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

作　　者：杜蛟[1,2] 刘春红[3] 庞善起[1,2] 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)

机构地区：[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

出　　处：《通信学报》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)。

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.

关 键 词：密码学 旋转对称函数 正交表 弹性函数 支撑矩阵 

分 类 号：TN918.1[电子电信—通信与信息系统]