NON-BOOLEAN ALMOST PERFECT NONLINEAR FUNCTIONS ON NON-ABELIAN GROUPS

被引：19

作者：

Poinsot, Laurent ^{[1
]}

Pott, Alexander ^{[2
]}

机构：

[1] Univ Paris 13, Inst Galilee, LIPN UMR CNRS 7030, F-93430 Villetaneuse, France

[2] Otto VonGuericke Univ Magdegurg, Dept Math, D-39106 Magdeburg, Germany

来源：

INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE | 2011年 / 22卷 / 06期

关键词：

Almost perfect nonlinear; bent function; maximal nonlinear; HADAMARD DIFFERENCE SETS; TRINOMIALS; BINOMIALS;

D O I：

10.1142/S0129054111008751

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

The purpose of this paper is to present extended definitions and characterizations of the classical notions of APN and maximum nonlinear Boolean functions to deal with the case of mappings from a finite group K to another one N with the possibility that one or both groups are non-Abelian.

引用

页码：1351 / 1367

页数：17

共 26 条

[1] New semifields, PN and APN functions [J].

Bierbrauer, Juergen .

DESIGNS CODES AND CRYPTOGRAPHY, 2010, 54 (03) :189-200

[2]

Biham E., 1991, Journal of Cryptology, V4, P3, DOI 10.1007/BF00630563

[3] The Magma algebra system .1. The user language [J].

Bosma, W ;

Cannon, J ;

Playoust, C .

JOURNAL OF SYMBOLIC COMPUTATION, 1997, 24 (3-4) :235-265

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

Bracken, Carl ;

Byrne, Eimear ;

Markin, Nadya ;

McGuire, Gary .

FINITE FIELDS AND THEIR APPLICATIONS, 2008, 14 (03) :703-714

[5]

Budaghyan L., CRYPTOGRAPH IN PRESS

[6]

Budaghyan L, 2008, LECT NOTES COMPUT SC, V5203, P403, DOI 10.1007/978-3-540-85912-3_35

[7] Two classes of quadratic APN binomials inequivalent to power functions [J].

Budaghyan, Lilya ;

Carlet, Claude ;

Leander, Gregor .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2008, 54 (09) :4218-4229

[8] Classes of quadratic APN trinomials and hexanomials and related structures [J].

Budaghyan, Lilya ;

Carlet, Claude .

IEEE Transactions on Information Theory, 2008, 54 (05) :2354-2357

[9] Highly nonlinear mappings [J].

Carlet, C ;

Ding, CS .

JOURNAL OF COMPLEXITY, 2004, 20 (2-3) :205-244

[10]

Carlet C., 2010, BOOLEAN MODELS METHO, P398, DOI DOI 10.1017/CBO9780511780448.012

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