IEICE TRANSACTIONS on Fundamentals
A Novel Construction of 2-Resilient Rotation Symmetric Boolean Functions
Summary :
In this paper, by using the properties of the cyclic Hadamard matrices of order 4t, an infinite class of (4t-1)-variable 2-resilient rotation symmetric Boolean functions is constructed, and the nonlinearity of the constructed functions are also studied. To the best of our knowledge, this is the first class of direct constructions of 2-resilient rotation symmetric Boolean functions. The spirit of this method is different from the known methods depending on the solutions of an equation system proposed by Du Jiao, et al. Several situations are examined, as the direct corollaries, three classes of (4t-1)-variable 2-resilient rotation symmetric Boolean functions are proposed based on the corresponding sequences, such as m sequences, Legendre sequences, and twin primes sequences respectively.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E105-A No.2 pp.93-99
- Publication Date
- 2022/02/01
- Publicized
- 2021/08/03
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2021EAP1037
- Type of Manuscript
- PAPER
- Category
- Cryptography and Information Security
Authors
Jiao DU
Henan Normal University
Shaojing FU
National University of Defense Technology
Longjiang QU
National University of Defense Technology
Chao LI
National University of Defense Technology
Tianyin WANG
Luoyang Normal University,Guilin University of Electronic Technology
Shanqi PANG
Henan Normal University
Keyword
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Jiao DU, Shaojing FU, Longjiang QU, Chao LI, Tianyin WANG, Shanqi PANG, "A Novel Construction of 2-Resilient Rotation Symmetric Boolean Functions" in IEICE TRANSACTIONS on Fundamentals,
vol. E105-A, no. 2, pp. 93-99, February 2022, doi: 10.1587/transfun.2021EAP1037.
Abstract: In this paper, by using the properties of the cyclic Hadamard matrices of order 4t, an infinite class of (4t-1)-variable 2-resilient rotation symmetric Boolean functions is constructed, and the nonlinearity of the constructed functions are also studied. To the best of our knowledge, this is the first class of direct constructions of 2-resilient rotation symmetric Boolean functions. The spirit of this method is different from the known methods depending on the solutions of an equation system proposed by Du Jiao, et al. Several situations are examined, as the direct corollaries, three classes of (4t-1)-variable 2-resilient rotation symmetric Boolean functions are proposed based on the corresponding sequences, such as m sequences, Legendre sequences, and twin primes sequences respectively.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2021EAP1037/_p
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@ARTICLE{e105-a_2_93,
author={Jiao DU, Shaojing FU, Longjiang QU, Chao LI, Tianyin WANG, Shanqi PANG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Novel Construction of 2-Resilient Rotation Symmetric Boolean Functions},
year={2022},
volume={E105-A},
number={2},
pages={93-99},
abstract={In this paper, by using the properties of the cyclic Hadamard matrices of order 4t, an infinite class of (4t-1)-variable 2-resilient rotation symmetric Boolean functions is constructed, and the nonlinearity of the constructed functions are also studied. To the best of our knowledge, this is the first class of direct constructions of 2-resilient rotation symmetric Boolean functions. The spirit of this method is different from the known methods depending on the solutions of an equation system proposed by Du Jiao, et al. Several situations are examined, as the direct corollaries, three classes of (4t-1)-variable 2-resilient rotation symmetric Boolean functions are proposed based on the corresponding sequences, such as m sequences, Legendre sequences, and twin primes sequences respectively.},
keywords={},
doi={10.1587/transfun.2021EAP1037},
ISSN={1745-1337},
month={February},}
Copy
TY - JOUR
TI - A Novel Construction of 2-Resilient Rotation Symmetric Boolean Functions
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 93
EP - 99
AU - Jiao DU
AU - Shaojing FU
AU - Longjiang QU
AU - Chao LI
AU - Tianyin WANG
AU - Shanqi PANG
PY - 2022
DO - 10.1587/transfun.2021EAP1037
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E105-A
IS - 2
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - February 2022
AB - In this paper, by using the properties of the cyclic Hadamard matrices of order 4t, an infinite class of (4t-1)-variable 2-resilient rotation symmetric Boolean functions is constructed, and the nonlinearity of the constructed functions are also studied. To the best of our knowledge, this is the first class of direct constructions of 2-resilient rotation symmetric Boolean functions. The spirit of this method is different from the known methods depending on the solutions of an equation system proposed by Du Jiao, et al. Several situations are examined, as the direct corollaries, three classes of (4t-1)-variable 2-resilient rotation symmetric Boolean functions are proposed based on the corresponding sequences, such as m sequences, Legendre sequences, and twin primes sequences respectively.
ER -
English
