| 利用有限域上2-幂零矩阵构作Cartesian认证码 |
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| 引用本文： | 李殿龙,郑宝东. 利用有限域上2-幂零矩阵构作Cartesian认证码[J]. 应用数学, 2004, 17(3): 383-388 |
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| 作者姓名： | 李殿龙 郑宝东 |
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| 作者单位： | 1. 江南大学理学院,无锡,214063
2. 哈尔滨工业大学数学系,哈尔滨,150001 |
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| 基金项目： | 江南大学 2 11基金 (314 0 0 0 2 10 5 0 30 6 ) |
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| 摘 要： | 给出 2 -幂零矩阵的Jordan标准型在相似变换下的稳定群的结构 ,利用有限域上 2 -幂零矩阵构作了一个Cartesian认证码 ,计算出了该认证码的参数 .在假定编码规则按等概率分布选取的条件下 ,计算出了该认证码被成功的模仿攻击的最大概率PI 及被成功的替换攻击的最大概率PS.
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| 关 键 词： | 2-幂零矩阵 有限域 认证码 编码规则 |
| 文章编号： | 1001-9847(2004)03-0383-06 |
| 修稿时间： | 2003-06-12 |
Using 2-nilpotent Matrices Over a Finite Fields to Construct Cartesian Authentication Codes |
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| LI Dian-long,ZHENG Bao-dong. Using 2-nilpotent Matrices Over a Finite Fields to Construct Cartesian Authentication Codes[J]. Mathematica Applicata, 2004, 17(3): 383-388 |
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| Authors: | LI Dian-long ZHENG Bao-dong |
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| Affiliation: | LI Dian-long1,ZHENG Bao-dong2 |
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| Abstract: | We give the structure of the stable group of the Jordan's normal form of 2-nilpotent matrices under the similarity transformation.One construction of Cartesian authentication codes from 2-nilpotent matrices over a finite fields is presented and its size parameters are computed.Moreover,assume that the encoding rules are chosen according to a uniform probability distribution,the P I and P S, which denote the largest probabilities of a successful impersonation attack and of a successful substitution attack respectively,of these codes are also computed. |
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| Keywords: | Nilpotent matrices Finite fields Authentication codes Encoding rules |
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