弹性旋转对称布尔函数的构造、计数和判别方法

发布时间：2018-03-17 00:04

本文选题：密码学　切入点：旋转对称布尔函数　出处：《河南师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：布尔函数一直是密码学研究的重要对象,因为它是密码体制设计与分析中一个不可缺少的工具.作为一类特殊的布尔函数,旋转对称布尔函数在对称密码学界一直受到广泛的关注,它对某些密码算法如MD4, MD5和HAVAL的快速实现有着重要作用,同时和试验设计也有联系.本文通过对n元(n为任意正整数)轨道矩阵性质的研究,给出了4p元,prqs(p,q为互异的素数,r,s为正整数)元1阶弹性旋转对称布尔函数(RSBFs)的构造方法和计数公式.借助于我们的方法,所有的12元1阶弹性RSBFs都可以构造出来.又利用RSBFs的特性,给出了n元3阶,4阶弹性RSBFs的判别方法,为它们的构造奠定了基础.文中又以12元为例,说明了我们方法的应用.全文共分为四章:第一章介绍了全文的研究背景、相关概念和已有的研究成果.第二章通过对n元(n为任意正整数)轨道矩阵性质的研究,给出了计算其轨道矩阵个数的方法,把4p元,prqs(p,q为互异的素数,r,s为正整数)元1阶弹性RSBFs的构造均转化为方程组的求解,进而确定了这两类函数的计数公式.同时给出了 12元1阶弹性RSBFs的构造方法和计数公式.第三章利用RSBFs的特性,给出了n元3阶,4阶弹性RSBFs的判别方法,最后给出了 12元RSBFs是3阶,4阶弹性函数的判别方法.第四章对本篇论文进行了小结,并提出了一些建议.
[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.

【学位授予单位】：河南师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN918.1;O174

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