A combinatorial condition and Boolean functions with optimal algebraic immunity

被引：4

作者：

Jin Qingfang ^{[1
]}

Liu Zhuojun ^{[2
]}

Wu Baofeng ^{[3
]}

Zhang Xiaoming ^{[2
]}

机构：

[1] Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China

[2] Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mech, Beijing 100190, Peoples R China

[3] Chinese Acad Sci, Inst Informat Engn, State Key Lab Informat Secur, Beijing 100093, Peoples R China

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; STREAM CIPHERS; ATTACKS; CONSTRUCTION;

D O I：

10.1007/s11424-014-2133-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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

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