一类密码函数的构造与分析

doi:10.3969/j.issn.1000-436x.2013.04.012

通信学报 ›› 2013, Vol. 34 ›› Issue (4): 106-113.doi: 10.3969/j.issn.1000-436x.2013.04.012

一类密码函数的构造与分析

欧智慧¹,赵亚群^1,²,李旭¹

¹ 信息工程大学四院，河南郑州450002
² 数学工程与先进计算国家重点实验室，河南郑州450002

出版日期:2013-04-25 发布日期:2017-07-17
基金资助:
国家自然科学基金资助项目;国家高技术研究发展计划（“863”计划）基金资助项目

Construction and analysis of one class of cryptographic functions

Zhi-hui OU¹,Ya-qun ZHAO^1,²,Xu LI¹

¹ The Fourth Institute,The Information Engineering University,Zhengzhou 450002,China
² State Key Laboratory of Mathematical Engineering and Advanced Computing,Zhengzhou 450002,China

Online:2013-04-25 Published:2017-07-17
Supported by:
The National Natural Science Foundation of China;The National High Technology Research and Development Program of China (863 Program)

摘要/Abstract

摘要：

利用t+ 1个n元布尔函数(称为基函数)级联构造了一类n+t元布尔函数G(x,y)，并给出了G(x,y)的Walsh循环谱和自相关系数。通过Krawtchouk多项式与Krawtchouk矩阵对G(x,y)和基函数的关系进行了研究。分析了G(x,y)的密码学性质：相关免疫性、扩散性和代数免疫性。特别地，当t=2时，分析了G(x,y)与基函数的具体关系。另外，一般化该构造方法构造了一类多输出布尔函数，给出了该类多输出布尔函数的广义Walsh循环谱，进而分析了该类多输出布尔函数的相关免疫性和代数免疫性。

关键词: 密码函数, Plateaued函数, Krawtchouk矩阵, 代数免疫性

Abstract:

A novel class of n+t -variable Boolean functions G (x,y) through adding t variables while concatenating t+ 1 Boolean functions (called basic function) was constructed and the Walsh spectrum and autocorrelation coefficient of G(x,y)were given.The relationship between G(x,y)and basic functions by Krawtchouk polynomial and Krawtchouk matrix was studied.Moreover,their cryptographic properties:correlation immunity,propagation and algebraic immunity were investigated.Specially,the detailed relationship between G (x,y) and basic functions when t= 2 was analyzed.In additional,a novel class of multioutput Boolean functions by generalizing the method was constructed and the general Walsh spectrum of the class of multioutput Boolean functions was proposed.Correlation immunity and algebraic immunity of the class of multioutput Boolean functions were analyzed.

Key words: cryptographic functions, Plateaued function, Krawtchouk matrix, algebraic immunity

欧智慧,赵亚群,李旭. 一类密码函数的构造与分析[J]. 通信学报, 2013, 34(4): 106-113.

Zhi-hui OU,Ya-qun ZHAO,Xu LI. Construction and analysis of one class of cryptographic functions[J]. Journal on Communications, 2013, 34(4): 106-113.

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一类密码函数的构造与分析

Construction and analysis of one class of cryptographic functions

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