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.
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.
Category / Keywords: foundations / Kloosterman sums, elliptic curves, Boolean functions, Walsh-Hadamard transform, bent functions Date: received 5 Jul 2011 Contact author: flori at enst fr Available formats: PDF | BibTeX Citation Version: 20110710:025438 (All versions of this report) Discussion forum: Show discussion | Start new discussion