Bent Functions
نویسنده
چکیده
Bent functions have connections into various areas of mathematics and computer science which makes them an interesting object to study. This thesis is meant as a comprehensive study summarizing many of the results published in the last 40 years. In the first chapter we will motivate the definition of bent functions before we discuss some basic properties in chapter 2. This is done with a special emphasis on the investigation of restrictions of bent functions to hyperspaces. The obtained results will be used in chapter 3 to deduce connections of bent functions to various other mathematical structures. Though most results are well-known, we present some new, compressed proofs. Chapter 4 presents four different constructions of bent functions. Besides the two classical methods proposed by Maiorana/McFarland and Dillon we study two recent constructions by Seberry and Carlet, the latter of which leads to some useful general results. The last chapter focuses on the investigation special classes of bent functions. I would like to thank everyone who bore with me during my work on this thesis. I’m particularly grateful to my family for their support not only in the last few weeks. They have been backing me up throughout all my time at university. Moreover, I would like to thankfully mention Prof. Dempwolff for his advise. I enjoyed our discussions we have had over the last years about mathematical as well as nonmathematical topics a lot.
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