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Beimel, Tassa and Weinreb (2008) and Farras and Padro (2010) partiallycharacterized access structures of ideal weighted threshold secret sharingschemes in terms of the operation of composition. They classifiedindecomposable ideal weighted threshold access structures, and proved that anyother ideal weighted threshold access structure is a composition ofindecomposable ones. It remained unclear which compositions of indecomposableweighted threshold access structures are weighted. In this paper we fill thegap. Using game-theoretic techniques we determine which compositions ofindecomposable ideal access structures are weighted, and obtain an if and onlyif characterization of ideal weighted threshold secret sharing schemes.

A Characterization of Ideal Weighted Secret Sharing Schemes