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A quadratic part of a bent function can be any. / Tokareva, N. N.

в: Siberian Electronic Mathematical Reports, Том 19, № 1, 2022, стр. 342-347.

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Harvard

Tokareva, NN 2022, 'A quadratic part of a bent function can be any', Siberian Electronic Mathematical Reports, Том. 19, № 1, стр. 342-347. https://doi.org/10.33048/semi.2022.19.029

APA

Tokareva, N. N. (2022). A quadratic part of a bent function can be any. Siberian Electronic Mathematical Reports, 19(1), 342-347. https://doi.org/10.33048/semi.2022.19.029

Vancouver

Tokareva NN. A quadratic part of a bent function can be any. Siberian Electronic Mathematical Reports. 2022;19(1):342-347. doi: 10.33048/semi.2022.19.029

Author

Tokareva, N. N. / A quadratic part of a bent function can be any. в: Siberian Electronic Mathematical Reports. 2022 ; Том 19, № 1. стр. 342-347.

BibTeX

@article{1478a4188abe43758d32658d0ff7a247,
title = "A quadratic part of a bent function can be any",
abstract = "Boolean functions in n variables that are on the maximal possible Hamming distance from all affine Boolean functions in n variables are called bent functions (n is even). They are intensively studied since sixties of XX century in relation to applications in cryptography and discrete mathematics. Often, bent functions are represented in their algebraic normal form (ANF). It is well known that the linear part of ANF of a bent function can be arbitrary. In this note we prove that a quadratic part of a bent function can be arbitrary too.",
keywords = "bent function, Boolean function, homogeneous function, linear function, quadratic function",
author = "Tokareva, {N. N.}",
note = "Funding Information: Tokareva, N.N., A quadratic part of a bent function can be any. {\textcopyright} 2022 Tokareva N.N. The work is supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2022-281 with the Ministry of Science and Higher Education of the Russian Federation. Received March, 13, 2022, published June, 29, 2022. Publisher Copyright: {\textcopyright} 2022. Tokareva N.N. All Rights Reserved.",
year = "2022",
doi = "10.33048/semi.2022.19.029",
language = "English",
volume = "19",
pages = "342--347",
journal = "Сибирские электронные математические известия",
issn = "1813-3304",
publisher = "Sobolev Institute of Mathematics",
number = "1",

}

RIS

TY - JOUR

T1 - A quadratic part of a bent function can be any

AU - Tokareva, N. N.

N1 - Funding Information: Tokareva, N.N., A quadratic part of a bent function can be any. © 2022 Tokareva N.N. The work is supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2022-281 with the Ministry of Science and Higher Education of the Russian Federation. Received March, 13, 2022, published June, 29, 2022. Publisher Copyright: © 2022. Tokareva N.N. All Rights Reserved.

PY - 2022

Y1 - 2022

N2 - Boolean functions in n variables that are on the maximal possible Hamming distance from all affine Boolean functions in n variables are called bent functions (n is even). They are intensively studied since sixties of XX century in relation to applications in cryptography and discrete mathematics. Often, bent functions are represented in their algebraic normal form (ANF). It is well known that the linear part of ANF of a bent function can be arbitrary. In this note we prove that a quadratic part of a bent function can be arbitrary too.

AB - Boolean functions in n variables that are on the maximal possible Hamming distance from all affine Boolean functions in n variables are called bent functions (n is even). They are intensively studied since sixties of XX century in relation to applications in cryptography and discrete mathematics. Often, bent functions are represented in their algebraic normal form (ANF). It is well known that the linear part of ANF of a bent function can be arbitrary. In this note we prove that a quadratic part of a bent function can be arbitrary too.

KW - bent function

KW - Boolean function

KW - homogeneous function

KW - linear function

KW - quadratic function

UR - http://www.scopus.com/inward/record.url?scp=85134549309&partnerID=8YFLogxK

U2 - 10.33048/semi.2022.19.029

DO - 10.33048/semi.2022.19.029

M3 - Article

AN - SCOPUS:85134549309

VL - 19

SP - 342

EP - 347

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

IS - 1

ER -

ID: 36745394