A New 10-Variable Cubic Bent Function Outside the Completed Maiorana-McFarland Class

Abstract

In this letter, we present a construction of bent functions which generalizes a work of Zhang et al. in 2016. Based on that, we obtain a cubic bent function in 10 variables and prove that, it has no affine derivative and does not belong to the completed Maiorana-McFarland class, which is opposite to all 6/8-variable cubic bent functions as they are inside the completed Maiorana-McFarland class. This is the first time a theoretical proof is given to show that the cubic bent functions in 10 variables can be outside the completed Maiorana-McFarland class. Before that, only a sporadic example with such properties was known by computer search. We also show that our function is EA-inequivalent to that sporadic one.