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In this paper, by using the properties of the cyclic Hadamard matrices of order 4*t*, an infinite class of (4*t*-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 (4*t*-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

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

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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 4*t*, an infinite class of (4*t*-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 (4*t*-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 4*t*, an infinite class of (4*t*-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 (4*t*-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},}

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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 4*t*, an infinite class of (4*t*-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 (4*t*-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 -