【摘要】 0-1矩阵常用于设计分组密码的扩散结构.首先证明,当GF(2n)上的矩阵重新定义在扩域GF(2mn)上时其分支数保持不变,据此补充了Choy等人关于GF(2n)上二元矩阵分支数上界的证明.构造了一批分支数达到最优的8阶二元可逆矩阵,给出了一类差分分支数和线性分支数相等的二元可逆矩阵,并从中搜索出了大量16阶分支数达到最优的二元矩阵和对合二元矩阵.更多还原

【Abstract】 0-1 matrices are often-used in the design of diffusion structures in block ciphers.This paper first proves that the branch number of matrix over GF(2n) does not change while it is redefined over the extension field GF(2mn).By this result,the study reinforces the proof given by Choy et al.,which is about the upper bound of branch number of binary matrices over GF(2n).This paper constructs a kind of invertible binary matrices with size 8 and largest branch number,proposes a kind of matrices with equal differential branch number and linear branch number,and also includes lots of matrices and involution matrices with order 16 and optimal branch number with this structure are searched out.更多还原