On the Walsh spectrum of a family of quadratic APN functions with five terms

被引：0

作者：

QU LongJiang ^{[1
]}

TAN Yin ^{[2
]}

LI Chao ^{[1
,3
]}

机构：

[1] Department of Mathematics and System Science,Science College,National University of Defense Technology

[2] Department of Electrical and Computer Engineering,University of Waterloo

来源：

ScienceChina(InformationSciences) | 2014年 / 57卷 / 02期

关键词：

APN function; Walsh spectrum; nonlinearity; quadratic polynomial; polynomial with no zeros;

D O I：

暂无

中图分类号：

O174.14 [多项式理论];

学科分类号：

070104 ;

摘要：

Recently,a family of quadratic APN functions was demonstrated by Bracken et al.to exist over F22k with k even and 3 k.This family of APN functions was firstly proposed by Budaghyan et al.and they exist provided the existence of a quadratic polynomial of the type x2s+1+cx2s+c2k x+1 with no zeros in F22k.Bracken et al.constructed such polynomials when k is even and 3 k.In this paper,we show that such polynomials exist for all even integers k.As a result,the APN functions over F22k exist for all even k.Furthermore,the Walsh spectra of these APN functions is shown to be the same as the one of the Gold APN functions.This gives a positive answer to one conjecture.

引用

页码：271 / 277

页数：7

共 5 条

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