一类广义布尔函数的相关函数分析

doi:10.3969/j.issn.0372-2112.2019.12.014

电子学报 ›› 2019, Vol. 47 ›› Issue (12): 2556-2560.DOI: 10.3969/j.issn.0372-2112.2019.12.014

一类广义布尔函数的相关函数分析

杨志耀¹, 卓泽朋¹, 崇金凤^1,2

1. 淮北师范大学数学科学学院, 安徽淮北 235000;
2. 淮北师范大学信息学院, 安徽淮北 235000

收稿日期:2018-12-14 修回日期:2019-03-11 出版日期:2019-12-25
- 通讯作者:
- 卓泽朋
- 作者简介:
- 杨志耀 男,1995年6月出生,安徽淮南人.现为淮北师范大学数学科学学院硕士生,研究方向为密码学、信息安全.E-mail:1782884933@qq.com;崇金凤 女,1979年10月出生,安徽天长人,现为淮北师范大学副教授,研究方向为密码学、信息安全.
- 基金资助:
- 国家自然科学基金 (No.60573026，No.10101008）; 安徽省自然科学基金 (No.1608085MF143）; 安徽高校省级自然科学研究重点项目 (No.KJ2018A0678）; 淮北师范大学研究生创新基金 (No.ycx201901008）

Analysis of Correlation Function of a Class of Generalized Boolean Functions

YANG Zhi-yao¹, ZHUO Ze-peng¹, CHONG Jin-feng^1,2

1. School of Mathematical Sciences, Huaibei Normal University, Huaibei, Anhui 235000, China;
2. Information College, Huaibei Normal University, Huaibei, Anhui 235000, China

Received:2018-12-14 Revised:2019-03-11 Online:2019-12-25 Published:2019-12-25
- Corresponding author:
- ZHUO Ze-peng
- Supported by:
- National Natural Science Foundation of China (No.60573026, No.10101008); Natural Science Foundation of Anhui Province (No.1608085MF143); Key Program of Provincial Natural Science Research Project of Anhui Colleges and Universities, China (No.KJ2018A0678); Graduate Innovation Fund of Huaibei Normal University (No.ycx201901008)

摘要/Abstract

摘要： 基于广义布尔函数的理论研究，利用广义Walsh-Hadamard变换、相关函数以及平方和指标，分析了一类广义布尔函数的相关函数关系，得到这类广义布尔函数互相关函数以及自相关函数的关系；基于所得结果，利用自相关函数证明了一类广义Bent函数与Bent函数之间的关系.最后，给出一类广义布尔函数的平方和指标关系.

Abstract: Based on the theoretical study of the generalized Boolean functions. The correlation functions of a class of generalized Boolean functions are analyzed by using generalized Walsh-Hadamard transform,correlation functions and sum-of-squares and indicator, and the relationship between correlation functions and auto-correlation functions of such generalized Boolean functions are obtained. Based on the results obtained, the relationship between a class of generalized Bent functions and Bent functions is proved by using auto-correlation functions. Finally, the relationship between sum-of-squares and indicator of a class of generalized Boolean functions is given.

Key words: generalized Boolean functions, correlation functions, Bent functions, sum-of-squares and indicator, generalized Walsh-Hadamard transform

中图分类号:

TN918.1

杨志耀, 卓泽朋, 崇金凤. 一类广义布尔函数的相关函数分析[J]. 电子学报, 2019, 47(12): 2556-2560.

YANG Zhi-yao, ZHUO Ze-peng, CHONG Jin-feng . Analysis of Correlation Function of a Class of Generalized Boolean Functions[J]. Acta Electronica Sinica, 2019, 47(12): 2556-2560.

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一类广义布尔函数的相关函数分析

Analysis of Correlation Function of a Class of Generalized Boolean Functions

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