IEICE TRANSACTIONS on Fundamentals
Characterization and Construction of Generalized Bent Functions with Flexible Coefficients
Summary :
In 2017, Tang et al. provided a complete characterization of generalized bent functions from ℤ2n to ℤq(q = 2m) 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
Latest Issue
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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 ℤq(q = 2m) 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 ℤq(q = 2m) 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},}
Copy
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 ℤq(q = 2m) 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 -
English
