计算机工程与应用 ›› 2011, Vol. 47 ›› Issue (11): 84-85.

• 网络、通信、安全 • 上一篇    下一篇

一阶相关免疫对称函数的构造

崇金凤1,曹 浩2,刘竹林3   

  1. 1.淮北煤炭师范学院 数学科学学院,安徽 淮北 235000
    2.安徽科技学院 理学院,安徽 凤阳 233100
    3.石家庄信息工程职业学院 软件工程系,石家庄 050035
  • 收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2011-04-11 发布日期:2011-04-11

Constructions of first order symmetric correlation-immune functions

CHONG Jinfeng1,CAO Hao2,LIU Zhulin3   

  1. 1.School of Mathematical Science,Huaibei Coal Industry Teachers College,Huaibei,Anhui 235000,China
    2.College of Science,Anhui Science and Technology University,Fengyang,Anhui 233100,China
    3.Department of Software Engineering,Shijiazhuang Information Engineering Vocational College,Shijiazhuan 050035,China
  • Received:1900-01-01 Revised:1900-01-01 Online:2011-04-11 Published:2011-04-11

摘要:

n元一阶相关免疫对称函数的构造等价于方程∑Cin-1xi=∑Cin-1xi+1在二元域上的求解。通过求解与其等价的方程C0n-1y0+∑(Cin-1-Ci-1n-1)yi=0构造了一阶相关免疫对称函数,并在两种情形下给出了具体的构造和计数。

关键词: 布尔函数, 一阶相关免疫函数, 对称函数

Abstract: The construction of symmetric correlation-immune functions with n variables is equivalent to the solution in the binary field for the eqution Cin-1xi=∑Cin-1xi+1.When solving the equivalent equation C0n-1y0+∑(Cin-1-Ci-1n-1)yi=0 of the linear eqution,first order symmetric corrrelation-immune function is constructed.The lower bound of enumeration of symmetric correlation-immune functions with first order is also given in two cases.

Key words: Boolean function, first order correlation-immune function, symmetric function