本文選題：密碼學　切入點：旋轉(zhuǎn)對稱布爾函數(shù)　出處：《河南師范大學》2017年碩士論文　論文類型：學位論文

【摘要】：布爾函數(shù)一直是密碼學研究的重要對象,因為它是密碼體制設(shè)計與分析中一個不可缺少的工具.作為一類特殊的布爾函數(shù),旋轉(zhuǎn)對稱布爾函數(shù)在對稱密碼學界一直受到廣泛的關(guān)注,它對某些密碼算法如MD4, MD5和HAVAL的快速實現(xiàn)有著重要作用,同時和試驗設(shè)計也有聯(lián)系.本文通過對n元(n為任意正整數(shù))軌道矩陣性質(zhì)的研究,給出了4p元,prqs(p,q為互異的素數(shù),r,s為正整數(shù))元1階彈性旋轉(zhuǎn)對稱布爾函數(shù)(RSBFs)的構(gòu)造方法和計數(shù)公式.借助于我們的方法,所有的12元1階彈性RSBFs都可以構(gòu)造出來.又利用RSBFs的特性,給出了n元3階,4階彈性RSBFs的判別方法,為它們的構(gòu)造奠定了基礎(chǔ).文中又以12元為例,說明了我們方法的應(yīng)用.全文共分為四章:第一章介紹了全文的研究背景、相關(guān)概念和已有的研究成果.第二章通過對n元(n為任意正整數(shù))軌道矩陣性質(zhì)的研究,給出了計算其軌道矩陣個數(shù)的方法,把4p元,prqs(p,q為互異的素數(shù),r,s為正整數(shù))元1階彈性RSBFs的構(gòu)造均轉(zhuǎn)化為方程組的求解,進而確定了這兩類函數(shù)的計數(shù)公式.同時給出了 12元1階彈性RSBFs的構(gòu)造方法和計數(shù)公式.第三章利用RSBFs的特性,給出了n元3階,4階彈性RSBFs的判別方法,最后給出了 12元RSBFs是3階,4階彈性函數(shù)的判別方法.第四章對本篇論文進行了小結(jié),并提出了一些建議.
[Abstract]:A Boolean function has been an important object in cryptography, because it is an indispensable system in the design and analysis of cryptographic tools. As a special class of Boolean functions, rotation symmetric Boolean function has attracted extensive attention in the field of some symmetrical cryptography, its cryptographic algorithms such as MD4, MD5 and HAVAL fast implementation has important at the same time, and the experimental design have also been linked. Based on the N element (n is any positive integer) of track matrix properties, gives the 4P element (P, prqs, q are distinct primes, R, s is a positive integer) 1 yuan order elastic rotation symmetric Boolean function (RSBFs) structure the method and the counting formula. With the help of our method, all of the 12 yuan 1 order elastic RSBFs can be constructed. By using the characteristics of RSBFs, given n yuan 3 order, 4 order elastic RSBFs method, which laid the foundation for their construction. This paper takes 12 yuan as an example, To illustrate the application of our method. The full text is divided into four chapters: the first chapter introduces the research background, related concepts and existing research results. The second chapter through to n yuan (n is any positive integer) of track matrix properties, given the number of track matrix method, 4P yuan, prqs (P, q are distinct primes, R, s is a positive integer) to construct 1 yuan order elastic RSBFs were transformed into equations, and the counting formula of the two kinds of functions were determined. At the same time gives the construction method and counting formula of 12 yuan of 1 order elastic RSBFs. In the third chapter with the characteristics of RSBFs, given n yuan 3 order, 4 order elastic RSBFs method, finally, 12 yuan RSBFs is 3 order, 4 order elastic method function. The fourth chapter is the summary of this thesis, and puts forward some suggestions.

【學位授予單位】：河南師范大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TN918.1;O174

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相關(guān)期刊論文 前9條

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本文編號：1622248