On the classification of APN functions up to dimension five

被引：57
|
作者：
Brinkmann, Marcus [1 ]
Leander, Gregor [2 ]
机构：
[1] Ruhr Univ Bochum, Bochum, Germany
[2] Univ Toulon & Var, La Garde, France
来源：
DESIGNS CODES AND CRYPTOGRAPHY | 2008年 / 49卷 / 1-3期
关键词：
APN functions; backtrack; affine equivalence; CCZ equivalence; affine subspaces;
D O I：
10.1007/s10623-008-9194-6
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We classify the almost perfect nonlinear (APN) functions in dimensions 4 and 5 up to affine and CCZ equivalence using backtrack programming and give a partial model for the complexity of such a search. In particular, we demonstrate that up to dimension 5 any APN function is CCZ equivalent to a power function, while it is well known that in dimensions 4 and 5 there exist APN functions which are not extended affine (EA) equivalent to any power function. We further calculate the total number of APN functions up to dimension 5 and present a new CCZ equivalence class of APN functions in dimension 6.
引用
收藏
页码：273 / 288
页数：16
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