Abstract: In order to transfer the stream ciphers algebraic attacks problems into low-degree annihilators of Boolean function problem, the characters of Boolean function is discussed. The special structure of matrix on {0,1} is introduced. The relations between them are researched. On this basis, the relations between the annihilator polynomial power number of n-variant Boolean function and their support points sets are studied. Experimental results show the problem of searching annihilators for Boolean function is the same as searching the maximum affine space in zero points sets of it.

Key words: Boolean function, support point set, annihilator, affine space

摘要： 为把流密码的代数攻击问题转化为求解布尔函数的低次数零化多项式问题，讨论布尔函数的性质，介绍{0,1}上矩阵的特殊结构，研究两者间的关系，在此基础上探讨n元布尔函数f的零化多项式次数与f的支撑点集之间的关系，实验结果表明，寻找布尔函数零化多项式等价于在布尔函数的零点集合中寻找最大的仿射空间。

关键词: 布尔函数, 支撑点集, 零化多项式, 仿射空间

CLC Number: 

• TP311.52