特殊逻辑函数布尔C-导数的性质研究

Research on the Properties of the Boolean C-derivative on Special Logic Functions

线性函数、冗余函数、自反函数、自双反函数、部分自反函数和部分自双反函数等特殊逻辑函数在密码学函数构造方面具有优越性。布尔C-导数能全面揭示布尔函数的密码学性质和函数结构的关系,是构造密码学函数的重要工具。本文从特殊逻辑函数和布尔-C导数的定义出发,讨论了这些逻辑函数的布尔C-导数性质,并给出了相应证明。该研究为快速构造密码学函数奠定理论基础。

Linear function,redundant function,self-negative function,self-dual function,partial selfnegative function and partial self-dual function have advantages in the construction of cryptographic functions. Boolean C-derivative can fully reveal the relation between the cryptographic properties of Boolean functions and the function structure. Boolean C-derivative is an important tool to construct cryptographic functions. In this paper,we start from the definition of the special logic function and the Boolean C-derivative,the properties of Boolean C-derivatives of these logical functions are discussed,the corresponding proof is given also. This work lays a theoretical foundation for the fast construction of cryptographic functions.