Constructions of first order symmetric correlation-immune functions

Computer Engineering and Applications ›› 2011, Vol. 47 ›› Issue (11): 84-85.

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Constructions of first order symmetric correlation-immune functions

CHONG Jinfeng1，CAO Hao2，LIU Zhulin3

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

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.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

Abstract

Abstract: The construction of symmetric correlation-immune functions with n variables is equivalent to the solution in the binary field for the eqution Cⁱ_n-1x_i=∑Cⁱ_n-1x_i+1.When solving the equivalent equation C⁰_n-1y₀+∑(Cⁱ_n-1-C^i-1_n-1)y_i=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

摘要：

n元一阶相关免疫对称函数的构造等价于方程∑Cⁱ_n-1x_i=∑Cⁱ_n-1x_i+1在二元域上的求解。通过求解与其等价的方程C⁰_n-1y₀+∑(Cⁱ_n-1-C^i-1_n-1)y_i=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

CHONG Jinfeng1，CAO Hao2，LIU Zhulin3. Constructions of first order symmetric correlation-immune functions[J]. Computer Engineering and Applications, 2011, 47(11): 84-85.

崇金凤1，曹浩2，刘竹林3. 一阶相关免疫对称函数的构造[J]. 计算机工程与应用, 2011, 47(11): 84-85.

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Constructions of first order symmetric correlation-immune functions

一阶相关免疫对称函数的构造

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