Classes of Quadratic APN Trinomials and Hexanomials and Related Structures

A method for constructing differentially 4-uniform quadratic hexanomials has been recently introduced by J. Dillon. We give various generalizations of this method and we deduce the constructions of new infinite classes of almost perfect nonlinear quadratic trinomials and hexanomials from F22m to F22m . We check for m = 3 that some of these functions are CCZ-inequivalent to power functions. Keywords. Affine equivalence, Almost bent, Almost perfect nonlinear, CCZ-equivalence, Differential uniformity, Nonlinearity, S-box, Vectorial Boolean function.

• Type: Journal
• Year: 2008
• Where: TIT
• Authors: Lilya Budaghyan, Claude Carlet
• Keywords: 4-uniform Quadratic Hexanomials, Nonlinear Quadratic Trinomials, TIT 2008, Vectorial Boolean Function