A Combinatorial Condition and Boolean Functions with Optimal Algebraic Immunity

被引：0

作者：

JIN Qingfang ^{[1
]}

LIU Zhuojun ^{[2
]}

WU Baofeng ^{[3
]}

ZHANG Xiaoming ^{[2
]}

机构：

[1] Key Laboratory of System and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences

[2] Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences

[3] State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences

来源：

Journal of Systems Science & Complexity | 2015年 / 28卷 / 03期

关键词：

Algebraic degree; algebraic immunity; balancedness; Bent function; Boolean function; nonlinearity;

D O I：

暂无

中图分类号：

O174 [函数论];

学科分类号：

070104 ;

摘要：

This paper first proposes an infinite class of 2k-variable Boolean functions with high nonlinearity and high algebraic degree. Then an infinite class of balanced Boolean functions are proposed by modifying the above Boolean functions. This class of balanced Boolean functions have optimal algebraic degree and high nonlinearity. Both classes have optimal algebraic immunity based on a general combinatorial conjecture.

引用

页码：725 / 742

页数：18

共 4 条

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[2] Further properties of several classes of Boolean functions with optimum algebraic immunity
Carlet, Claude
Zeng, Xiangyong
Li, Chunlei
Hu, Lei
[J]. DESIGNS CODES AND CRYPTOGRAPHY, 2009, 52 (03) : 303 - 338
[3] Maximal values of generalized algebraic immunity
Feng, Keqin
Liao, Qunying
Yang, Jing
[J]. DESIGNS CODES AND CRYPTOGRAPHY, 2009, 50 (02) : 243 - 252
[4] An infinite class of balanced functions with optimal algebraic immunity, good immunity to fast algebraic attacks and good nonlinearity .2 C. Carlet,K. Feng. Asiacrypt 2006 . 2008

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