ON BENT AND HYPER-BENT FUNCTIONS
Mathematics, Master Thesis, 2012
Prof. Dr. Alev Topuzoğlu (Thesis Supervisor), Prof. Dr. Henning Stichtenoth,
Assoc. Prof. Cem Güneri, Assoc. Prof. Erkay Savaş,
Asst. Prof. Kağan Kurşungöz
Date &Time: February 3rd, 2012 - 10:20
Place: FENS G029
Keywords: Bent functions, Hyper-bent functions, Kloosterman sums, Cubic sums, Dickson polynomials.
Bent functions are Boolean functions which have maximum possible nonlinearity i.e. maximal distance to the set of affine functions. They were introduced by Rothaus in 1976. In the last two decades, they have been studied widely due to their interesting combinatorial properties and their applications in cryptography. However the complete classification of bent functions has not been achieved yet. In 2001 Youssef and Gong introduced a subclass of bent functions which they called hyper-bent functions. The construction of hyper-bent functions is generally more difficult than the constructing bent functions. In this thesis we give a survey of recent constructions of infinite classes of bent and hyper-bent functions where the classification is obtained through the use of Kloosterman and cubic sums and Dickson polynomials.