小汉明重量的布尔函数代数厚度上界研究  

Research on Upper Bound of Algebraic Thickness for Boolean Functions with Small Hamming Weight

作　　者：周宇[1] 张文政[1] 祝世雄[1] 

机构地区：[1]中国电子科技集团公司第三十研究所保密通信重点实验室,成都610041

出　　处：《计算机工程》2012年第5期120-121,125,共3页Computer Engineering

基　　金：保密通信重点实验室基金资助项目(9140C11020110C1102)

摘　　要：根据布尔函数代数厚度的定义,总结变量不交布尔函数的组合函数代数厚度与各布尔函数代数厚度的联系,指出代数厚度上界证明的局限性,得到布尔函数与其补布尔函数代数厚度的限制关系式。利用该关系式得到汉明重量为2和3的布尔函数及其补布尔函数的代数厚度上界,计算满足一定代数厚度的布尔函数的概率值。According to definition of algebraic thickness of Boolean functions,the relationship between addition of two Boolean functions and their algebraic thickness is given.Limitation property of upper bound on algebraic thickness is descripted.Meanwhile,the restrictive relationship of algebraic thickness between Boolean function and complement Boolean function is derived.By these results,the upper bounds on algebraic thickness of Boolean functions with small hamming weights and their complement functions are deduced.The probability value of Boolean functions with some algebraic thickness is estimated.

关 键 词：布尔函数 代数厚度 汉明重量 代数正规型 代数免疫 

分 类 号：TN918.1[电子电信—通信与信息系统]