摘要： 具有最大分支数的0-1可逆矩阵被广泛应用于分组密码的扩散结构设计中。为构造16阶该类矩阵，将16阶0-1矩阵划分为以4阶0-1矩阵为单元的4阶块矩阵，根据特征和域上重量均为2的4维0-1向量相加后所得向量的重量分布特点，在行置换同构意义下构造满足某种特殊结构的4阶0-1矩阵单元组，以此为基础，根据Hadamard矩阵的结构特点，利用矩阵的分块构造思想，给出一类分支数达到最大值8的16阶0-1可逆矩阵和对合矩阵构造方法，并在行置换同构意义下给出对合矩阵的计数。

关键词: 分组密码, 扩散结构, 分支数, 0-1矩阵, Hadamard矩阵

Abstract: 0-1 invertible matrice which has the largest branch number is widely used in the design of diffusion structures in block ciphers. In view of how to construct such 16×16 matrix, this paper divides 16×16 matrix into 4×4 block matrix by 4×4 0-1 matrix as a unit. Using the weight distribution peculiarity of the sum of 4-dimensional 0-1vectors with weight 2 in field of characteristic 2, it constructs 4×4 0-1 matrix unit group with some special structures in the permutation of isomorphism. On the basis of the structure characteristic of Hadamard matrice, it presents the methods of constructing 16×16 invertible 0-1 matrice with maximum branch number 8 using the matrix block construction method. Further, it presents the methods of constructing 16×16 involutory 0-1 matrice with maximum branch number 8 and their number in the permutation of isomorphism.

Key words: block cipher, diffusion structure, branch number, 0-1 matrice, Hadamard matrice

中图分类号: 

• TP309