本文選題：有限域 + 多項(xiàng)式��； 參考：《中國民航大學(xué)》2017年碩士論文

【摘要】：現(xiàn)代信息技術(shù)使得人們的信息交流和信息共享更加的方便和快捷,但同時也給人們帶來信息泄露、信息欺詐等安全隱患。因此,信息安全已成為信息科學(xué)中的核心研究領(lǐng)域之一。認(rèn)證是保障信息安全的重要手段之一,而消息認(rèn)證碼是一種無條件安全認(rèn)證系統(tǒng)。收方和發(fā)方相互可信的認(rèn)證碼稱之為A-碼;在收方和發(fā)方不可信的情況下,仲裁可信的認(rèn)證碼稱之為A2-碼,仲裁不可信的認(rèn)證碼稱之為A3-碼。A3-碼作為A2-碼的一種擴(kuò)張,由于三個參與方:發(fā)方、收方和仲裁都是不可信的,它更滿足現(xiàn)代通訊認(rèn)證系統(tǒng)。本文主要是探索A3-碼的新的構(gòu)造方法,得到兩方面的研究成果。一是基于有限域上的多項(xiàng)式和線性方程理論,構(gòu)造了一類A3-碼,特別地,該碼在參數(shù)取特殊值時是完善的;二是基于有限域上的酉幾何,充分運(yùn)用酉空間的子空間結(jié)構(gòu)和計(jì)數(shù)原理,構(gòu)造了一類A3-碼。同時,也計(jì)算了兩類碼的參數(shù)和受到的各種攻擊成功的最大概率。最后,與一些已知的A3-碼相比較,所構(gòu)造的碼節(jié)省存儲空間且安全性能較高,有一定的優(yōu)勢。
[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.
【學(xué)位授予單位】：中國民航大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O157.4;TP309

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