7阶拟群的密码学分类

发布时间：2018-04-13 23:01

本文选题：拟群 + 拉丁方　；参考：《宁波大学》2017年硕士论文

【摘要】：本文以对拟群的理论研究为主题,基于其在密码学中的应用,对7阶拟群进行分类,选择出适合于加密的拟群.第一章综述了密码学理论的发展过程.由欧洲序列密码计划中4阶拟群在流密码中的应用及因其产生的弱密钥性引申出7阶拟群的密码学分类和所产生的密钥安全性分析的重要性.第二章介绍了拟群的定义并给出基于拟群运算的e-变换函数.经过有限次的e-变换可以得到密钥流.在对变换函数的分析中,以序列的周期为基提出了拟群周期因子f*的概念,并给出了对应于拟群的k次周期因子fk*的概率分布.第三章介绍了本原群的概念及其与拟群相关的知识.第四章给出了7阶拟群的分类.对于在某一较低阶的本原群中形成的拉丁方,根据所具有的列置换的循环型进行分类.对于在高阶的本原群(交错群T6和对称群T7)中形成的拉丁方,由于其具体表示形式无法一一列出,在此,根据能够形成拉丁方的基本条件,将所有能够生成拉丁方的列置换的循环型的组合列出来并据此进行分类.第五章计算出每一类中的拟群的周期因子的期望值.第六章对文章做了总结.对各阶本原群中能够得到的拉丁方的周期因子及其期望值进行分析,只有在交错群T6中的所有拉丁方及对称群T7中部分型类中的拉丁方是适合用于加密的.
[Abstract]:Based on its application in cryptography, this paper classifies the quasi groups of order 7 and selects the quasi groups suitable for encryption.The first chapter summarizes the development of cryptography theory.Based on the application of quasi groups of order 4 in the European sequence cryptosystem, the importance of cryptographic classification of order 7 quasi groups and the key security analysis generated by them are derived from the weak keys generated by them.In chapter 2, the definition of quasi group is introduced and the e- transformation function based on quasi group operation is given.After a finite number of e-transformations, the key stream can be obtained.In the analysis of transformation function, the concept of quasi group periodic factor f * is put forward based on the period of sequence, and the probability distribution of k order periodic factor f K * corresponding to quasi group is given.The third chapter introduces the concept of primitive group and its knowledge related to quasi group.In chapter 4, the classification of quasi groups of order 7 is given.The Latin square formed in a lower order primitive group is classified according to the cyclic type of column permutation.For the Latin square formed in higher order primitive groups (staggered group T6 and symmetric group T7), because of its specific representation, the Latin square can not be listed in detail. In this paper, according to the basic conditions of forming Latin square,All cyclic combinations of column permutations that generate Latin squares are listed and classified accordingly.In chapter 5, the expected values of periodic factors of quasi groups in each class are calculated.Chapter six summarizes the article.The periodic factors and expected values of Latin squares in primitive groups of order are analyzed. Only all Latin squares in interlaced group T6 and Latin squares in partial classes of symmetric group T7 are suitable for encryption.
【学位授予单位】：宁波大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O152

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