| 最优代数免疫布尔函数的完全构造 |
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| 引用本文： | 王永娟,张世武.最优代数免疫布尔函数的完全构造[J].计算机应用,2012,32(1):49-51. |
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| 作者姓名： | 王永娟 张世武 |
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| 作者单位： | 解放军外国语学院 基础部，河南 洛阳 471003 |
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| 基金项目： | 国防973项目(6138403005) |
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| 摘 要： | 任意的布尔函数可以唯一地表示成有限域上的单变元多项式函数，利用布尔函数的单变元多项式表示和代数编码理论，讨论了布尔函数的代数免疫达到最优的判别条件，得到了布尔函数的变元个数为奇数时，布尔函数具有最优代数免疫(MAI)的等价判别条件。利用该等价判别条件，给出3元布尔函数满足MAI的等价判别条件，进而构造出所有3元的MAI布尔函数。
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| 关 键 词： | 布尔函数 代数免疫 代数攻击 Reed-Soloman码 代数编码 |
| 收稿时间： | 2011-08-03 |
| 修稿时间： | 2011-09-08 |
Construction of Boolean functions with optimum algebraic immunity |
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| WANG Yong-juan ZHANG Shi-wu.Construction of Boolean functions with optimum algebraic immunity[J].journal of Computer Applications,2012,32(1):49-51. |
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| Authors: | WANG Yong-juan ZHANG Shi-wu |
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| Affiliation: | Basic Course Department, PLA University of Foreign Language, Luoyang Henan 471003, China |
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| Abstract: | Any Boolean function can be uniquely expressed as a univariate polynomial function on finite field. By using this representation and algebraic coding theory to discuss the criterion, by which a Boolean function achieves its Maximum Algebraic Immunity (MAI), the authors provided an equivalent criterion by which the algebraic immunity of a Boolean function with odd variables reaches MAI. According to the criterion, an equivalent condition to Boolean function of three variables that achieves MAI was reached. Thus, all MAI Boolean functions of three variables got constructed. |
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| Keywords: | Boolean function algebraic immunity algebraic attack Reed-Soloman codes algebraic code |
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