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Construction of Odd-Variable Boolean Function with Maximum Algebraic Immunity Using Univariate Polynomial Representation

Construction of Odd-Variable Boolean Function with Maximum Algebraic Immunity Using Univariate Polynomial Representation
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摘要 To protect against algebraic attacks, a high algebraic immunity is now an important criterion for Boolean functions used in stream ciphers. In this paper, a new method based on a univariate polynomial representation of Boolean functions is proposed. The proposed method is used to construct Boolean functions with an odd number of variables and with maximum algebraic immunity. We also discuss the nonlinearity of the constructed functions. Moreover, a lower bound is determined for the number of Boolean functions with maximum algebraic immunity. To protect against algebraic attacks, a high algebraic immunity is now an important criterion for Boolean functions used in stream ciphers. In this paper, a new method based on a univariate polynomial representation of Boolean functions is proposed. The proposed method is used to constmct Boolean functions with an odd number of variables and with maximum algebraic immunity. We also discuss the nonlinearity of the constructed functions. Moreover, a lower bound is deter- mined for the number of Boolean functions with rmximum algebraic immunity.
作者 Zhao Wentao Fu Shaojing Li Chao Qu Longjiang
机构地区 College of Computer Department of Mathematics and System Science Key Laboratory of Network Security and Cryptology State key Laboratory of Information Security
出处 《China Communications》 SCIE CSCD 2012年第10期33-39,共7页 中国通信（英文版）
基金 This work was supported by the National Natural Science Foundation of China under Grants No. 61103191, No. 61070215 the Funds of Key Lab of Fujian Province University Network Security and Cryptology under Crant No. 2011003 and the Open Research Fund of State Key Laboratory of Inforrmtion Security.
关键词 布尔函数 代数攻击 多项式表示 免疫 奇数 构造函数 流密码 非线性 cryptography boolean function alge- braic attack algebraic immunity
分类号 O153.2 [理学—基础数学] TP391 [自动化与计算机技术—计算机应用技术]
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参考文献21

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二级参考文献26

  • 1LIAO QunYing1, LIU Feng2 & FENG KeQin2 1 College of Mathematics and Software Sciences, Sichuan Normal University, Chengdu 610066, China 2 Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China.On (2~m + 1)-variable symmetric Boolean functions with submaximum algebraic immunity 2^(m-1)[J].Science China Mathematics,2009,52(1):17-28. 被引量：4
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China Communications
2012年 第10期

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