NDLI: The exact values of the optimal average information ratio of perfect secret-sharing schemes for tree-based access structures

Content Provider	Springer Nature Link
Author	Lu, Hui Chuan Fu, Hung Lin
Copyright Year	2013
Abstract	A perfect secret-sharing scheme is a method of distributing a secret among a set of participants such that only qualified subsets of participants can recover the secret and the joint shares of the participants in any unqualified subset is statistically independent of the secret. The set of all qualified subsets is called the access structure of the scheme. In a graph-based access structure, each vertex of a graph $$G$$ represents a participant and each edge of $$G$$ represents a minimal qualified subset. The information ratio of a perfect secret-sharing scheme is defined as the ratio between the maximum length of the share given to a participant and the length of the secret. The average information ratio is the ratio between the average length of the shares given to the participants and the length of the secret. The infimum of the (average) information ratios of all possible perfect secret-sharing schemes realizing a given access structure is called the (average) information ratio of the access structure. Very few exact values of the (average) information ratio of infinite families of access structures are known. Csirmaz and Tardos have found the information ratio of all trees. Based on their method, we develop our approach to determining the exact values of the average information ratio of access structures based on trees.
Ending Page	46
Page Count	10
Starting Page	37
File Format	PDF
ISSN	09251022
e-ISSN	15737586
Journal	Designs, Codes and Cryptography
Issue Number	1
Volume Number	73
Language	English
Publisher	Springer US
Publisher Date	2013-03-07
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Secret-sharing scheme Information and Communication, Circuits Data Encryption Entropy Measures of information, entropy Factorization, matching, partitioning, covering and packing Data Structures, Cryptology and Information Theory Star covering Discrete Mathematics in Computer Science Graph-based access structure Average information ratio Tree Coding and Information Theory Authentication and secret sharing Cryptography Combinatorics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Discrete Mathematics and Combinatorics Theoretical Computer Science Computer Science Applications

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