Abstract: With Walsh spectrum of Boolean functions, a necessary and sufficient condition is given on Boolean functions satisfying k-strengthened propagation criterion. Based on the relationship between k-strengthened propagation criterion and k-propagation criterion, two constructions of Boolean functions satisfying k-strengthened propagation criterion are presented. With Walsh spectrum of Boolean functions satisfying balance and correlation immune, a necessary and sufficient condition of the defining functions of k-cheating immune secret sharing is obtained.

Key words: strengthened propagation criterion, correlation immune, cheating immune, secret sharing

摘要： 利用概率方法和频谱理论，给出布尔函数满足强扩散准则的一个新的等价判别条件，并根据强扩散准则与扩散准则之间的关系，得到满足k次强扩散准则的布尔函数的2种构造方法。结合具有平衡性和相关免疫性的布尔函数的谱特征，给出k-欺骗免疫秘密共享定义函数的谱判别条件。

关键词: 强扩散准则, 相关免疫, 欺骗免疫, 秘密共享

CLC Number: 

• TN918.1