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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 >2^{n-1}-2^{n/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

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

The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.

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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 >2^{n-1}-2^{n/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 >2^{n-1}-2^{n/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 >2^{n-1}-2^{n/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 -