信息安全中删位纠错码与MAI函数的构造

发布时间：2019-02-12 14:27

【摘要】：编码学与密码学均为信息安全的两重要内容之一,它们依靠的数学基础均为有限域或者是有限环.首先,本文依据刻化空间中向量间距离方式的不同,可以定义不同的纠错码Levenshtein定义了莱文斯坦距离,由此定义了删位纠错码.本文利用组合设计理论中的成对平衡设计和初等数论的方法及技巧,给出了一类新的删位纠错码.其次,具有多种密码学性质的布尔函数的构造是密码学中重要的研究课题.本文对两类具有多种密码学性质的MAI函数的构造进行了综述：(1)基于2009年涂自然与邓映蒲提出的组合猜想以及该猜想的推广形式,利用有限域本原元的性质,构造了具有多种密码学性质的MAI函数.(2)根据布尔函数的零化子在其支撑集上的取值与某类齐次线性方程组的解的密切联系,构造了一系列MAI函数.再计算该函数其他密码学指标,从而获得具有多种密码学性质的MAI函数的构造方法.
[Abstract]:Encoder and cryptography are two important contents of information security. They depend on finite fields or finite rings. Firstly, according to the different distance between vectors in the etched space, we can define different error-correcting codes Levenshtein and define the Levenstein distance, and define error-correcting codes (error-correcting codes). In this paper, a new error-correcting code is given by using the methods and techniques of pairwise equilibrium design and elementary number theory in combinatorial design theory. Secondly, the construction of Boolean functions with many cryptographic properties is an important research topic in cryptography. In this paper, two kinds of MAI functions with various cryptographic properties are reviewed. (1) based on the combination conjecture put forward by Tu nature and Deng Yingpu in 2009 and its extension form, the properties of primitive elements in finite fields are used. MAI functions with many cryptographic properties are constructed. (2) A series of MAI functions are constructed according to the close relation between the zerons of Boolean functions on their support sets and the solutions of a class of homogeneous linear equations. The other cryptographic indexes of the function are calculated and the construction method of the MAI function with various cryptographic properties is obtained.
【学位授予单位】：四川师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O157.4;TP309

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