Properties of Bent Functions in the Truth Domain

Martin Lukac, Claudio Moraga, Michitaka Kameyama

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper we study bent functions in the truth vector domain. While in general bent functions are defined on the Walsh basis [-1,1] we look on their properties and classification in the standard Boolean basis [0,1]. We show that applying the Welsh transform to Boolean functions of n variables in the truth domain, results in a classification that allows to rank bent functions. We investigate the classification of bent vs non bent functions using standard machine learning and compare the performance difference. Finally we extend our search for efficient classification criteria to functions with smaller amount of variables and show the amount of classification possible.

Original languageEnglish
Title of host publicationProceedings of the International Conference on Information and Digital Technologies 2019, IDT 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages304-310
Number of pages7
ISBN (Electronic)9781728114019
DOIs
Publication statusPublished - Jun 2019
Event2019 International Conference on Information and Digital Technologies, IDT 2019 - Zilina, Slovakia
Duration: Jun 25 2019Jun 27 2019

Publication series

NameProceedings of the International Conference on Information and Digital Technologies 2019, IDT 2019

Conference

Conference2019 International Conference on Information and Digital Technologies, IDT 2019
CountrySlovakia
CityZilina
Period6/25/196/27/19

Fingerprint

Bent Function
Boolean functions
Boolean Functions
Learning systems
Machine Learning
Truth
Transform

Keywords

  • Bent Functions
  • Classification
  • Truth Domain

ASJC Scopus subject areas

  • Strategy and Management
  • Management of Technology and Innovation
  • Computer Networks and Communications
  • Decision Sciences (miscellaneous)
  • Information Systems and Management
  • Control and Optimization

Cite this

Lukac, M., Moraga, C., & Kameyama, M. (2019). Properties of Bent Functions in the Truth Domain. In Proceedings of the International Conference on Information and Digital Technologies 2019, IDT 2019 (pp. 304-310). [8813751] (Proceedings of the International Conference on Information and Digital Technologies 2019, IDT 2019). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/DT.2019.8813751

Properties of Bent Functions in the Truth Domain. / Lukac, Martin; Moraga, Claudio; Kameyama, Michitaka.

Proceedings of the International Conference on Information and Digital Technologies 2019, IDT 2019. Institute of Electrical and Electronics Engineers Inc., 2019. p. 304-310 8813751 (Proceedings of the International Conference on Information and Digital Technologies 2019, IDT 2019).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Lukac, M, Moraga, C & Kameyama, M 2019, Properties of Bent Functions in the Truth Domain. in Proceedings of the International Conference on Information and Digital Technologies 2019, IDT 2019., 8813751, Proceedings of the International Conference on Information and Digital Technologies 2019, IDT 2019, Institute of Electrical and Electronics Engineers Inc., pp. 304-310, 2019 International Conference on Information and Digital Technologies, IDT 2019, Zilina, Slovakia, 6/25/19. https://doi.org/10.1109/DT.2019.8813751
Lukac M, Moraga C, Kameyama M. Properties of Bent Functions in the Truth Domain. In Proceedings of the International Conference on Information and Digital Technologies 2019, IDT 2019. Institute of Electrical and Electronics Engineers Inc. 2019. p. 304-310. 8813751. (Proceedings of the International Conference on Information and Digital Technologies 2019, IDT 2019). https://doi.org/10.1109/DT.2019.8813751
Lukac, Martin ; Moraga, Claudio ; Kameyama, Michitaka. / Properties of Bent Functions in the Truth Domain. Proceedings of the International Conference on Information and Digital Technologies 2019, IDT 2019. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 304-310 (Proceedings of the International Conference on Information and Digital Technologies 2019, IDT 2019).
@inproceedings{31a94935e06b4a2b9f30de1f8c886eba,
title = "Properties of Bent Functions in the Truth Domain",
abstract = "In this paper we study bent functions in the truth vector domain. While in general bent functions are defined on the Walsh basis [-1,1] we look on their properties and classification in the standard Boolean basis [0,1]. We show that applying the Welsh transform to Boolean functions of n variables in the truth domain, results in a classification that allows to rank bent functions. We investigate the classification of bent vs non bent functions using standard machine learning and compare the performance difference. Finally we extend our search for efficient classification criteria to functions with smaller amount of variables and show the amount of classification possible.",
keywords = "Bent Functions, Classification, Truth Domain",
author = "Martin Lukac and Claudio Moraga and Michitaka Kameyama",
year = "2019",
month = "6",
doi = "10.1109/DT.2019.8813751",
language = "English",
series = "Proceedings of the International Conference on Information and Digital Technologies 2019, IDT 2019",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "304--310",
booktitle = "Proceedings of the International Conference on Information and Digital Technologies 2019, IDT 2019",
address = "United States",

}

TY - GEN

T1 - Properties of Bent Functions in the Truth Domain

AU - Lukac, Martin

AU - Moraga, Claudio

AU - Kameyama, Michitaka

PY - 2019/6

Y1 - 2019/6

N2 - In this paper we study bent functions in the truth vector domain. While in general bent functions are defined on the Walsh basis [-1,1] we look on their properties and classification in the standard Boolean basis [0,1]. We show that applying the Welsh transform to Boolean functions of n variables in the truth domain, results in a classification that allows to rank bent functions. We investigate the classification of bent vs non bent functions using standard machine learning and compare the performance difference. Finally we extend our search for efficient classification criteria to functions with smaller amount of variables and show the amount of classification possible.

AB - In this paper we study bent functions in the truth vector domain. While in general bent functions are defined on the Walsh basis [-1,1] we look on their properties and classification in the standard Boolean basis [0,1]. We show that applying the Welsh transform to Boolean functions of n variables in the truth domain, results in a classification that allows to rank bent functions. We investigate the classification of bent vs non bent functions using standard machine learning and compare the performance difference. Finally we extend our search for efficient classification criteria to functions with smaller amount of variables and show the amount of classification possible.

KW - Bent Functions

KW - Classification

KW - Truth Domain

UR - http://www.scopus.com/inward/record.url?scp=85072531377&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85072531377&partnerID=8YFLogxK

U2 - 10.1109/DT.2019.8813751

DO - 10.1109/DT.2019.8813751

M3 - Conference contribution

AN - SCOPUS:85072531377

T3 - Proceedings of the International Conference on Information and Digital Technologies 2019, IDT 2019

SP - 304

EP - 310

BT - Proceedings of the International Conference on Information and Digital Technologies 2019, IDT 2019

PB - Institute of Electrical and Electronics Engineers Inc.

ER -