一次扩散布尔函数的一些密码学性质

通过将导数和自定义的e-导数结合,作为新的研究工具引入到布尔函数密码学性质研究中来。利用导数和e-导数可将布尔函数内部取值不同特点进行区分的特性,系统地证明了不同重量一次扩散布尔函数相关免疫最高阶数问题,得出了一些用传统研究工具,如频谱理论等,不易导出的布尔函数密码学性质。这一结果对提高密码系统抵抗相关攻击的能力,提供了理论依据。

Cryptographic Properties of Linear Proliferation Boolean Function

Derivative and the e-derivative defined by the authors are combined and introduced as a new research tool in studying the cryptographic properties of Boolean functions.With the feature in differentiating the different characteristics of Boolean function values by derivative and e-derivative,the problem of Boolean diffusion linear functions correlation immune highest order with different weights is systematically verified,and some cryptographic properties of Boolean function are acquired,which are not so easily deduced by traditional research tools,such as spectral theory,etc.This reseach result could lay a theoretical foundation for improving the attack-resistant ability of the password system.