Some results on Boolean functions with two order algebraic immunity

Computer Engineering and Applications ›› 2011, Vol. 47 ›› Issue (30): 68-71.

• 研究、探讨 • Previous Articles Next Articles

Some results on Boolean functions with two order algebraic immunity

DU Jiao1，2，WANG Shouyin1，WANG Rui3

1.Department of Mathematics，Xinxiang University，Xinxiang，Henan 453003，China
2.State Key Laboratory of Networking and Switching Technology，Beijing University of Posts and Telecommunications，Beijing 100876，China
3.Faculty of Science，Henan University of Technology，Zhengzhou 450001，China

Received:1900-01-01 Revised:1900-01-01 Online:2011-10-21 Published:2011-10-21

关于二阶代数免疫布尔函数的几个结果

杜蛟1，2，王守印1，王蕊3

1.新乡学院数学系，河南新乡 453003
2北京邮电大学网络与交换技术国家重点实验室，北京 100876
3河南工业大学理学院，郑州 450001

Abstract

Abstract: The properties of Boolean functions such as resiliency order，algebraic immunity，algebraic，nonlinearity，and the relationships among them are still small.The satured Best Boolean functions are important in stream ciphers，in this paper，it is demonstrated that the 5-variable satured Best Boolean functions are 2-order algebraic immunity，which are given in lemma 8 of reference [1]，based on this result，it is improved.

Key words: Boolean function, satured Best functions, annihilator, algebraic immunity

摘要： 关于布尔函数的代数免疫性与弹性、代数次数、非线性度之间的关系的结果至今仍然很少，饱和最优布尔函数在流密码领域具有较高的理论价值，通过计算证明文献[1]中命题8给出的5元最优布尔函数都是2阶代数免疫函数，并在此基础上对这个结果做了进一步推广。

关键词: 布尔函数, 饱和最优函数, 零化子, 代数免疫

DU Jiao1，2，WANG Shouyin1，WANG Rui3. Some results on Boolean functions with two order algebraic immunity[J]. Computer Engineering and Applications, 2011, 47(30): 68-71.

杜蛟1，2，王守印1，王蕊3. 关于二阶代数免疫布尔函数的几个结果[J]. 计算机工程与应用, 2011, 47(30): 68-71.

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Some results on Boolean functions with two order algebraic immunity

关于二阶代数免疫布尔函数的几个结果

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