带有仲裁认证码的新构造

发布时间：2018-05-20 08:04

本文选题：有限域 + 多项式　；参考：《中国民航大学》2017年硕士论文

【摘要】：现代信息技术使得人们的信息交流和信息共享更加的方便和快捷,但同时也给人们带来信息泄露、信息欺诈等安全隐患。因此,信息安全已成为信息科学中的核心研究领域之一。认证是保障信息安全的重要手段之一,而消息认证码是一种无条件安全认证系统。收方和发方相互可信的认证码称之为A-码;在收方和发方不可信的情况下,仲裁可信的认证码称之为A2-码,仲裁不可信的认证码称之为A3-码。A3-码作为A2-码的一种扩张,由于三个参与方:发方、收方和仲裁都是不可信的,它更满足现代通讯认证系统。本文主要是探索A3-码的新的构造方法,得到两方面的研究成果。一是基于有限域上的多项式和线性方程理论,构造了一类A3-码,特别地,该码在参数取特殊值时是完善的;二是基于有限域上的酉几何,充分运用酉空间的子空间结构和计数原理,构造了一类A3-码。同时,也计算了两类码的参数和受到的各种攻击成功的最大概率。最后,与一些已知的A3-码相比较,所构造的码节省存储空间且安全性能较高,有一定的优势。
[Abstract]:Modern information technology makes people's information exchange and information sharing more convenient and faster, but also brings people information leakage, information fraud and other security risks. Therefore, information security has become one of the core research fields in information science. Authentication is one of the important means to guarantee information security, and message authentication code is an unconditional security authentication system. The authentication codes that are trusted by the receiver and the sender are called A- codes; when the receiver and the sender are not trusted, the arbitration trusted authentication codes are called A2- codes, and the arbitration untrusted authentication codes are called A3- codes. A3- codes are used as an extension of A2-codes. Because the three participants: issuer, receiver and arbitration are not credible, it is more suitable for modern communication authentication system. In this paper, a new construction method of A 3-code is explored, and two research results are obtained. First, based on the theory of polynomial and linear equations over finite fields, a class of A _ 3-codes is constructed. In particular, the code is perfect when the parameters are given a special value, and the second is based on unitary geometry over finite fields. Based on the subspace structure and counting principle of unitary space, a class of A _ 3-codes is constructed. At the same time, the parameters of two kinds of codes and the maximum probability of successful attack are calculated. Finally, compared with some known A3- codes, the constructed codes save storage space and have higher security performance.
【学位授予单位】：中国民航大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.4;TP309

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