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

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