利用有限域上奇异辛几何构造一个新的带仲裁的认证码  

A New Construction of the Authentication Codes with Arbitration from Singular Symplectic Geometry over the Finite Fields

作　　者：高有[1] 霍立群[1] 

机构地区：[1]中国民航大学理学院,天津300300

出　　处：《工程数学学报》2011年第5期629-641,共13页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(61179026);天津自然科学基金(08JCYBJC13900)~~

摘　　要：带仲裁的认证码可以解决通信系统中发方、收方和敌方之间的相互欺骗问题.本文利用有限域上奇异辛几何的子空间构作了一个新的带仲裁的认证码,采用矩阵与组合计数的方法计算了这个码的各种参数.当发方的编码规则和收方的解码规则按等概率分布选取时,计算出了敌方的模仿攻击,敌方的替换攻击,发方的模仿攻击,收方的模仿攻击,收方的替换攻击等五种攻击成功的最大概率PI,PS,PT,PR0,PR1.The authentication codes with arbitration can deal with the distrust problem of the trans-mitter,the receiver and the opponent in the communications system.In this paper,a new construction of the authentication codes with arbitration from subspaces of singular symplectic geometry over the finite fields is presented.The parameters of the code are computed by the method of the matrix and the combinatorial enumeration.The transmitter’s encoding rules and the receiver’s decoding rules are chosen according to a uniform probability distribution.PI,PS,PT,PR0 and PR1 denote the largest probabilities of the successful impersonation attack and the successful substitution attack of the oppo-nent,the successful impersonation attack of the transmitter,the successful impersonation attack and the successful substitution attack of receiver,respectively.Then the probabilities of five attacks for the construction of the authentication codes with arbitration are computed.

关 键 词：有限域 带仲裁的认证码 奇异辛几何 

分 类 号：O157.4[理学—数学]