IEICE TRANSACTIONS on Fundamentals
Construction of Resilient Boolean and Vectorial Boolean Functions with High Nonlinearity
Summary :
Boolean functions and vectorial Boolean functions are the most important components of stream ciphers. Their cryptographic properties are crucial to the security of the underlying ciphers. And how to construct such functions with good cryptographic properties is a nice problem that worth to be investigated. In this paper, using two small nonlinear functions with t-1 resiliency, we provide a method on constructing t-resilient n variables Boolean functions with strictly almost optimal nonlinearity >2n-1-2n/2 and optimal algebraic degree n-t-1. Based on the method, we give another construction so that a large class of resilient vectorial Boolean functions can be obtained. It is shown that the vectorial Boolean functions also have strictly almost optimal nonlinearity and optimal algebraic degree.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E102-A No.10 pp.1397-1401
- Publication Date
- 2019/10/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E102.A.1397
- Type of Manuscript
- LETTER
- Category
- Cryptography and Information Security
Authors
Luyang LI
the Xi'an University of Posts and Telecommunications
Dong ZHENG
the Xi'an University of Posts and Telecommunications
Qinglan ZHAO
the Xi'an University of Posts and Telecommunications
Keyword
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Luyang LI, Dong ZHENG, Qinglan ZHAO, "Construction of Resilient Boolean and Vectorial Boolean Functions with High Nonlinearity" in IEICE TRANSACTIONS on Fundamentals,
vol. E102-A, no. 10, pp. 1397-1401, October 2019, doi: 10.1587/transfun.E102.A.1397.
Abstract: Boolean functions and vectorial Boolean functions are the most important components of stream ciphers. Their cryptographic properties are crucial to the security of the underlying ciphers. And how to construct such functions with good cryptographic properties is a nice problem that worth to be investigated. In this paper, using two small nonlinear functions with t-1 resiliency, we provide a method on constructing t-resilient n variables Boolean functions with strictly almost optimal nonlinearity >2n-1-2n/2 and optimal algebraic degree n-t-1. Based on the method, we give another construction so that a large class of resilient vectorial Boolean functions can be obtained. It is shown that the vectorial Boolean functions also have strictly almost optimal nonlinearity and optimal algebraic degree.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E102.A.1397/_p
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@ARTICLE{e102-a_10_1397,
author={Luyang LI, Dong ZHENG, Qinglan ZHAO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Construction of Resilient Boolean and Vectorial Boolean Functions with High Nonlinearity},
year={2019},
volume={E102-A},
number={10},
pages={1397-1401},
abstract={Boolean functions and vectorial Boolean functions are the most important components of stream ciphers. Their cryptographic properties are crucial to the security of the underlying ciphers. And how to construct such functions with good cryptographic properties is a nice problem that worth to be investigated. In this paper, using two small nonlinear functions with t-1 resiliency, we provide a method on constructing t-resilient n variables Boolean functions with strictly almost optimal nonlinearity >2n-1-2n/2 and optimal algebraic degree n-t-1. Based on the method, we give another construction so that a large class of resilient vectorial Boolean functions can be obtained. It is shown that the vectorial Boolean functions also have strictly almost optimal nonlinearity and optimal algebraic degree.},
keywords={},
doi={10.1587/transfun.E102.A.1397},
ISSN={1745-1337},
month={October},}
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TY - JOUR
TI - Construction of Resilient Boolean and Vectorial Boolean Functions with High Nonlinearity
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1397
EP - 1401
AU - Luyang LI
AU - Dong ZHENG
AU - Qinglan ZHAO
PY - 2019
DO - 10.1587/transfun.E102.A.1397
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E102-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 2019
AB - Boolean functions and vectorial Boolean functions are the most important components of stream ciphers. Their cryptographic properties are crucial to the security of the underlying ciphers. And how to construct such functions with good cryptographic properties is a nice problem that worth to be investigated. In this paper, using two small nonlinear functions with t-1 resiliency, we provide a method on constructing t-resilient n variables Boolean functions with strictly almost optimal nonlinearity >2n-1-2n/2 and optimal algebraic degree n-t-1. Based on the method, we give another construction so that a large class of resilient vectorial Boolean functions can be obtained. It is shown that the vectorial Boolean functions also have strictly almost optimal nonlinearity and optimal algebraic degree.
ER -
English
