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This is a free offprint provided to the author by the publisher. Copyright restrictions may apply. Contemporary Mathematics
 

Summary: This is a free offprint provided to the author by the publisher. Copyright restrictions may apply.
Contemporary Mathematics
Differentially 4-uniform functions
Yves Aubry and Fran¸cois Rodier
Abstract. We give a geometric characterization of vectorial Boolean func-
tions with differential uniformity 4. This enables us to give a necessary
condition on the degree of the base field for a function of degree 2r - 1 to be
differentially 4-uniform.
1. Introduction
We are interested in vectorial Boolean functions from the F2-vectorial space Fm
2
to itself in m variables, viewed as polynomial functions f : F2m - F2m over the
field F2m in one variable of degree at most 2m
-1. For a function f : F2m - F2m ,
we consider, after K. Nyberg (see [16]), its differential uniformity
(f) = max
=0,
{x F2m | f(x + ) + f(x) = }.
This is clearly a strictly positive even integer.
Functions f with small (f) have applications in cryptography (see [16]). Such

  

Source: Aubry, Yves - Institut de Mathématiques de Toulon, Université du Sud Toulon -Var

 

Collections: Mathematics