Generic Constructions of (Boolean and Vectorial) Bent Functions and Their Consequences

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成果类型：

期刊论文

作者：

Li, Yanjun;Kan, Haibin;Mesnager, Sihem;Peng, Jie;Tan, Chik How;...

通讯作者：

Mesnager, S

作者机构：

[Li, Yanjun] Anhui Univ Finance & Econ, Inst Stat & Appl Math, Bengbu 233030, Anhui, Peoples R China.

[Peng, Jie; Li, Yanjun] Shanghai Normal Univ, Math & Sci Coll, Shanghai 200234, Peoples R China.

[Kan, Haibin] Fudan Univ, Sch Comp Sci, Key Lab Intelligent Informat Proc, Shanghai 200433, Peoples R China.

[Mesnager, S; Mesnager, Sihem] Univ Paris VIII, Dept Math, F-93526 St Denis, France.

[Mesnager, Sihem] Univ Sorbonne Paris Nord, LAGA, Lab Geometry Anal & Applicat, CNRS,UMR 7539, F-93430 Villetaneuse, France.

通讯机构：

[Mesnager, S ] U

Univ Paris VIII, Dept Math, F-93526 St Denis, France.

语种：

英文

关键词：

Codes;Ciphers;Boolean functions;Roads;Telecommunications;Technological innovation;Robustness;Boolean function;vectorial function;Boolean bent function;idempotent bent function;dual;self-dual bent function;vectorial bent function

期刊：

IEEE Transactions on Information Theory

ISSN：

0018-9448

年：

2022

卷：

期：

页码：

2735-2751

DOI：

10.1109/TIT.2022.3140180

基金类别：

10.13039/501100012166-National Key Research and Development Program of China (Grant Number: 2019YFB2101703) 10.13039/501100001809-National Natural Science Foundation of China (Grant Number: 61972258 and U19A2066) Innovation Action Plan of Shanghai Science and Technology (Grant Number: 20222420800 and 20511102200) 10.13039/501100015956-Special Project for Research and Development in Key areas of Guangdong Province (Grant Number: 2020B0101090001) Scientific Research Fund of Hunan Provincial Education Department (Grant Number: 19B485) 10.13039/100007836-Open Research Program of Shanghai Key Lab of Intelligent Information Processing (Grant Number: IIPL201902)

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本校为其他机构

院系归属：

数理学院

摘要：

This article is devoted to Boolean and vectorial bent functions and their duals. Our ultimate objective is to increase such functions' corpus by designing new ones covering many previous bent functions' constructions. To this end, we provide several new infinite families of bent functions, including idempotent bent functions of any algebraic degree, bent functions in univariate trace form, and self-dual bent functions. Those bent functions are of great theoretical and practical interest because of their special structures and relationship with ...

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Generic Constructions of (Boolean and Vectorial) Bent Functions and Their Consequences

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