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轮换矩阵密码学性质 被引量：3

Research on Cryptology Characteristics
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摘要 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.
作者 韩海清 张焕国
机构地区 武汉大学计算机学院 黄石理工学院数理学院
出处 《武汉大学学报（理学版）》 CAS CSCD 北大核心 2010年第6期673-677,共5页 Journal of Wuhan University:Natural Science Edition
基金 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)
关键词 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
分类号 TN918 [电子电信—通信与信息系统]
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参考文献12

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共引文献1

同被引文献24

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武汉大学学报（理学版）
2010年 第6期

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