对合Cauchy-Hadamard型MDS矩阵的构造
doi: 10.3724/SP.J.1146.2009.00070
Construction of Involution Cauchy-Hadamard Type MDS Matrices
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摘要: MDS矩阵和对合MDS矩阵在分组密码中有广泛应用。该文将考察同时是Hadamard矩阵和Cauchy矩阵的那些MDS矩阵，给出了这类矩阵的结构、构造方法和个数，从而得到了MDS矩阵一种新的构造方法。该文还证明了Cauchy-Hadamard型MDS矩阵都等效于对合的Cauchy-Hadamard型MDS矩阵，并给出了由Cauchy-Hadamard型MDS矩阵构造对合的Cauchy-Hadamard型MDS矩阵的方法。Abstract: MDS matrices and involution MDS matrices are widely used in block ciphers. This paper deals with those MDS matrices which are Hadamard matrices and Cauchy matrices simultaneously. Then the structure, the method of constructing and the count value of this kind of matrices are presented. By this, a new method for constructing MDS matrices is obtained. Additionally, this paper proves that a Cauchy-Hadamard type MDS matrix can be transformed into an involution Cauchy-Hadamard type MDS, and then proposes a new method to construct an involution Cauchy-Hadamard type MDS matrix from a Cauchy-Hadamard type MDS matrix.
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