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。
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 16x16 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 16x 16 involutory 0-1 matrice with maximum branch number 8 and their number in the permutation of isomorphism.
出处
《计算机工程》
CAS
CSCD
2013年第12期118-121,共4页
Computer Engineering
基金
国家自然科学基金资助项目(61272041)
