| 布尔函数的代数免疫与扩散阶的关系 |
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| 引用本文： | 周宇,曹云飞,张文政,祝世雄. 布尔函数的代数免疫与扩散阶的关系[J]. 计算机工程与科学, 2011, 33(10): 34. DOI: 10.3969/j.issn.1007-130X.2011.10.006 |
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| 作者姓名： | 周宇 曹云飞 张文政 祝世雄 |
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| 作者单位： | 保密通信重点实验室,四川成都,610041 |
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| 摘 要： | 本文利用布尔函数全局雪崩准则得到平方和指标与代数免疫的联系,通过Walsh谱与自相关函数的关系式得到布尔函数满足扩散时自相关值的分布,由此推出了变元数、代数免疫、扩散阶和代数次数之间的不等式,利用计算机搜索得到变元数在4~30之间时这四个指标的简洁表达式。最后得到了扩散阶与线性结构、正规性的关系。
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| 关 键 词： | 布尔函数 代数免疫 扩散阶 全局雪崩准则 |
Relationship Between Algebraic Immunity and Propagation Characteristics of the Boolean Functions |
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| ZHOU Yu,CAO Yun-fei,ZHANG Wen-zheng,ZHU Shi-xiong. Relationship Between Algebraic Immunity and Propagation Characteristics of the Boolean Functions[J]. Computer Engineering & Science, 2011, 33(10): 34. DOI: 10.3969/j.issn.1007-130X.2011.10.006 |
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| Authors: | ZHOU Yu CAO Yun-fei ZHANG Wen-zheng ZHU Shi-xiong |
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| Abstract: | Using the relationship between the sum of square and algebraic immunity by GAC,the divisibility properties concerning the auto-correlation coefficient of the Boolean functions with propagation criterion is derived by Walsh-spectrum and coefficient,and the inequality among variables,algebraic immunity,propagation criteria and algebraic degree is deduced by this divisibility,and by the computer search methods a compactly expression among these four parameters is given from 4 variables to 30 variables.Finally,the relationships between the propagation criterion and the liner structure and normality are discussed. |
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| Keywords: | Boolean functions Algebraic immunity Propagation criteria GAC |
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