NDLI: Characterizing Ideal Weighted Threshold Secret Sharing

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Beimel, Amos Tassa, Tamir Weinreb, Enav
Copyright Year	2008
Abstract	Weighted threshold secret sharing was introduced by Shamir in his seminal work on secret sharing. In such settings, there is a set of users where each user is assigned a positive weight. A dealer wishes to distribute a secret among those users so that a subset of users may reconstruct the secret if and only if the sum of weights of its users exceeds a certain threshold. On one hand, there are nontrivial weighted threshold access structures that have an ideal schemea scheme in which the size of the domain of shares of each user is the same as the size of the domain of possible secrets (this is the smallest possible size for the domain of shares). On the other hand, other weighted threshold access structures are not ideal. In this work we characterize all weighted threshold access structures that are ideal. We show that a weighted threshold access structure is ideal if and only if it is a hierarchical threshold access structure (as introduced by Simmons), or a tripartite access structure (these structures generalize the concept of bipartite access structures due to Padr and Sez), or a composition of two ideal weighted threshold access structures that are defined on smaller sets of users. We further show that in all those cases the weighted threshold access structure may be realized by a linear ideal secret sharing scheme. The proof of our characterization relies heavily on the strong connection between ideal secret sharing schemes and matroids, as proved by Brickell and Davenport.
Starting Page	360
Ending Page	397
Page Count	38
File Format	PDF
ISSN	08954801
DOI	10.1137/S0895480104445654
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	1
Volume Number	22
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2008-03-07
Access Restriction	Subscribed
Subject Keyword	matroids tripartite access structures ideal secret sharing hierarchical access structures Authentication and secret sharing Cryptography
Content Type	Text
Resource Type	Article
Subject	Mathematics

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