Acta Scientiarum Naturalium Universitatis Pekinensis

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New Construction of Boolean Function with Maximum Algebraic Immunity

CAO Hao1, WEI Shimin2, ZHUO Zepeng2, WANG Huige1   

  1. 1. College of Science, Anhui Science and Technology University, Chuzhou 233100; 2. Huaibei Normal University, Huaibei 235000;
  • Received:2010-04-20 Online:2010-09-20 Published:2010-09-20

具有最大代数免疫阶的布尔函数的新构造

曹浩1,魏仕民2,卓泽鹏2,王会歌1   

  1. 1. 安徽科技学院理学院, 滁州 233100; 2.淮北师范大学, 淮北 235000;

Abstract: Focusing on algebraic normal form and the construction requirements of Boolean function, the conditions that Boolean functionf does not exist annihator with deg(f) ≤m are analysed and the sufficient conditions satisfied by Boolean functionf with maximum algebraic immunity are obtained. Therefore a class of Boolean functions with optimal algebraic immunity are constructed, and the balanceness and count of the constructed functions are discussed.

Key words: Boolean function, algebraic normal form, algebraic immunity

摘要: 针对密码学中布尔函数的构造需求, 利用布尔函数的代数标准型, 分析了布尔函数不存在次数低于 m 的非零零化子的充分条件, 得到布尔函数达到最大代数免疫阶的条件, 从而构造了一类具有最高代数免疫阶的布尔函数, 并对所构造函数的平衡性和计数问题进行了分析。

关键词: 布尔函数, 代数标准型, 代数免疫阶

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