多发送或多接收认证码的新构造

发布时间：2018-02-28 15:07

本文关键词： 有限域认证码仲裁多项式保密辛几何多接收　出处：《中国民航大学》2017年硕士论文　论文类型：学位论文

【摘要】：保密和认证是更好地保障信息安全的两种主要手段。但是,认证系统既能够具备保密功能,也能够不具备保密功能。为防止发方与收方彼此欺骗,增加一个绝对可以信赖的仲裁方来处理内部纠纷,进而构成具有可信仲裁方的认证码,简称A~2-码。本文的主要研究目的是构造具备保密功能的A~2-码和多接收认证码,并且获得了两类新的认证码。主要结果为:一是基于有限域上的多项式构造了两个具备保密功能的A~2-码;二是利用有限域上的辛几何构造了一类多接收认证码。证明了两类认证码的合理性。然后,充分运用多项式的性质、线性方程组理论和辛几何的子空间结构及其计数原理,计算相关参数以及在加密密钥集合、解密密钥集合和信源集合都遵循均匀分布的条件下,被攻击成功的最大概率。最后,将所构造的两个具备保密功能的A~2-码与已有A~2-码进行比较,本文的构造更能节约存储空间,更好地防御内部攻击,并且具备保密功能。对构造的多接收认证码所受到的来自发方的假冒攻击进行仿真。仿真结果充分表明随着发方假冒攻击的次数不断增多,被攻击成功的概率趋向于稳定。同时,也充分证明被攻击成功的概率的实际值要远远小于被攻击成功的最大概率的理论值。
[Abstract]:Confidentiality and authentication are the two main means to better protect the security of information. However, the authentication system can not only have the function of confidentiality, but also can not have the function of confidentiality, in order to prevent the sender and the receiver from cheating each other, An absolutely reliable arbiter is added to deal with internal disputes, and then the authentication code of a trusted arbiter is formed. The main purpose of this paper is to construct a secure AF2-code and a multi-receive authentication code. Two kinds of new authentication codes are obtained. The main results are as follows: one is to construct two secure Ag-2- codes based on the polynomials over finite fields; Secondly, a class of multi-receiving authentication codes is constructed by using symplectic geometry in finite fields. The rationality of the two kinds of authentication codes is proved. Then, the properties of polynomial, the theory of linear equations, the subspace structure of symplectic geometry and its counting principle are fully used. Calculate the relevant parameters and the maximum probability of being attacked successfully under the condition that the encryption key set, decryption key set and source set all follow the condition of uniform distribution. Comparing the two AF2-codes with security function with the existing AH2-codes, the structure of this paper can save storage space and defend against internal attacks. The simulation results show that the number of counterfeiting attacks is increasing with the increase of the number of counterfeiting attacks by the sender. The probability of successful attack tends to be stable. At the same time, it is fully proved that the actual value of successful attack probability is much smaller than the theoretical value of the maximum probability of successful attack.
【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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