25 research outputs found
On the Fourier Spectra of the Infinite Families of Quadratic APN Functions
It is well known that a quadratic function defined on a finite field of odd
degree is almost bent (AB) if and only if it is almost perfect nonlinear (APN).
For the even degree case there is no apparent relationship between the values
in the Fourier spectrum of a function and the APN property. In this article we
compute the Fourier spectrum of the new quadranomial family of APN functions.
With this result, all known infinite families of APN functions now have their
Fourier spectra and hence their nonlinearities computed.Comment: 12 pages, submitted to Adavances in the Mathematics of communicatio
On Some Properties of Quadratic APN Functions of a Special Form
In a recent paper, it is shown that functions of the form
, where and 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
Bounds on the degree of APN polynomials The Case of
We prove that functions f:\f{2^m} \to \f{2^m} of the form
where is any non-affine polynomial are APN on at most a
finite number of fields \f{2^m}. Furthermore we prove that when the degree of
is less then 7 such functions are APN only if where these
functions are equivalent to
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
Non-Boolean almost perfect nonlinear functions on non-Abelian groups
The purpose of this paper is to present the extended definitions and
characterizations of the classical notions of APN and maximum nonlinear Boolean
functions to deal with the case of mappings from a finite group K to another
one N with the possibility that one or both groups are non-Abelian.Comment: 17 page