高级加密标准Mixcolumn变换设计分析

高级加密标准Mixcolumn变换设计分析 Analysis of Design for Mixcolumn Transformation of AES 曾祥勇 ZENG Xiang-yong 1 2 first-author 张焕国 ZHANG Huan-guo 1 2 武汉大学计算机学院 武汉大学计算机学院 School of Computer, Wuhan University School of Computer, Wuhan University 武汉大学计算机学院,湖北,武汉,430072 武汉大学计算机学院,湖北,武汉,430072 将最优线性映射的定义推广到一般域K上,由定义证明了域K上的方阵是最优的当且仅当它的所有子方阵可逆;发现了高级加密标准AES扩散层的一个新的性质:用同规模的任意循环最优线性映射取代AES的Mixcol umn变换,系统依然呈现出相同的抗差分攻击能力;因为AES的Mixcolumn变换是最优的线性映射,且其对应矩阵选取合理、便于软硬件的快速实现,所以其设计的确很好. 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. 分组密码 差分特征 AES 最优线性映射 block cipher differential character AES optimal linear mapping TP309.7 国家自然科学基金重点资助项目（90104005）;国家863项目（2002AA141051）;武汉晨光计划（20025001007）;湖北省自然科学基金资助项目（2002AB0037） 2003-05-01 2021-04-01 5