A conjecture about binary strings and its applications on constructing Boolean functions with optimal algebraic immunity

被引：92
作者：
Tu, Ziran [1 ,2 ]
Deng, Yingpu [1 ,3 ]
机构：
[1] Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mechanizat, Beijing 100190, Peoples R China
[2] Henan Univ Sci & Technol, Fac Sci, Luoyang 471003, Peoples R China
[3] Chinese Acad Sci, Grad Univ, State Key Lab Informat Secur, Beijing 100049, Peoples R China
来源：
DESIGNS CODES AND CRYPTOGRAPHY | 2011年 / 60卷 / 01期
关键词：
Boolean function; Algebraic immunity; Bent function; Balancedness; Nonlinearity; Algebraic degree; LINEAR FEEDBACK; STREAM CIPHERS; ATTACKS;
D O I：
10.1007/s10623-010-9413-9
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
In this paper, a combinatorial conjecture about binary strings is proposed. Under the assumption that the proposed conjecture is correct, two classes of Boolean functions with optimal algebraic immunity can be obtained. The functions in first class are bent, and then it can be concluded that the algebraic immunity of bent functions can take all possible values except one. The functions in the second class are balanced, and they have optimal algebraic degree and the best nonlinearity up to now.
引用
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页码：1 / 14
页数：14
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