偶数元择多逻辑函数的稳定性和代数结构

The Stability and Algebra Structure of Maximum Logic Functions with Even Number of Variables

与变元个数一定为奇数的SML函数相对应,本文定义了偶数元择多逻辑函数,考查了其中一部分函数的Walsh谱性质和代数结构,证明了当变元个数较多时这部分函数同样具有理想的稳定性和较高的非线性度。同时这部分函数的代数结构当n=2p,p是正整数时也是理想的。因而此类函数在非线性组合和非线性滤波密码环境中同样有密码学价值。

Relative to SML functions, we propose the conception of maximum logic functions with even number of variables and study Walsh transform and the algebraic structure of a part of them. Then we prove these functions with large number of variables that have perfect stability and upper nonlinearity and show that the algebraic structure of these functions is also perfect.