A new class of monomial bent functions

We study the Boolean functions f :F2n F2, n = 6r, of the form f (x) = Tr(xd) with d = 22r + 2r + 1 and F2n . Our main result is the characterization of those for which f are bent. We show also that the set of these cubic bent functions contains a subset, which with the constantly zero function forms a vector space of dimension 2r over F2. Further we determine the Walsh spectra of some related quadratic functions, the derivatives of the functions f.

• Type: Journal
• Year: 2008
• Where: FFA
• Authors: Anne Canteaut, Pascale Charpin, Gohar M. M. Kyureghyan
• Keywords: Boolean Functions, Cubic Bent Functions, FFA 2008, Related Quadratic Functions