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

作　　者：宋元凤[1] 南基洙[2] 

机构地区：[1]通化师范学院数学系,吉林通化134002 [2]大连理工大学数学科学学院,辽宁大连116024

出　　处：《东北师大学报（自然科学版）》2010年第3期37-42,共6页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10771023)

摘　　要：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.

关 键 词：Ⅱ-Jordan型幂零矩阵 有限域 群在集合上的作用 CARTESIAN认证码 

分 类 号：O241.6[理学—计算数学]