Constructions of Three Classes of Semi-Bent Functions

HE Ye-feng; MA Wen-ping

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Constructions of Three Classes of Semi-Bent Functions

更新时间：2025-07-16

- Constructions of Three Classes of Semi-Bent Functions
- Acta Electronica Sinica Vol. 39, Issue 1, Pages: 233-236(2011)
- 作者机构：
  
  1. 西安电子科技大学计算机网络与信息安全教育部重点实验室,陕西,西安,710071
  2. 西安邮电学院通信与信息工程学院,陕西,西安,710121
  3. 西安电子科技大学计算机网络与信息安全教育部重点实验室陕西西安,710071
  4. 西安邮电学院通信与信息工程学院陕西西安,710121
- 作者简介：
- 基金信息：
- DOI：
  CLC： TN918.1
- Published：2011
- 稿件说明：
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HE Ye-feng, MA Wen-ping. Constructions of Three Classes of Semi-Bent Functions[J]. Acta Electronica Sinica, 2011, 39(1): 233-236.
DOI：

HE Ye-feng, MA Wen-ping. Constructions of Three Classes of Semi-Bent Functions[J]. Acta Electronica Sinica, 2011, 39(1): 233-236. DOI：

摘要

Semi-bent函数是一种具有高非线性度的布尔函数

它们在密码和通信领域中都有重要的应用价值.本文构造了三类由迹函数表示的semi-bent函数.证明了当限制某些参数的取值范围时

这些新构造函数的semi-bent性与Kloosterman和密切相关.并且证明了每一类新构造的含有

个变元的semi-bent函数

都存在一个semi-bent函数的子类

它们的代数次数是

/2.利用Kloosterman和的零点

也给出了小域上semi-bent函数的例子.

Abstract

Semi-bent functions are a kind of Boolean functions with high nonlinearity.They have important applications in cryptography and communications.This paper gives three classes of semi-bent functions represented by trace.It is shown that the semi-bentness of the new functions is closely related to Kloosterman sums when the values of some parameters are restricted.It is also proved there exists a subclass of semi-bent functions with degree

/2 in each class of the new semi-bent functions on

variables.Several examples of the semi-bent functions in a small field are given by using the zeros of some Kloosterman sums.

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