FOURIER SPECTRA OF BINOMIAL APN FUNCTIONS

被引：10

作者：

Bracken, Carl ^{[1
]}

Byrne, Eimear ^{[1
]}

Markin, Nadya ^{[1
]}

McGuire, Gary ^{[1
]}

机构：

[1] Univ Coll Dublin, Sch Math Sci, Dublin 4, Ireland

来源：

SIAM JOURNAL ON DISCRETE MATHEMATICS | 2009年 / 23卷 / 02期

基金：

爱尔兰科学基金会;

关键词：

almost perfect nonlinear; APN; Fourier spectrum;

D O I：

10.1137/080717079

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we compute the Fourier spectra of some recently discovered binomial almost perfect nonlinear (APN) functions. One consequence of this is the determination of the nonlinearity of the functions, which measures their resistance to linear cryptanalysis. Another consequence is that certain error-correcting codes related to these functions have the same weight distribution as the 2-error-correcting Bose-Chaudury-Hocquenghem (BCH) code. Furthermore, for field extensions of F(2) of odd degree, our results provide an alternative proof of the APN property of the functions.

引用

页码：596 / 608

页数：13

共 15 条

[1]

[Anonymous], BOOLEAN MET IN PRESS

[2] New families of quadratic almost perfect nonlinear trinomials and multinomials [J].