轮换矩阵密码学性质

轮换矩阵密码学性质 Research on Cryptology Characteristics 韩海清 HAN Haiqing1 1 2 first-author 张焕国 ZHANG Huanguo1 1 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 黄石理工学院数理学院 黄石理工学院数理学院 School of Mathematics and Physics,Huangshi Institute of Technology School of Mathematics and Physics,Huangshi Institute of Technology 从AES中的列混淆出发,研究了有限域上轮换矩阵的一些性质,给出了轮换矩阵求逆算法和生成分支数最大的四阶轮换矩阵算法;讨论了轮换正形矩阵及轮换对合矩阵的一些性质,给出生成分支数达最大的四阶轮换正形矩阵的算法,得到了分支数最大的轮换对合矩阵不存在的结论. The Mixcolumns operation of AES can be represented as a matrix,which plays an important role in confusion operation.Based no the Mixcolumns operation of AES,this paper mainly researches the properties of circulunt matrix over finite field,and presents a novel algorithm that generates the circulunt inverse matrices and the circulunt matrices with the maximal branch number.At last,this paper has discussed some characteristics of orthormorphic circulunt matrix and symmetrical circulunt matrix that have arrived at the maximal branch number,also then obtained an algorithm for generating the orthormorphic circulunt matrices with the maximal branch number.Furthermore,the conclusion that the symmetrical matrix with maximal branch number not exist have been gained. 轮换矩阵 分支数 正形矩阵 对合置换 密码学 circulant matrix branch number orthormorphic matrix symmetrical permutation cryptology 10.14188/j.1671-8836.2010.06.010 TN918.1 国家高技术研究发展计划（863）项目（2006AA01z442,2007AA01Z411）;国家自然科学基金资助项目（60673071,60970115,60970116） 2010-06-01 2021-04-01 6 56