Abstract: A construction of Cartesian authentication code from the vector space over finite field is presented. The parameters of the code are computed. Assuming the encoding rules are chosen according to a uniform probability distribution, the probabilities of successful impersonation attack PI and successful substitution attack of opponent PS are also computed. It is an optimal Cartesian authentication code of PI.

Key words: finite fields, vector space, Cartesian, authentication code, impersonation attack, substitution attack

摘要： 利用有限域上的向量空间构造了一个新的Cartesian认证码，并计算了该认证码的参数。当编码规则按等概率分布选取时，求出了敌方模仿攻击成功的概率PI和替换攻击成功的概率PS，进而得到此认证码为一个PI最优的Cartesian认证码。

关键词: 有限域, 向量空间, Cartesian, 认证码, 模仿攻击, 替换攻击