Characterization and Construction of Generalized Bent Functions with Flexible Coefficients

Zhiyao YANG; Pinhui KE; Zhixiong CHEN

doi:10.1587/transfun.2021EAL2079

Characterization and Construction of Generalized Bent Functions with Flexible Coefficients

Zhiyao YANG, Pinhui KE, Zhixiong CHEN

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In 2017, Tang et al. provided a complete characterization of generalized bent functions from ℤ₂ⁿ to ℤ_q(q = 2^m) in terms of their component functions (IEEE Trans. Inf. Theory. vol.63, no.7, pp.4668-4674). In this letter, for a general even q, we aim to provide some characterizations and more constructions of generalized bent functions with flexible coefficients. Firstly, we present some sufficient conditions for a generalized Boolean function with at most three terms to be gbent. Based on these results, we give a positive answer to a remaining question proposed by Hodžić in 2015. We also prove that the sufficient conditions are also necessary in some special cases. However, these sufficient conditions whether they are also necessary, in general, is left as an open problem. Secondly, from a uniform point of view, we provide a secondary construction of gbent function, which includes several known constructions as special cases.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E105-A No.5 pp.887-891

Publication Date: 2022/05/01

Publicized: 2021/10/29

Online ISSN: 1745-1337

DOI: 10.1587/transfun.2021EAL2079

Type of Manuscript: LETTER

Category: Cryptography and Information Security

Authors

Zhiyao YANG
  Fujian Normal University
Pinhui KE
  Fujian Normal University
Zhixiong CHEN
  Putian University

Keyword

generalized bent function, bent function, flexible coefficients, Walsh-Hadamard transform, secondary construction

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Zhiyao YANG, Pinhui KE, Zhixiong CHEN, "Characterization and Construction of Generalized Bent Functions with Flexible Coefficients" in IEICE TRANSACTIONS on Fundamentals, vol. E105-A, no. 5, pp. 887-891, May 2022, doi: 10.1587/transfun.2021EAL2079.
Abstract: In 2017, Tang et al. provided a complete characterization of generalized bent functions from ℤ₂ⁿ to ℤ_q(q = 2^m) in terms of their component functions (IEEE Trans. Inf. Theory. vol.63, no.7, pp.4668-4674). In this letter, for a general even q, we aim to provide some characterizations and more constructions of generalized bent functions with flexible coefficients. Firstly, we present some sufficient conditions for a generalized Boolean function with at most three terms to be gbent. Based on these results, we give a positive answer to a remaining question proposed by Hodžić in 2015. We also prove that the sufficient conditions are also necessary in some special cases. However, these sufficient conditions whether they are also necessary, in general, is left as an open problem. Secondly, from a uniform point of view, we provide a secondary construction of gbent function, which includes several known constructions as special cases.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2021EAL2079/_p

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@ARTICLE{e105-a_5_887,
author={Zhiyao YANG, Pinhui KE, Zhixiong CHEN, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Characterization and Construction of Generalized Bent Functions with Flexible Coefficients},
year={2022},
volume={E105-A},
number={5},
pages={887-891},
abstract={In 2017, Tang et al. provided a complete characterization of generalized bent functions from ℤ₂ⁿ to ℤ_q(q = 2^m) in terms of their component functions (IEEE Trans. Inf. Theory. vol.63, no.7, pp.4668-4674). In this letter, for a general even q, we aim to provide some characterizations and more constructions of generalized bent functions with flexible coefficients. Firstly, we present some sufficient conditions for a generalized Boolean function with at most three terms to be gbent. Based on these results, we give a positive answer to a remaining question proposed by Hodžić in 2015. We also prove that the sufficient conditions are also necessary in some special cases. However, these sufficient conditions whether they are also necessary, in general, is left as an open problem. Secondly, from a uniform point of view, we provide a secondary construction of gbent function, which includes several known constructions as special cases.},
keywords={},
doi={10.1587/transfun.2021EAL2079},
ISSN={1745-1337},
month={May},}

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TY - JOUR
TI - Characterization and Construction of Generalized Bent Functions with Flexible Coefficients
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 887
EP - 891
AU - Zhiyao YANG
AU - Pinhui KE
AU - Zhixiong CHEN
PY - 2022
DO - 10.1587/transfun.2021EAL2079
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E105-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 2022
AB - In 2017, Tang et al. provided a complete characterization of generalized bent functions from ℤ₂ⁿ to ℤ_q(q = 2^m) in terms of their component functions (IEEE Trans. Inf. Theory. vol.63, no.7, pp.4668-4674). In this letter, for a general even q, we aim to provide some characterizations and more constructions of generalized bent functions with flexible coefficients. Firstly, we present some sufficient conditions for a generalized Boolean function with at most three terms to be gbent. Based on these results, we give a positive answer to a remaining question proposed by Hodžić in 2015. We also prove that the sufficient conditions are also necessary in some special cases. However, these sufficient conditions whether they are also necessary, in general, is left as an open problem. Secondly, from a uniform point of view, we provide a secondary construction of gbent function, which includes several known constructions as special cases.
ER -