Analysis of Design for Mixcolumn Transformation of AES
Huanguo Zhang · Wuhan University Journal · 2003
The definition of optimal invertible linear transformation is generalized to general field. The theorem of existence for optimal invertible linear transformation over general field, an invertible linear transformation is optimal if and only if every sub-matrix of its corresponding matrix is invertible, is given without any knowledge of code theory. A formula in the algorithm of Sugita, Kobara, Uehara, et al. for computing differential and truncated differential of word-oriented block cipher is simplified. A new property of AES, the system presents the same strength against differential attack when implementing the Mix-column transformation of AES with any optimal invertible circular matrix of suitable size, is found with this simplified formula. The design for Mix-column transformation of AES is reasonable since the Mix-column of AES is optimal invertible linear transformation and the entries (01, 02 and 03) in its corresponding matrix are easy to implement with software or hardware.