A NEW ALMOST PERFECT NONLINEAR FUNCTION WHICH IS NOT QUADRATIC

被引：106

作者：

Edel, Yves ^{[1
]}

Pott, Alexander ^{[2
]}

机构：

[1] Univ Ghent, Dept Pure Math & Comp Algebra, B-9000 Ghent, Belgium

[2] Otto VonGuericke Univ Magdegurg, Fac Math, D-39016 Magdeburg, Germany

来源：

ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2009年 / 3卷 / 01期

关键词：

Almost perfect nonlinear; equivalence of functions; Walsh spectrum; almost bent; CROSS-CORRELATION; DIFFERENCE SETS; POWER FUNCTIONS; CODES; TRINOMIALS; SEQUENCES; BINOMIALS;

D O I：

10.3934/amc.2009.3.59

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Following an example in [12], we show how to change one coordinate function of an almost perfect nonlinear (APN) function in order to obtain new examples. It turns out that this is a very powerful method to construct new APN functions. In particular, we show that our approach can be used to construct a "non-quadratic" APN function. This new example is in remarkable contrast to all recently constructed functions which have all been quadratic. An equivalent function has been found independently by Brinkmann and Leander [8]. However, they claimed that their function is CCZ equivalent to a quadratic one. In this paper we give several reasons why this new function is not equivalent to a quadratic one.

引用

页码：59 / 81

页数：23

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