利用非交错矩阵构造带仲裁的认证码

设Fq是q元特征为2的有限域,q是素数的幂．令信源集S为Fq上所有的n×n非交错矩阵的合同标准型,编码规则集ET和解码规则集ER为Fq上所有的n×n非奇异矩阵,信息集为Fq上所有的n×n奇异的非交错矩阵,构造映射f：s×ET｜→M g：M×ER→S∪（欺诈）（Sr,P）｜→PS,P^t, （A,X）｜→{Sr,如果XKAKX^T=Sr,秩A=r 欺诈, 其他 其中K=（^In-1 0 0 0 ）.证明了该六元组（S,ET,ER,M;f,g）是一个带仲裁的Cartesian认证码,并计算了该认证码的参数．进而,当收方与发方的编码规则按照等概率均匀分布选取时,计算出该码敌方模仿攻击成功的概率P1,敌方替换攻击成功的概率Ps,发方模仿攻击成功的概率PT,收方模仿攻击成功的概率PR0,收方替换攻击成功的概率PR1．

Construction of authentication codes with arbitration by non-alternation symmetric matrices

Let Fq be the finite fields of characteristic 2 with q elements, where q is a power of a prime. Suppose the set of source states S is a cogredient normal form of all the n X n non-alternation matrices over Fq, the set of encoding rules ET and decoding rules ER are all of the n ）× n nonsingular matrices over Fq, and the set of messages M is all of the n X n singular non-alternation matrices over Fq. Construct the maps f：s×ET｜→M g：M×ER→S∪（reject）（Sr,P）｜→PS,P^t, （A,X）｜→{Sr,if XKAKX^T=Sr,rank（A）=r reject, otherwise where K=（^In-1 0 0 0 ） In this paper it is proved that （S, Er, ER, M;f, g）is a Cartesian authentication codes with arbitration, and the associated parameters are calculated. Moreover, when the encoding rules obey a uniform probability distribution,the probabilities of successful impersonation attack by the opponent, successful impersonation attack by the receiver and successful substitution attack by the receiver are computed.