On the Δ-equivalence of Boolean functions

被引：1

作者：

Logachev, OlegA ^{[1
]}

Fedorov, Sergey N. ^{[1
]}

Yashchenko, Valerii V. ^{[1
]}

机构：

[1] Lomonosov Univ, Informat Secur Inst, Moscow, Russia

来源：

DISCRETE MATHEMATICS AND APPLICATIONS | 2020年 / 30卷 / 02期

关键词：

Boolean function; discrete Fourier transform; Walsh-Hadamard transform; cross-correlation; autocorrelation; nonlinearity; curvature; correlation immunity; propagation criterion; global avalanche characteristics;

D O I：

10.1515/dma-2020-0009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A new equivalence relation on the set of Boolean functions is introduced: functions are declared to be Delta-equivalent if their autocorrelation functions are equal. It turns out that this classification agrees well with the cryptographic properties of Boolean functions: for functions belonging to the same Delta-equivalence class a number of their cryptographic characteristics do coincide. For example, all bent-functions (of a fixed number of variables) make up one class.

引用

页码：93 / 101

页数：9

共 12 条

[1] On some measures of nonlinearity for Boolean functions [J].

Alekseev, E. K. .

PRIKLADNAYA DISKRETNAYA MATEMATIKA, 2011, 12 (02) :5-16

[2] Classification of correlation-immune and minimal correlation-immune Boolean functions of 4 and 5 variables [J].

Alekseev, Evgeniy K. ;

Karelina, Ekaterina K. .

DISCRETE MATHEMATICS AND APPLICATIONS, 2015, 25 (04) :193-202

[3]

Cheremushkin A. V., 2005, MATEMATICHESKIE VOPR, P261

[4] The sum of modules of Walsh coefficients of Boolean functions [J].

Jimenez, Reynier A. De la Cruz ;

Kamlovskiy, Oleg V. .

DISCRETE MATHEMATICS AND APPLICATIONS, 2016, 26 (05) :259-272

[5]

[Камловский Олег Витальевич Kamlovskii Oleg Vital'evich], 2017, [Математические вопросы криптографии, Matematicheskie voprosy kriptografii], V8, P75, DOI 10.4213/mvk240

[6]

Logachev O. A., 2011, BOOLEAN FUNCTIONS CO

[7] Boolean functions as points on the hypersphere in the Euclidean space [J].

Logachev, Oleg A. ;

Fedorov, Sergey N. ;

Yashchenko, Valerii V. .

DISCRETE MATHEMATICS AND APPLICATIONS, 2019, 29 (02) :89-101

[8]

MacWilliams E. J., 1977, THEORY ERROR CORRE 1

[9]

O'Donnell R, 2014, ANAL BOOLEAN FUNCTIO, DOI DOI 10.1017/CBO9781139814782

[10] BENT FUNCTIONS [J].

ROTHAUS, OS .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 1976, 20 (03) :300-305

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