IEICE TRANSACTIONS on Fundamentals
Further Results on Autocorrelation of Vectorial Boolean Functions
Summary :
In this paper, we study the properties of the sum-of-squares indicator of vectorial Boolean functions. Firstly, we give the upper bound of $sum_{uin mathbb{F}_2^n,vin mathbb{F}_2^m}mathcal{W}_F^3(u,v)$. Secondly, based on the Walsh-Hadamard transform, we give a secondary construction of vectorial bent functions. Further, three kinds of sum-of-squares indicators of vectorial Boolean functions are defined by autocorrelation function and the lower and upper bounds of the sum-of-squares indicators are derived. Finally, we study the sum-of-squares indicators with respect to several equivalence relations, and get the sum-of-squares indicator which have the best cryptographic properties.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E106-A No.10 pp.1305-1310
- Publication Date
- 2023/10/01
- Publicized
- 2023/03/27
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2022EAP1096
- Type of Manuscript
- PAPER
- Category
- Cryptography and Information Security
Authors
Zeyao LI
Huaibei Normal University
Niu JIANG
Huaibei Normal University
Zepeng ZHUO
Huaibei Normal University
Keyword
Latest Issue
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Zeyao LI, Niu JIANG, Zepeng ZHUO, "Further Results on Autocorrelation of Vectorial Boolean Functions" in IEICE TRANSACTIONS on Fundamentals,
vol. E106-A, no. 10, pp. 1305-1310, October 2023, doi: 10.1587/transfun.2022EAP1096.
Abstract: In this paper, we study the properties of the sum-of-squares indicator of vectorial Boolean functions. Firstly, we give the upper bound of $sum_{uin mathbb{F}_2^n,vin mathbb{F}_2^m}mathcal{W}_F^3(u,v)$. Secondly, based on the Walsh-Hadamard transform, we give a secondary construction of vectorial bent functions. Further, three kinds of sum-of-squares indicators of vectorial Boolean functions are defined by autocorrelation function and the lower and upper bounds of the sum-of-squares indicators are derived. Finally, we study the sum-of-squares indicators with respect to several equivalence relations, and get the sum-of-squares indicator which have the best cryptographic properties.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2022EAP1096/_p
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@ARTICLE{e106-a_10_1305,
author={Zeyao LI, Niu JIANG, Zepeng ZHUO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Further Results on Autocorrelation of Vectorial Boolean Functions},
year={2023},
volume={E106-A},
number={10},
pages={1305-1310},
abstract={In this paper, we study the properties of the sum-of-squares indicator of vectorial Boolean functions. Firstly, we give the upper bound of $sum_{uin mathbb{F}_2^n,vin mathbb{F}_2^m}mathcal{W}_F^3(u,v)$. Secondly, based on the Walsh-Hadamard transform, we give a secondary construction of vectorial bent functions. Further, three kinds of sum-of-squares indicators of vectorial Boolean functions are defined by autocorrelation function and the lower and upper bounds of the sum-of-squares indicators are derived. Finally, we study the sum-of-squares indicators with respect to several equivalence relations, and get the sum-of-squares indicator which have the best cryptographic properties.},
keywords={},
doi={10.1587/transfun.2022EAP1096},
ISSN={1745-1337},
month={October},}
Copy
TY - JOUR
TI - Further Results on Autocorrelation of Vectorial Boolean Functions
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1305
EP - 1310
AU - Zeyao LI
AU - Niu JIANG
AU - Zepeng ZHUO
PY - 2023
DO - 10.1587/transfun.2022EAP1096
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E106-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 2023
AB - In this paper, we study the properties of the sum-of-squares indicator of vectorial Boolean functions. Firstly, we give the upper bound of $sum_{uin mathbb{F}_2^n,vin mathbb{F}_2^m}mathcal{W}_F^3(u,v)$. Secondly, based on the Walsh-Hadamard transform, we give a secondary construction of vectorial bent functions. Further, three kinds of sum-of-squares indicators of vectorial Boolean functions are defined by autocorrelation function and the lower and upper bounds of the sum-of-squares indicators are derived. Finally, we study the sum-of-squares indicators with respect to several equivalence relations, and get the sum-of-squares indicator which have the best cryptographic properties.
ER -
English
