On the Nonlinearity of Exponential Welch Costas Functions

被引：18

作者：

Drakakis, Konstantinos ^{[1
,2
]}

Requena, Veronica ^{[3
]}

McGuire, Gary ^{[2
,4
]}

机构：

[1] Natl Univ Ireland Univ Coll Dublin, Sch Elect Elect & Mech Engn, Dublin 4, Ireland

[2] UCD CASL, Dublin, Ireland

[3] Univ Alicante, Dept Ciencia Computacio & Intel Ligencia Artifici, E-03080 Alicante, Spain

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

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2010年 / 56卷 / 03期

基金：

爱尔兰科学基金会;

关键词：

Almost perfect nonlinear (APN) functions; Welch Costas permutations; nonlinearity; class number; Walsh transform; CRYPTANALYSIS;

D O I：

10.1109/TIT.2009.2039164

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We study the nonlinearity of the Exponential Welch Costas functions, using the Fourier Transform on. These functions have been proposed for use in nonbinary cryptosystems. High nonlinearity is required to ensure resistance to linear cryptanalysis. We prove some properties of the nonlinearity of these functions, and we suggest a plausible connection of the nonlinearity to the class number of a quadratic field.

引用

页码：1230 / 1238

页数：9

共 26 条

[1]

Baignères T, 2007, LECT NOTES COMPUT SC, V4876, P184

[2]

BIHAM E, 1991, LECT NOTES COMPUT SC, V537, P2

[3]

Borevich Z.I., 1966, Number Theory

[4]

Bracken C, 2007, LECT NOTES COMPUT SC, V4851, P72

[5]

CAMION P, 1996, LECT NOTES COMPUTER, V1109, P372

[6] Highly nonlinear mappings [J].

Carlet, C ;

Ding, CS .

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

[7] A STUDY OF A CLASS OF DETECTION WAVEFORMS HAVING NEARLY IDEAL RANGE-DOPPLER AMBIGUITY PROPERTIES [J].

COSTAS, JP .

PROCEEDINGS OF THE IEEE, 1984, 72 (08) :996-1009

[8]

DOBBERTIN H, 1995, LECT NOTES COMPUTER, V1008, P61

[9]

DRAKAKIS K, DISCR APPL IN PRESS

[10] Results of the enumeration of Costas arrays of order 27 [J].

Drakakis, Konstantinos ;

Rickard, Scott ;

Beard, James K. ;

Caballero, Rodrigo ;

Iorio, Francesco ;

O'Brien, Gareth ;

Walsh, John .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2008, 54 (10) :4684-4687

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