303 research outputs found
A New Family of Perfect Nonlinear Binomials
We prove that the binomials
define perfect nonlinear mappings in for an appropriate choice of the integer and . We show that these binomials are inequivalent to known perfect nonlinear monomials. As a consequence we obtain new commutative semifields for and odd
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
A new family of semifields with 2 parameters
A new family of commutative semifields with two parameters is presented. Its
left and middle nucleus are both determined. Furthermore, we prove that for any
different pairs of parameters, these semifields are not isotopic. It is also
shown that, for some special parameters, one semifield in this family can lead
to two inequivalent planar functions. Finally, using similar construction, new
APN functions are given
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
On Equivalence of Known Families of APN Functions in Small Dimensions
In this extended abstract, we computationally check and list the
CCZ-inequivalent APN functions from infinite families on for n
from 6 to 11. These functions are selected with simplest coefficients from
CCZ-inequivalent classes. This work can simplify checking CCZ-equivalence
between any APN function and infinite APN families.Comment: This paper is already in "PROCEEDING OF THE 20TH CONFERENCE OF FRUCT
ASSOCIATION
Generalization of a class of APN binomials to Gold-like functions
In 2008 Budaghyan, Carlet and Leander generalized a known instance of an APN function over the finite field F212 and constructed two new infinite families of APN binomials over the finite field F2n , one for n divisible by 3, and one for n divisible by 4. By relaxing conditions, the family of APN binomials for n divisible by 3 was generalized to a family of differentially 2t -uniform functions in 2012 by Bracken, Tan and Tan; in this sense, the binomials behave in the same way as the Gold functions. In this paper, we show that when relaxing conditions on the APN binomials for n divisible by 4, they also behave in the same way as the Gold function x2s+1 (with s and n not necessarily coprime). As a counterexample, we also show that a family of APN quadrinomials obtained as a generalization of a known APN instance over F210 cannot be generalized to functions with 2t -to-1 derivatives by relaxing conditions in a similar way.acceptedVersio
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