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
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
CLC Number:
ZHANG Feng-rong; XIE Min; MA Hua. Construction of Multi-dimension Plateaued Functions[J]. Computer Engineering, 2009, 35(20): 170-172.
张凤荣;谢 敏;马 华. 多维Plateaued函数的构造[J]. 计算机工程, 2009, 35(20): 170-172.