【摘要】 对有限域GF(2k)上的“遍历矩阵”进行了探讨.通过本文的分析,可以发现GF(2k)上的遍历矩阵具有很多可应用于密码学的良好特性.为了寻找所需的遍历矩阵,我们引入了GF(2k)中的一个递推公式,并基于此给出了一个寻找算法.通过该算法可以有效地找到GF(2k)上特定数目的n阶遍历矩阵,且每一个n阶遍历矩阵均可用GF(2k)上的一个n维向量来表示,因此可大大节省存储和传输相应矩阵所需的空间及带宽.更多还原

【Abstract】 Discussed the matrix over GF(2~k) what is called "ergodic matrix".By the analyses that we done in this paper,one can find the ergodic matrix has a number of good features that can be applied to cryptography.In order to look for the required ergodic matrix,this paper introduced a recursion formula and giving a searching algorithm.by which one can find the certain number of such matrices and generate an n×n ergodic matrix Q_g only by a n-dimension vector g over GF(2~k).So that enables using a n-dimension vector to express a n×n ergodic matrix.thereby saving the storage and bandwidth.更多还原