A new class of monomial bent functions

Anne Canteaut (1) , Pascale Charpin (1) , Gohar Kyureghyan (2)

1 SECRET - Security, Cryptology and Transmissions
2 OVGU - Otto-von-Guericke-Universität Magdeburg = Otto-von-Guericke University [Magdeburg]

We study the Boolean functions fλ :F2n →F2, n = 6r, of the form f (x) = Tr(λxd ) with d = 22r + 2r + 1 and λ ∈ F2n . Our main result is the characterization of those λ for which fλ 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 fλ.

Domaines: Cryptographie et sécurité [cs.CR]; Théorie de l'information [cs.IT]; Théorie de l'information et codage [math.IT]

Anne Canteaut, Pascale Charpin, Gohar Kyureghyan. A new class of monomial bent functions. Finite Fields and Their Applications, 2008, 14 (1), pp.221-241. ⟨10.1016/j.ffa.2007.02.004⟩. ⟨hal-00328631⟩