IEICE TRANSACTIONS on Fundamentals
Highly Nonlinear Resilient Functions without Linear Structures
Summary :
In this paper, we provide several methods to construct nonlinear resilient functions with multiple good cryptographic properties, including high nonlinearity, high algebraic degree, and non-existence of linear structures. Firstly, we present an improvement on a known construction of resilient S-boxes such that the nonlinearity and the algebraic degree will become higher in some cases. Then a construction of highly nonlinear t-resilient Boolean functions without linear structures is given, whose algebraic degree achieves n-t-1, which is optimal for n-variable t-resilient Boolean functions. Furthermore, we construct a class of resilient S-boxes without linear structures, which possesses the highest nonlinearity and algebraic degree among all currently known constructions.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E97-A No.6 pp.1405-1417
- Publication Date
- 2014/06/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E97.A.1405
- Type of Manuscript
- PAPER
- Category
- Cryptography and Information Security
Authors
Jian LIU
Nankai University
Lusheng CHEN
Nankai University
Xuan GUANG
Nankai University
Keyword
Latest Issue
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Jian LIU, Lusheng CHEN, Xuan GUANG, "Highly Nonlinear Resilient Functions without Linear Structures" in IEICE TRANSACTIONS on Fundamentals,
vol. E97-A, no. 6, pp. 1405-1417, June 2014, doi: 10.1587/transfun.E97.A.1405.
Abstract: In this paper, we provide several methods to construct nonlinear resilient functions with multiple good cryptographic properties, including high nonlinearity, high algebraic degree, and non-existence of linear structures. Firstly, we present an improvement on a known construction of resilient S-boxes such that the nonlinearity and the algebraic degree will become higher in some cases. Then a construction of highly nonlinear t-resilient Boolean functions without linear structures is given, whose algebraic degree achieves n-t-1, which is optimal for n-variable t-resilient Boolean functions. Furthermore, we construct a class of resilient S-boxes without linear structures, which possesses the highest nonlinearity and algebraic degree among all currently known constructions.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E97.A.1405/_p
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@ARTICLE{e97-a_6_1405,
author={Jian LIU, Lusheng CHEN, Xuan GUANG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Highly Nonlinear Resilient Functions without Linear Structures},
year={2014},
volume={E97-A},
number={6},
pages={1405-1417},
abstract={In this paper, we provide several methods to construct nonlinear resilient functions with multiple good cryptographic properties, including high nonlinearity, high algebraic degree, and non-existence of linear structures. Firstly, we present an improvement on a known construction of resilient S-boxes such that the nonlinearity and the algebraic degree will become higher in some cases. Then a construction of highly nonlinear t-resilient Boolean functions without linear structures is given, whose algebraic degree achieves n-t-1, which is optimal for n-variable t-resilient Boolean functions. Furthermore, we construct a class of resilient S-boxes without linear structures, which possesses the highest nonlinearity and algebraic degree among all currently known constructions.},
keywords={},
doi={10.1587/transfun.E97.A.1405},
ISSN={1745-1337},
month={June},}
Copy
TY - JOUR
TI - Highly Nonlinear Resilient Functions without Linear Structures
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1405
EP - 1417
AU - Jian LIU
AU - Lusheng CHEN
AU - Xuan GUANG
PY - 2014
DO - 10.1587/transfun.E97.A.1405
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E97-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 2014
AB - In this paper, we provide several methods to construct nonlinear resilient functions with multiple good cryptographic properties, including high nonlinearity, high algebraic degree, and non-existence of linear structures. Firstly, we present an improvement on a known construction of resilient S-boxes such that the nonlinearity and the algebraic degree will become higher in some cases. Then a construction of highly nonlinear t-resilient Boolean functions without linear structures is given, whose algebraic degree achieves n-t-1, which is optimal for n-variable t-resilient Boolean functions. Furthermore, we construct a class of resilient S-boxes without linear structures, which possesses the highest nonlinearity and algebraic degree among all currently known constructions.
ER -
English
