布尔函数的代数免疫与扩散阶的关系

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.%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.