One Method for Constructing Bent Functions of Class PS

CHANG Zu-ling; CHEN Lu-sheng; FU Fang-wei

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One Method for Constructing Bent Functions of Class PS

更新时间：2025-07-16

- One Method for Constructing Bent Functions of Class PS
- Acta Electronica Sinica Vol. 32, Issue 10, Pages: 1649-1653(2004)
- 作者机构：
  
  1. 北京邮电大学理学院,北京,100876
  2. 南开大学数学科学学院,天津,300071
  3. 北京邮电大学理学院北京,100876
  4. 南开大学数学科学学院天津,300071
- 作者简介：
- 基金信息：
- DOI：
  CLC： TN918.1
- Published：2004
- 稿件说明：
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CHANG Zu-ling, CHEN Lu-sheng, FU Fang-wei. One Method for Constructing Bent Functions of Class PS[J]. Acta Electronica Sinica, 2004, 32(10): 1649-1653.
DOI：

CHANG Zu-ling, CHEN Lu-sheng, FU Fang-wei. One Method for Constructing Bent Functions of Class PS[J]. Acta Electronica Sinica, 2004, 32(10): 1649-1653. DOI：

摘要

PS 类bent函数类是所有

(n/2)-1

或2

(n/2)-1

+1个F

的"不交的" n 2

维子空间的指示函数的模2和所组成的函数的集合.这些函数具有很好的代数结构并在密码学中有很多应用.如何来刻画 PS bent函数的代数范式一直是公开的难题.构造 PS 类bent函数关键在于如何将

划分为2

n/2

+1个 n 2

维子空间.本文给出一种划分的方法

从而构造出 PS 类bent函数

并给出了对应的代数范式.

Abstract

The class of PS bent functions is one interesting class of bent functions

they have good algebraic structure and have many applications in cryptography.They are also useful for studying the general structure of bent functions.Unfortunately

the construction of PS bent functions is theoretic

it is still an open problem to characterize the algebraic normal forms of PS bent functions.In this paper we study the properties of such functions

and one method to construct PS bent functions and the corresponding algebraic normal forms are provided.

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