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

共 37 条

[31]

Janwa H., 1993, Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. 10th International Symposium, AAECC-10 Proceedings, P180

[32] WEIGHT ENUMERATORS FOR SEVERAL CLASSES OF SUBCODES OF 2ND ORDER BINARY REED-MULLER CODES [J].

KASAMI, T .

INFORMATION AND CONTROL, 1971, 18 (04) :369-&

[33] Crooked maps in F2n [J].

Kyureghyan, Gohar M. .

FINITE FIELDS AND THEIR APPLICATIONS, 2007, 13 (03) :713-726

[34] THE WEIGHTS OF THE ORTHOGONALS OF THE EXTENDED QUADRATIC BINARY GOPPA CODES [J].

LACHAUD, G ;

WOLFMANN, J .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1990, 36 (03) :686-692

[35]

Lidl R., 1997, Finite Fields

[36]

Nyberg K., 1994, Advances in Cryptology - EUROCRYPT '93. Workshop on the Theory and Application of Cryptographic Techniques Proceedings, P55

[37]

ZHA Z, 2008, NEW FAMILY PER UNPUB

← 1 2 3 4 →