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

• 学术论文 • 上一篇    下一篇

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. 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-feng1,2   

  1. 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: 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.

关键词: 广义布尔函数, 相关函数, Bent函数, 平方和指标, 广义Walsh-Hadamard变换

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

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