On Almost Perfect Nonlinear Functions Over $mmb F_2^n$

Author

Berger, Thierry P. ; Canteaut, Anne ; Charpin, Pascale ; Laigle-Chapuy, Yann

Author_Institution

Faculte des Sci. de Limoges, XLIM, Limoges

Volume

Issue

fYear

2006

Firstpage

4160

Lastpage

4170

Abstract

We investigate some open problems on almost perfect nonlinear (APN) functions over a finite field of characteristic 2. We provide new characterizations of APN functions and of APN permutations by means of their component functions. We generalize some results of Nyberg (1994) and strengthen a conjecture on the upper bound of nonlinearity of APN functions. We also focus on the case of quadratic functions. We contribute to the current works on APN quadratic functions by proving that a large class of quadratic functions cannot be APN

Keywords

Boolean functions; cryptography; nonlinear functions; APN function; almost perfect nonlinear function; component function; quadratic function; Australia; Boolean functions; Cryptography; Electrical resistance measurement; Galois fields; Information theory; Linear code; Polynomials; Security; Upper bound; Almost bent function; almost perfect nonlinear (APN) function; permutation polynomial; power function;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2006.880036

Filename

1683931

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1167132