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Ideal secret sharing schemes on graph-based $3$-homogeneous access structures | ||
| Transactions on Combinatorics | ||
| دوره 10، شماره 2، شهریور 2021، صفحه 107-120 اصل مقاله (297.71 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2021.123661.1739 | ||
| نویسندگان | ||
| Shahrooz Janbaz* 1؛ Bagher Bagherpour2؛ Ali Zaghian2 | ||
| 1Electrical and computer faculty, Malek Ashtar University of Technology, Tehran, Iran | ||
| 2Department of Mathematics and Cryptography, Malek Ashtar University of Technology, Isfahan, Iran | ||
| چکیده | ||
| The characterization of the ideal access structures is one of the main open problems in secret sharing and is important from both practical and theoretical points of views. A graph-based $3-$homogeneous access structure is an access structure in which the participants are the vertices of a connected graph and every subset of the vertices is a minimal qualified subset if it has three vertices and induces a connected graph. In this paper, we introduce the graph-based $3-$homogeneous access structures and characterize the ideal graph-based $3$-homogeneous access structures. We prove that for every non-ideal graph-based $3$-homogeneous access structure over the graph $G$ with the maximum degree $d$ there exists a secret sharing scheme with an information rate $\frac{1}{d+1}$. Furthermore, we mention three forbidden configurations that are useful in characterizing other families of ideal access structures. | ||
| کلیدواژه‌ها | ||
| Cryptography؛ Secret sharing؛ Ideal access structures؛ Graph-based access structures؛ 3-homogeneous access structures | ||
| مراجع | ||
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