平衡H布尔函数的相关免疫性研究

Correlation-immunity study of balanced H-Boolean functions

引入布尔函数的E-导数,并结合导数一起作为工具讨论关系密码系统安全性能的平衡H布尔函数的相关免疫性。通过E-导数和导数深入揭示了平衡H布尔函数0和1值的分布结构,得出判定H布尔函数是否相关免疫的重要结果。并得以采用区分不同结构的计算方法来简化计算,解决了平衡H布尔函数相关免疫最高阶数这一问题。

As a novel definition, E-derivative was introduced to study problems that are extremely difficult to handle in the cryptographic system. By using the way of combining derivative with E-derivative and correlation-immunity of H-Boolean functions, the distribution structure of balanced H-Boolean functions were deeply analyzed, and some impor- tant results on how to determine whether or not a H-Boolean function has correlation-immunity with the relatively sim- plified method of distinguishing different structure were also obtained, which are going to play important roles in the field of cryptology and future worldwide applications. Beyond that, the problem of the most higher-order correla- tion-immunity of H-Booleanfimction which is also one of the most difficult unsolved problems in cryptology was solved successfully to improve the anti-attack ability of cryptosystem and ensured the secure transmission of secret information on the network effectively.