电子学报 ›› 2013, Vol. 41 ›› Issue (2): 220-226.DOI: 10.3969/j.issn.0372-2112.2013.02.003

• 学术论文 • 上一篇    下一篇

基于极小线性码上的秘密共享方案

宋云1, 李志慧1, 李永明2   

  1. 1. 陕西师范大学数学与信息科学学院,陕西西安 710062;
    2. 陕西师范大学计算机科学学院,陕西西安 710062
  • 收稿日期:2011-11-03 修回日期:2012-05-15 出版日期:2013-02-25
    • 通讯作者:
    • 李志慧
    • 作者简介:
    • 宋 云 女,1987年生于陕西西安,陕西师范大学数学与信息科学学院博士研究生.研究方向为有限域、密码学. E-mail:songyun19871109@yahoo.com.cn
    • 基金资助:
    • 国家自然科学基金 (No.60873119)

Secret Sharing Schemes Based on Minimal Linear Codes

SONG Yun1, LI Zhi-hui1, LI Yong-ming2   

  1. 1. College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710062, China;
    2. College of Computer Science, Shaanxi Normal University, Xi'an, Shaanxi 710062, China
  • Received:2011-11-03 Revised:2012-05-15 Online:2013-02-25 Published:2013-02-25
    • Supported by:
    • National Natural Science Foundation of China (No.60873119)

摘要: 从理论上说,每个线性码都可用于构造秘密共享方案,但是在一般情况下,所构造的秘密共享方案的存取结构是难以确定的.本文提出了极小线性码的概念,指出基于这种码的对偶码所构造的秘密共享方案的存取结构是容易确定的.本文首先证明了极小线性码的缩短码一定是极小线性码.然后对几类不可约循环码给出它们为极小线性码的判定条件,并在理论上研究了基于几类不可约循环码的对偶码上的秘密共享方案的存取结构.最后用编程具体求出了一些实例中方案的存取结构.

关键词: 极小线性码, 存取结构, 极小码字, 秘密共享方案, 不可约循环码

Abstract: Theoretically,every linear code can be used to construct secret sharing schemes.However,determining the access structure of the schemes based on linear codes is very hard.The concept of minimal linear code is proposed,which makes the determination of the access structure of the schemes based on the duals of minimal linear codes easier.It is shown that the shortening codes of minimal linear codes are minimal as well.Then the conditions whether several types of irreducible cyclic codes are minimal or not are presented.Furthermore,the access structures of secret sharing schemes based on the duals of minimal linear codes are studied.Finally,the access structures of the schemes in specific examples are obtained through programming.

Key words: minimal linear code, access structures, minimal codeword, secret sharing scheme, irreducible cyclic codes

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