基于矩阵方法的Cartesian认证码构造

在有限域上利用矩阵方法构造一类新的Cartesian认证码，得到全部参数。假定编码规则按等概率均匀分布，分析敌手对该码成功模仿攻击和替换攻击的2种概率。该认证码基于立方幂零矩阵的若当型，较先前由矩阵方法构造的方案拥有更大源状态数。该方案在相同条件下可以认证更多比特数的源状态，一定程度上降低了通信代价，提高了认证码的安全性。

Construction of Cartesian Authentication Code Based on Matrices Method

A new kind of Cartesian authentication code is constructed by using matrices method over finite fields and all its parameters are obtained. Supposing the encoding rules are chosen according to the uniform probability distribution, the two probabilities of successful impersonation attack and substitution attack of opponent are computed. This authentication code is based on Jordan form of cubic nilpotent matrices and has the greater number of the source state than some schemes constructed by matrices method before. On the same condition, the scheme can authenticate more source state, which reduces the communication cost and improves the security of authentication code to some extent.