对3条超边的超圈存取结构最优信息率的一点注记

doi:10.6040/j.issn.1671-9352.0.2014.568

山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (11): 60-66.doi: 10.6040/j.issn.1671-9352.0.2014.568

对3条超边的超圈存取结构最优信息率的一点注记

薛丽霞, 李志慧, 谢佳丽

陕西师范大学数学与信息科学学院, 陕西西安 710119

收稿日期:2014-12-22 修回日期:2015-11-11 出版日期:2015-11-20 发布日期:2015-12-09
通讯作者: 李志慧(1966-),女,博士,教授,研究方向为密码学.E-mail:lizhihui@snnu.edu.cn E-mail:lizhihui@snnu.edu.cn
作者简介:薛丽霞(1989-),女,硕士研究生,研究方向为密码学.E-mail:xuelixia@snnu.edu.cn
基金资助:
国家自然科学基金资助项目(61373150);陕西省科学技术研究发展计划工业攻关项目(2013K0611)

A note on the optimal information rate of hypercycle access structure with three hyperedges

XUE Li-xia, LI Zhi-hui, XIE Jia-li

College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710119, Shaanxi, China

Received:2014-12-22 Revised:2015-11-11 Online:2015-11-20 Published:2015-12-09

摘要/Abstract

摘要： 将含有3条超边的超圈存取结构分为两类:一类是任意一条超边都没有属于自己的独立点集;另一类是至少存在一条超边有属于自己的独立点集。对第一类超圈存取结构,用Shamir方案构造了一个理想的秘密共享方案,从而证明了其最优信息率等于1;对第二类超圈存取结构用信息论和λ-分解方法证明了其最优信息率等于2/3。给出了参与者人数为6、7且含有3条超边共86种互不同构的超圈存取结构,并计算了其最优信息率。

关键词: 理想秘密共享方案, 超圈, 最优信息率, 存取结构

Abstract: The hypercycle access structures with three hyperedges is divided into two kinds:one kind is that any hyperedge has no its own independent point set, another kind is that there is at least one hyperedge which has its own independent point set. By using Shamir-threshold scheme, an ideal secret sharing scheme is constructed, and it is proved that the optimal information rate of the first kind of hypercycle access structures are equal to 1; Using information theory and λ-decomposition method, it is shown that the optimal information rate of the second kind of hypercycle access structures are equal to 2/3. Eighty-six hypercycle access structures with three hyperedges on six and seven participants, in which all of each other are not isomorphic, and their optimal information rates are calculated.

Key words: access structure, ideal secret sharing scheme, hypercycle, optimal information rate

中图分类号:

TP309

薛丽霞, 李志慧, 谢佳丽. 对3条超边的超圈存取结构最优信息率的一点注记[J]. 山东大学学报（理学版）, 2015, 50(11): 60-66.

XUE Li-xia, LI Zhi-hui, XIE Jia-li. A note on the optimal information rate of hypercycle access structure with three hyperedges[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(11): 60-66.

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对3条超边的超圈存取结构最优信息率的一点注记

A note on the optimal information rate of hypercycle access structure with three hyperedges

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