信息网络安全

信息网络安全 ›› 2016, Vol. 16 ›› Issue (5): 15-22.doi: 10.3969/j.issn.1671-1122.2016.05.003

• 技术研究 • 上一篇    下一篇

一类理想的存取结构的构造

李志慧(), 徐廷廷, 张娜   

  1. 陕西师范大学数学与信息科学学院,陕西西安 710119
  • 收稿日期:2016-03-21 出版日期:2016-05-20 发布日期:2020-05-13
  • 作者简介:

    李志慧（1966—）,女,陕西,教授,博士,主要研究方向为有限域和密码学;徐廷廷（1990—）,女,山东,硕士研究生,主要研究方向为有限域和密码学;张娜（1989—）,女,宁夏,硕士研究生,主要研究方向为有限域和密码学。

  • 基金资助:
    国家自然科学基金[61373150].陕西省科学技术研究发展计划工业攻关项目[2013K0611].中央高校基本科研业务费专项资金[GK201603087]

The Construction of a Type of Ideal Access Structures

Zhihui LI(), Tingting XU, Na ZHANG   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an Shaanxi 710119, China
  • Received:2016-03-21 Online:2016-05-20 Published:2020-05-13

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摘要：

构造理想的存取结构对于设计信息率高的秘密共享方案具有重要作用。Shamir(k,n)型方案（区别于Shamir门限方案）对应的存取结构是理想的,但如何求出这类方案对应的互不同构的存取结构是一个需要解决的问题。文章首先提出Shamir(k,n)型方案中两组迹等价的概念,然后将Shamir(k,n)型方案中极小存取结构的同构的判定转化为对应的两组迹的等价问题。文章进而给出了Shamir(k,n)型方案中求极小特权数组的一个算法,利用这个算法可以求出Shamir(k,n)型方案中所有互不等价的迹,从而在理论上完满地解决了Shamir(k,n)型方案中互不同构的理想的存取结构的构造问题。特别地,文章给出有限域F13中当有7个参与者时的所有极小特权数组,并得到了互不等价的迹,进而利用文中的判定方法给出了当有7个参与者时,Shamir(k,n)型方案的所有互不同构的理想的极小存取结构。

关键词: Shamir(k, n)型方案, 迹, 极小特权数组, 极小存取结构, 理想的存取结构

Abstract:

The construction of ideal access structure has an important role for designing secret sharing scheme with high information rate. The access structures corresponding to Shamir(k,n)’s type scheme( different from Shamir’s threshold type scheme) are ideal, but how to get these access structures which are not mutually isomorphic is a problem needed to be solved. First of all, the definition that the tracks are mutually equivalent is proposed, and then the problem for judging whether two minimal access structures are isomorphic in Shamir(k,n)’s type scheme is converted into the problem for judging whether their corresponding tracks are equivalent. This paper designs an algorithm which can be used to calculate all minimal privileged arrays that exist in the Shamir(k,n)’s type scheme and can be used to calculate all the tracks existing in the Shamir(k,n)’s type scheme that are not mutually equivalent. So this paper perfectly solves the problem that how to construct all ideal access structures which are not mutually isomorphic in the Shamir(k,n)’s type scheme. Particularly, this paper gives all the minimal privileged arrays with 7 participants in finite field F13 and obtains all the tracks that are not mutually equivalent, and thus gives all the ideal minimal access structures with 7 participants that are not mutually isomorphic by the above judgment.

Key words: Shamir(k, n)’s type scheme, tracks, minimal privileged arrays, minimal access structure, ideal access structure

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