摘要
MDS矩阵在密码学中具有分支数大、扩散性好及安全性高等优点,并且MDS矩阵的异或数越小,实用性越强。以十六阶二元MDS循环矩阵为例,为得到异或数最小的矩阵,首先,根据循环矩阵构造MDS矩阵的充分条件,构造出四阶二元循环MDS矩阵;再由矩阵分块原理,将矩阵的元素扩展到四阶矩阵;最后构造出若干异或数最小的十六阶二元MDS循环矩阵,并给出其中一个异或数最小的最优矩阵的具体形式。
MDS matrix has many advantages in cryptography,such as large branch number,good diffusion and high security. And the xor number of MDS matrix becomes more smaller,the practicability becomes more stronger. Taking the sixteen order of two element MDS circulant matrices as an example,in order to get the minimum number of XOR matrix,firstly,according to the sufficient conditions for constructing MDS matrix based on cyclic matrices,we constructed four order of two element MDS circulant matrices;Because of the principle of block matrix,the element in MDS circulant matrices can be extended to four order matrix;finally we constructed some the sixteen order of two element MDS circulant matrices with the minimum xor number,and gave the specific form of the optimal matrix which xor number is minimized.
出处
《长春理工大学学报（自然科学版）》
2017年第4期112-114,119,共4页
Journal of Changchun University of Science and Technology(Natural Science Edition)
基金
国家自然科学基金(11601039)
