DocumentCode :
1167132
Title :
On Almost Perfect Nonlinear Functions Over 
Author :
Berger, Thierry P. ; Canteaut, Anne ; Charpin, Pascale ; Laigle-Chapuy, Yann
Author_Institution :
Faculte des Sci. de Limoges, XLIM, Limoges
Volume :
52
Issue :
9
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 :
