基于有限域上的射影空间构造完善的A3码

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基于有限域上的射影空间构造完善的A3码

陈尚弟，梁俊英

（taptap下载安装安卓理学院，天津300300）

收稿日期:2017-09-15 修回日期:2017-10-31 出版日期:2018-04-25 发布日期:2018-05-02
作者简介:陈尚弟（1964—），男，山西应县人，教授，博士，研究方向为代数、编码与密码.
基金资助:
中央高校基本科研业务费专项（3122016L005）

Construction of perfect A³-codes from projective geometry over finite fields

CHEN Shangdi, LIANG Junying

(Intelligent Signal and Image Processing Key Lab of Tianjin, CAUC, Tianjin 300300, China)

Received:2017-09-15 Revised:2017-10-31 Online:2018-04-25 Published:2018-05-02

摘要/Abstract

摘要： 为了解决具有仲裁的认证码中仲裁不可信的问题，提出了A³码的概念。在认证系统中，3 个参与方(发方、收方和仲裁方)都不可信，这是一个符合现实环境的认证系统，具有广泛的应用前景。运用有限域上射影几何的子空间结构和计数方法，构造了一个完善的A³码，给出所构造码的参数，计算该码受到的各种攻击成功的最大概率。与一些已知的A³码相比，该码有明显的优势。仿真结果表明，该码具有良好的安全性。

关键词: A³码, 射影几何, 有限域

Abstract: To solve the problem of incredible arbitration in the authentication codes with arbitration, the concept of A3-codes is proposed. In an A3-code, none of the three participants is assumed trustable including transmitter,receiver and arbiter. This authentication system is more suitable for realistic environment with extensive application prospect. A perfect A3-code is constructed by using subspace structure and counting method of projective geometry over finite fields, parameters of the constructed code are given, and the maximum success probabilities of various cheating attacks are also calculated. Compared with some known A3 codes, this code has obvious advantages. Simulation results show that this code has good security.

Key words: A3-code, projective geometry, finite field

中图分类号:

TP309

陈尚弟，梁俊英. 基于有限域上的射影空间构造完善的A3码[J]. taptap下载安装安卓学报.

CHEN Shangdi, LIANG Junying. Construction of perfect A³-codes from projective geometry over finite fields[J]. .

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基于有限域上的射影空间构造完善的A3码

Construction of perfect A³-codes from projective geometry over finite fields

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基于有限域上的射影空间构造完善的A3码

Construction of perfect A3-codes from projective geometry over finite fields

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Construction of perfect A³-codes from projective geometry over finite fields