Differentially 4-uniform functions

We give a geometric characterization of vectorial boolean functions with differential uniformity less or equal to 4

On Some Properties of Quadratic APN Functions of a Special Form

In a recent paper, it is shown that functions of the form $L_1(x^3)+L_2(x^9)$, where $L_1$ and $L_2$ are linear, are a good source for construction of new infinite families of APN functions. In the present work we study necessary and sufficient conditions for such functions to be APN

A new large class of functions not APN infinitely often

In this paper, we show that there is no vectorial Boolean function of degree 4e, with e satisfaying certain conditions, which is APN over infinitely many extensions of its field of definition. It is a new step in the proof of the conjecture of Aubry, McGuire and Rodie

A Generalization of APN Functions for Odd Characteristic

Almost perfect nonlinear (APN) functions on finite fields of characteristic two have been studied by many researchers. Such functions have useful properties and applications in cryptography, finite geometries and so on. However APN functions on finite fields of odd characteristic do not satisfy desired properties. In this paper, we modify the definition of APN function in the case of odd characteristic, and study its properties

Class of Quadratic Almost Bent Functions That Is EA-Inequivalent to Permutations

The permutation relationship for the almost bent (AB) functions in the finite field is a significant issue. Li and Wang proved that a class of AB functions with algebraic degree 3 is extended affine- (EA-) inequivalent to any permutation. This study proves that another class of AB functions, which was developed in 2009, is EA-inequivalent to any permutation. This particular AB function is the first known quadratic class EA-inequivalent to permutation