, proper-ties, relations etc.) not completely but by means of their reflections (i.e. approx-imations) in the chosen language. The most important issues in this induction process are: – construction of relevant primitive concepts from which approximations of more complex concepts are assembled, – measures of inclusion and similarity (closeness) on concepts, – construction of operations producing complex concepts from the primitive ones.

I declare that this thesis is my own account of my research and contains as its main content work which has not previously been submitted for a degree at any tertiary education institution.

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