On the (non-) existence of APN (n,n) -functions of algebraic degree n

被引：0

作者：

Budaghyan, Lilya ^{[1
,2
]}

Carlet, Claude ^{[3
,4
,5
]}

Helleseth, Tor ^{[1
]}

Li, Nian ^{[1
]}

机构：

[1] Univ Bergen, Dept Informat, PB 7803, N-5020 Bergen, Norway

[2] ITMO Univ, St Petersburg, Russia

[3] Univ Paris 08, Dept Math, LAGA, St Denis 02, France

[4] Paris 13, St Denis 02, Reunion, France

[5] CNRS, St Denis 02, Reunion, France

来源：

2016 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY | 2016年

关键词：

almost perfect nonlinear; almost bent; Boolean function; differential uniformity; nonlinearity;

D O I：

暂无

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We study the problem of existence of APN functions of algebraic degree n over F(2)n. We characterize such functions by means of derivatives and power moments of the Walsh transform. We deduce some non-existence results which mean, in particular, that for most of the known APN functions F over F(2)n the function x(2n-1) + F(x) is not APN, and changing a value of F in a single point results in non-APN functions.

引用

页码：480 / 484

页数：5

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