Characterizing Ideal Weighted Threshold Secret Sharing

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 scheme – a 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 stru...

• Type: Conference
• Year: 2005
• Where: TCC
• Authors: Amos Beimel, Tamir Tassa, Enav Weinreb
• Keywords: Cryptography, Secret Sharing, TCC 2005, Threshold Access Structure, Weighted Threshold Access