摘要： 布尔函数在编码、组合设计和序列设计等中扮演重要的角色。利用Maiorana-McFarland构造法构造出一类Plateaued函数，在此基础上，结合m-序列的状态转移矩阵，构造出n元(n+1)/2维的n-1阶Plateaued函数。所构造的多维Plateaued函数可以满足多个密码指标，即高非线性度、没有非零线性结构、平衡、代数次数达到最高等。

关键词: 多维Plateaued函数, 代数次数, 密码函数, S-盒, 布尔函数

Abstract: Boolean functions play important roles in coding theory, combinatorial design and sequence design. A class of Plateaued functions is gotten by way of using the Maiorana-McFarland construction. Combined with the characteristic of the state transform matrix of m-sequence, a class of (n+1)/2-dimension Plateaued functions with n variables is constructed. A variety of cryptographically desirable criteria for multi-dimension functions can be satisfied, such as high nonlinearity, nonexistence of nonzero linear structures, balance and the highest algebraic degree.

Key words: multi-dimension Plateaued functions, algebraic degree, cryptographic function, S-boxes, Boolean functions

中图分类号: 

• TN918.1