摘要
在特征为2的有限域F2上的n维线性空间F2^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+…+xn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。
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 4 t-1 number of variables were presented by modifying the support of the linear rotation symmetric functions,such as f0(x)=x1+x2+…+xn,where n=4 t-1.At last,an example was demonstrated to introduce the spirit of the proposed method to construct 2-resilient rotation symmetric functions with 4 t-1 number of variables.
作者
杜蛟
刘春红
庞善起
DU Jiao;LIU Chunhong;PANG Shanqi(College of Mathematics and Information Science,Henan Normal University,Xinxiang 453007,China;Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control,Henan Normal University,Xinxiang 453007,China;College of Computer and Information Engineering,Henan Normal University,Xinxiang 453007,China)
出处
《通信学报》
EI
CSCD
北大核心
2020年第11期169-175,共7页
Journal on Communications
基金
国家自然科学基金资助项目(No.11971004)
河南省重点研发与推广专项(科技攻关)基金资助项目(No.202102210163)
河南省高等教学改革研究与实践基金资助项目(No.2019SJGLX033Y)
国家级大学生创新创业训练计划基金资助项目(No.202010476001)。
关键词
密码学
旋转对称函数
正交表
弹性函数
支撑矩阵
cryptography
rotation symmetric function
orthogonal array
resilient function
support table
