二次密码函数的线性结构和非线性度

ON LINEAR STRUCTURES ANDNONLINEARITY OF QUADRATIC CRYPTOGRAPHIC FUNCTIONS

研究二次密码函数的非线性度和线性结构 ,得到两者之间的一个关系式 ,并由此得到二次函数为Bent函数的两个充要条件以及一般二次函数的非线性度上界和下界 .

The nonlinearity and linear structures are both important concepts of cryptographic functions as they can describe the capability of the functions to withstand the linear attacks to the cryptographic system.In the paper,the relationship of the two notions are discussed and some criteria for a Boolean function being a Bent function are obtained.