Characterization and Properties of Bent-Negabent Functions

JIANG Niu; ZHAO Min; YANG Zhiyao; ZHUO Zepeng; CHEN Guolong

doi:10.1049/cje.2021.00.417

Volume 31 Issue 4

Jul. 2022

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JIANG Niu, ZHAO Min, YANG Zhiyao, et al., “Characterization and Properties of Bent-Negabent Functions,” Chinese Journal of Electronics, vol. 31, no. 4, pp. 786-792, 2022, doi: 10.1049/cje.2021.00.417

Citation:

JIANG Niu, ZHAO Min, YANG Zhiyao, et al., “Characterization and Properties of Bent-Negabent Functions,” Chinese Journal of Electronics, vol. 31, no. 4, pp. 786-792, 2022, doi: 10.1049/cje.2021.00.417

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Characterization and Properties of Bent-Negabent Functions

doi: 10.1049/cje.2021.00.417

JIANG Niu^1
,,
ZHAO Min¹,
YANG Zhiyao²,
ZHUO Zepeng^{1, 3
,},
CHEN Guolong^{1, 4}

1.
School of Mathematical Sciences, Huaibei Normal University, Huaibei 235000, China
2.
Fujian Provincial Key Laboratory of Network Security and Cryptology, Fujian Normal University, Fuzhou 350117, China
3.
School of Cyber Science, University of Science and Technology of China, Hefei 230027, China
4.
School of Computer Engineering, Bengbu University, Bengbu 233030, China

Funds: This work was supported by the Graduate Scientific Research Project of Anhui University (YJS20210464), the Key Research and Development Projects in Anhui Province (202004a05020043), the Natural Science Foundation of Anhui Higher Education Institutions of China (KJ2020ZD008), and the Graduate Innovation Fund of Huaibei Normal University (yc2021022)

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Author Bio:
is a graduate in the School of Mathematical Sciences, Huaibei Normal University. Her research interests include cryptography and information theory. (Email: 1401471403@qq.com)

(corresponding author) received the M.S. degree from Huaibei Normal University in 2007, and the Ph.D. degree from Xidian University in 2012. Since 2002, he has been with the School of Mathematical Science, Huaibei Normal University, where he is now a Professor. His research interests include cryptography and information theory. (Email: zzp781021@sohu.com)
Received Date: 2021-11-28
Accepted Date: 2022-03-21

Available Online: 2022-06-16

Publish Date: 2022-07-05

Abstract

Abstract

A further characterization of the bent-negabent functions is presented. Based on the concept of complete mapping polynomial, we provide a necessary and sufficient condition for a class of quadratic Boolean functions to be bent-negabent. A new characterization of negabent functions can be described by using the parity of Hamming weight. We further generalize the classical convolution theorem and give the nega-Hadamard transform of the composition of a Boolean function and a vectorial Boolean function. The nega-Hadamard transform of a generalized indirect sum is calculated by this composition method.
- Boolean function,
- Bent-negabent function,
- Walsh-Hadamard transform,
- Nega-Hadamard transform

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References(18)

References

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