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First of all, I would like to thank Prof. Johannes Buchmann for giving me the opportunity to write my thesis under this topic and gain knowledge in the field of fully homomorphic schemes and moreover in the area of lattices. Furthermore, many thanks go to my two supervisors Dr. Richard Lindner and Michael Schneider who offered and spent much time answering me all my investigating questions and guiding me in the right direction. In addition I would like to thank all people that supported my work on this thesis by proofreading it, finding spelling mistakes and logical errors as well as supporting me in improving the structure of my thesis and its fluent reading; as there are: Richard Frankland, Maina Olembo, Denise Demirel, and Dr. Melanie Volkamer. Lastly, I thank all whom I have forgotten to mention before! Without your contributions this work would not be what it actually is. Warranty I hereby declare that the content of this thesis is the direct result of my own work and that any use of published or unpublished material in this thesis is fully and correctly referenced