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The group of automorphisms of the set of self-dual bent functions. / Kutsenko, Aleksandr.

In: Cryptography and Communications, Vol. 12, No. 5, 01.09.2020, p. 881-898.

Research output: Contribution to journal › Article › peer-review

Harvard

Kutsenko, A 2020, 'The group of automorphisms of the set of self-dual bent functions', Cryptography and Communications, vol. 12, no. 5, pp. 881-898. https://doi.org/10.1007/s12095-020-00438-y

APA

Kutsenko, A. (2020). The group of automorphisms of the set of self-dual bent functions. Cryptography and Communications, 12(5), 881-898. https://doi.org/10.1007/s12095-020-00438-y

Vancouver

Kutsenko A. The group of automorphisms of the set of self-dual bent functions. Cryptography and Communications. 2020 Sept 1;12(5):881-898. doi: 10.1007/s12095-020-00438-y

Author

Kutsenko, Aleksandr. / The group of automorphisms of the set of self-dual bent functions. In: Cryptography and Communications. 2020 ; Vol. 12, No. 5. pp. 881-898.

BibTeX

@article{400cb704b32d4de69db2892e14ec841f,
title = "The group of automorphisms of the set of self-dual bent functions",
abstract = "A bent function is a Boolean function in even number of variables which is on the maximal Hamming distance from the set of affine Boolean functions. It is called self-dual if it coincides with its dual. It is called anti-self-dual if it is equal to the negation of its dual. A mapping of the set of all Boolean functions in n variables to itself is said to be isometric if it preserves the Hamming distance. In this paper we study isometric mappings which preserve self-duality and anti-self-duality of a Boolean bent function. The complete characterization of these mappings is obtained for n≥ 4. Based on this result, the set of isometric mappings which preserve the Rayleigh quotient of the Sylvester Hadamard matrix, is characterized. The Rayleigh quotient measures the Hamming distance between bent function and its dual, so as a corollary, all isometric mappings which preserve bentness and the Hamming distance between bent function and its dual are described.",
keywords = "Boolean functions, Isometric mappings, Self-dual bent, The group of automorphisms, The Rayleigh quotient",
author = "Aleksandr Kutsenko",
note = "Publisher Copyright: {\textcopyright} 2020, Springer Science+Business Media, LLC, part of Springer Nature. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2020",
month = sep,
day = "1",
doi = "10.1007/s12095-020-00438-y",
language = "English",
volume = "12",
pages = "881--898",
journal = "Cryptography and Communications",
issn = "1936-2447",
publisher = "Springer Publishing Company",
number = "5",

}

RIS

TY - JOUR

T1 - The group of automorphisms of the set of self-dual bent functions

AU - Kutsenko, Aleksandr

N1 - Publisher Copyright: © 2020, Springer Science+Business Media, LLC, part of Springer Nature. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/9/1

Y1 - 2020/9/1

N2 - A bent function is a Boolean function in even number of variables which is on the maximal Hamming distance from the set of affine Boolean functions. It is called self-dual if it coincides with its dual. It is called anti-self-dual if it is equal to the negation of its dual. A mapping of the set of all Boolean functions in n variables to itself is said to be isometric if it preserves the Hamming distance. In this paper we study isometric mappings which preserve self-duality and anti-self-duality of a Boolean bent function. The complete characterization of these mappings is obtained for n≥ 4. Based on this result, the set of isometric mappings which preserve the Rayleigh quotient of the Sylvester Hadamard matrix, is characterized. The Rayleigh quotient measures the Hamming distance between bent function and its dual, so as a corollary, all isometric mappings which preserve bentness and the Hamming distance between bent function and its dual are described.

AB - A bent function is a Boolean function in even number of variables which is on the maximal Hamming distance from the set of affine Boolean functions. It is called self-dual if it coincides with its dual. It is called anti-self-dual if it is equal to the negation of its dual. A mapping of the set of all Boolean functions in n variables to itself is said to be isometric if it preserves the Hamming distance. In this paper we study isometric mappings which preserve self-duality and anti-self-duality of a Boolean bent function. The complete characterization of these mappings is obtained for n≥ 4. Based on this result, the set of isometric mappings which preserve the Rayleigh quotient of the Sylvester Hadamard matrix, is characterized. The Rayleigh quotient measures the Hamming distance between bent function and its dual, so as a corollary, all isometric mappings which preserve bentness and the Hamming distance between bent function and its dual are described.

KW - Boolean functions

KW - Isometric mappings

KW - Self-dual bent

KW - The group of automorphisms

KW - The Rayleigh quotient

UR - http://www.scopus.com/inward/record.url?scp=85086386091&partnerID=8YFLogxK

U2 - 10.1007/s12095-020-00438-y

DO - 10.1007/s12095-020-00438-y

M3 - Article

AN - SCOPUS:85086386091

VL - 12

SP - 881

EP - 898

JO - Cryptography and Communications

JF - Cryptography and Communications

SN - 1936-2447

IS - 5

ER -

ID: 24518805