利用有限域上Ⅱ-Jordan型幂零矩阵构造Cartesian认证码

Using Ⅱ-Jordan nilpotent matrices over finite fields to construct Cartesian authentication code

定义了Ⅱ-Jordan型幂零矩阵,计算了它的相似标准形,并利用它构造了一个Cartesian认证码,计算了该认证码的各个参数.在假定信源和编码规则按照等概率均匀分布的条件下,给出了该认证码的成功模仿攻击概率PI和替换攻击概率PS.

The definition of Ⅱ-Jordan nilpotent matrix is defined and its transmission to a simpler form is discussed in the present paper.One construction of Cartesian authentication codes from Ⅱ-Jordan nilpotent matrices over finite fields is presented and its size parameters are computed.And assuming that the encoding rules are chosen according to a uniform probability distribution,P_I and P_S denote the largest probabilities of a successful impersonation attack and a successful substitution attack respectively,then P_I and P_S are also computed.