Generalized Construction of Boolean Function with Maximum Algebraic Immunity Using Univariate Polynomial Representation

被引：2

作者：

Fu, Shaojing ^{[1
]}

Li, Chao ^{[2
]}

Qu, Longjiang ^{[2
]}

机构：

[1] Natl Univ Def Technol, Coll Comp, Changsha, Hunan, Peoples R China

[2] Natl Univ Def Technol, Dept Math & Syst Sci, Changsha, Hunan, Peoples R China

来源：

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES | 2013年 / E96A卷 / 01期

基金：

中国国家自然科学基金;

关键词：

cryptography; Boolean function; algebraic immunity;

D O I：

10.1587/transfun.E96.A.360

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

Because of the algebraic attacks, a high algebraic immunity is now an important criteria for Boolean functions used in stream ciphers. In 2011, X.Y. Zeng et al. proposed three constructions of balanced Boolean functions with maximum algebraic immunity, the constructions are based on univariate polynomial representation of Boolean functions. In this paper, we will improve X.Y. Zeng et al.' constructions to obtain more even-variable Boolean functions with maximum algebraic immunity. It is checked that, our new functions can have as high nonlinearity as X.Y. Zeng et al.' functions.

引用

页码：360 / 362

页数：3

共 15 条

[1] Algebraic immunity for cryptographically significant Boolean functions: Analysis and construction [J].

Carlet, Claude ;

Dalai, Deepak Kumar ;

Gupta, Kishan Chand ;

Maitra, Subhamoy .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2006, 52 (07) :3105-3121

[2]

Carlet C, 2008, LECT NOTES COMPUT SC, V5350, P425, DOI 10.1007/978-3-540-89255-7_26

[3] Two Classes of Symmetric Boolean Functions With Optimum Algebraic Immunity: Construction and Analysis [J].

Chen, Yindong ;

Lu, Peizhong .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2011, 57 (04) :2522-2538

[4] Construction of Boolean functions with maximum algebraic immunity and count of their annihilators at lowest degree [J].

Du YuSong ;

Pei DingYi .

SCIENCE CHINA-INFORMATION SCIENCES, 2010, 53 (04) :780-787

[5] Balanced rotation symmetric boolean functions with maximum algebraic immunity [J].

Fu, S. ;

Qu, L. ;

Li, C. ;

Sun, B. .

IET INFORMATION SECURITY, 2011, 5 (02) :93-99

[6]

Fu S., 2012, SCI CHINA INFORM SCI, DOI [10.1007/s11432-011-4350, DOI 10.1007/S11432-011-4350]

[7] On the construction of Boolean functions with optimal algebraic immunity [J].

Li, Na ;

Qu, LongJiang ;

Qi, Wen-Feng ;

Feng, GuoZhu ;

Li, Chao ;

Xie, DuanQiang .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2008, 54 (03) :1330-1334

[8] On designated-weight Boolean functions with highest algebraic immunity [J].

Liu MeiCheng ;

Du YuSong ;

Pei DingYi ;

Lin DongDai .

SCIENCE CHINA-MATHEMATICS, 2010, 53 (11) :2847-2854

[9]

Meier W, 2004, LECT NOTES COMPUT SC, V3027, P474

[10] Construction of 1-Resilient Boolean Functions with Optimal Algebraic Immunity and Good Nonlinearity [J].

Pan, Sen-Shan ;

Fu, Xiao-Tong ;

Zhang, Wei-Guo .

JOURNAL OF COMPUTER SCIENCE AND TECHNOLOGY, 2011, 26 (02) :269-275

← 1 2 →