發(fā)布時間：2018-04-13 23:01

  本文選題：擬群 + 拉丁方��； 參考：《寧波大學》2017年碩士論文

【摘要】：本文以對擬群的理論研究為主題,基于其在密碼學中的應用,對7階擬群進行分類,選擇出適合于加密的擬群.第一章綜述了密碼學理論的發(fā)展過程.由歐洲序列密碼計劃中4階擬群在流密碼中的應用及因其產生的弱密鑰性引申出7階擬群的密碼學分類和所產生的密鑰安全性分析的重要性.第二章介紹了擬群的定義并給出基于擬群運算的e-變換函數(shù).經過有限次的e-變換可以得到密鑰流.在對變換函數(shù)的分析中,以序列的周期為基提出了擬群周期因子f*的概念,并給出了對應于擬群的k次周期因子fk*的概率分布.第三章介紹了本原群的概念及其與擬群相關的知識.第四章給出了7階擬群的分類.對于在某一較低階的本原群中形成的拉丁方,根據(jù)所具有的列置換的循環(huán)型進行分類.對于在高階的本原群(交錯群T6和對稱群T7)中形成的拉丁方,由于其具體表示形式無法一一列出,在此,根據(jù)能夠形成拉丁方的基本條件,將所有能夠生成拉丁方的列置換的循環(huán)型的組合列出來并據(jù)此進行分類.第五章計算出每一類中的擬群的周期因子的期望值.第六章對文章做了總結.對各階本原群中能夠得到的拉丁方的周期因子及其期望值進行分析,只有在交錯群T6中的所有拉丁方及對稱群T7中部分型類中的拉丁方是適合用于加密的.
[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.
【學位授予單位】：寧波大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O152

【參考文獻】

相關期刊論文 前2條

1 劉依依;;eSTREAM和流密碼分析現(xiàn)狀[J];信息安全與通信保密;2009年12期

2 馮登國;NESSIE工程簡介[J];信息安全與通信保密;2001年03期

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本文編號：1746578