Kloosterman sums have recently become the focus of much research, most notably due to their applications in cryptography and their relations to coding theory.#R##N##R##N#Very recently Mesnager has showed that the value 4 of binary Kloosterman sums gives rise to several infinite classes of bent functions, hyper-bent functions and semi-bent functions in even dimension.#R##N##R##N#In this paper we analyze the different strategies used to find zeros of binary Kloosterman sums to develop and implement an algorithm to find the value 4 of such sums. We then present experimental results showing that the value 4 of binary Kloosterman sums gives rise to bent functions for small dimensions, a case with no mathematical solution so far.
['Jean-Pierre Flori', 'Sihem Mesnager', 'Gérard D. Cohen']
Binary kloosterman sums with value 4