4t-1元旋转对称2-弹性函数的构造

doi:10.11959/j.issn.1000-436x.2020213

通信学报 ›› 2020, Vol. 41 ›› Issue (11): 169-175.doi: 10.11959/j.issn.1000-436x.2020213

4t-1元旋转对称2-弹性函数的构造

杜蛟^1,²,刘春红³,庞善起^1,²

¹ 河南师范大学数学与信息科学学院，河南新乡 453007
² 河南师范大学大数据统计与优化控制河南省工程实验室，河南新乡 453007
³ 河南师范大学计算机与信息工程学院，河南新乡 453007

修回日期:2020-09-27 出版日期:2020-11-25 发布日期:2020-12-19
作者简介:杜蛟（1978- ），男，湖北英山人，博士，河南师范大学副教授、硕士生导师，主要研究方向为现代密码学中的布尔函数与序列设计、编码密码的数学理论|刘春红（1969- ），女，河南新乡人，博士，河南师范大学副教授、硕士生导师，主要研究方向为云计算安全、云计算资源管理与机器学习、网络空间安全等|庞善起（1965- ），男，河南卫辉人，博士，河南师范大学教授、博士生导师，主要研究方向为试验设计、量子信息与编码密码的数学理论
基金资助:
国家自然科学基金资助项目(11971004);河南省重点研发与推广专项（科技攻关）基金资助项目(202102210163);河南省高等教学改革研究与实践基金资助项目(2019SJGLX033Y);国家级大学生创新创业训练计划基金资助项目(202010476001)

Constructions of rotation symmetric 2-resilient functions with 4t_-1 number of variables

Jiao DU^1,²,Chunhong LIU³,Shanqi PANG^1,²

¹ College of Mathematics and Information Science,Henan Normal University,Xinxiang 453007,China
² Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control,Henan Normal University,Xinxiang 453007,China
³ College of Computer and Information Engineering,Henan Normal University,Xinxiang 453007,China

Revised:2020-09-27 Online:2020-11-25 Published:2020-12-19
Supported by:
The National Natural Science Foundation of China(11971004);The Science and Technology Research Project of Henan Province(202102210163);The Research and Practice Project of Higher Education Teaching Reform in Henan Province(2019SJGLX033Y);The National Undergraduate Innovation and Entrepreneurship Training Program(202010476001)

摘要/Abstract

摘要：

在特征为2的有限域F₂上的n维线性空间 $F_{2}^{n}$ 中，给出了旋转对称轨道的若干性质，定义了旋转对称轨道的数对00、01和11的分布矩阵，给出了一个2-弹性旋转对称函数的新刻画，通过修改已有的线性旋转对称弹性函数f₀(x)=x₁+x₂+…+x_n的支撑集（其中n=4t-1），给出了一个基于轨道交换技术的一类4t-1元旋转对称2-弹性函数的构造方法，并通过实例说明了所提构造方法的思想。

关键词: 密码学, 旋转对称函数, 正交表, 弹性函数, 支撑矩阵

Abstract:

Some properties of rotation symmetric orbits were proposed in n dimensional vector space over finite field of characteristic 2,a matrix on the distributions of number pairs such as 00,01 and 11 was defined,and a new characterization of 2-resilient rotation symmetric functions was introduced.Constructions of rotation symmetric 2-resilient Boolean functions with 4t-1 number of variables were presented by modifying the support of the linear rotation symmetric functions,such as f₀(x)=x₁+x₂+…+x_n,where n=4t-1.At last,an example was demonstrated to introduce the spirit of the proposed method to construct 2-resilient rotation symmetric functions with 4t-1 number of variables.

Key words: cryptography, rotation symmetric function, orthogonal array, resilient function, support table

中图分类号:

TN918.1

杜蛟,刘春红,庞善起. 4t-1元旋转对称2-弹性函数的构造[J]. 通信学报, 2020, 41(11): 169-175.

Jiao DU,Chunhong LIU,Shanqi PANG. Constructions of rotation symmetric 2-resilient functions with 4t_-1 number of variables[J]. Journal on Communications, 2020, 41(11): 169-175.

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4t-1元旋转对称2-弹性函数的构造

Constructions of rotation symmetric 2-resilient functions with 4t_-1 number of variables

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4t-1元旋转对称2-弹性函数的构造

Constructions of rotation symmetric 2-resilient functions with 4t-1 number of variables

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Constructions of rotation symmetric 2-resilient functions with 4t_-1 number of variables