轻量级MDS矩阵的构造

The Construction of Lightweight MDS Matrix

MDS矩阵在密码学中有重要的应用,可以用来构造分组密码。MDS矩阵的异或数是衡量密码算法的有效性的一个重要指标。本文研究MDS矩阵的性质,考虑循环、矩阵分块和迭代等思想,分别针对几类特殊性质的MDS矩阵构造,包括循环MDS矩阵、Hadar MDS矩阵和迭代MDS矩阵等。在m = 4, 8情况下,使用程序来搜索满足条件的MDS矩阵,给出了具有最小异或数的MDS矩阵的数目和例子,得到m = 4, 8情况下许多具有已知最小异或数的MDS矩阵,得到了m = 4时具有异或数12的循环MDS矩阵,也构造了m = 8时具有异或数10的最佳MDS矩阵。

MDS Matrix has important applications in cryptography and it can be used to construct block ciphers. The number of XOR of a MDS Matrix is an important index to measure the validity of cipher algorithm. In this paper, we study the properties of MDS matrix and consider the ideas of cycle, block matrix and so on. The MDS matrix is constructed for several special properties, including cyclic MDS matrix, Hadamard MDS matrix and iterative MDS matrix etc. When the number m = 4, 8, we use the program to search the MDS matrix that satisfies the condition. The number of MDS matrix with the minimum number of XOR and examples are given and we get many MDS matrices with the minimum number of XOR;when m = 4, we have given the circulating MDS Matrix with the number of XOR with 12, when m = 8 we have given the best MDS Matrix with the number of XOR with 10.