It is shown that Perfect Secret Sharing Schemes are Simple Weak Effectivity Functions. Namely for any finite set K of Keys and any finite set N of participants the set of all Perfect Secret Sharing Schemes having 0-normalized security level #K-1is characterized as the set of all Simple Weak Effectivity Functions on (N,K): perfection in secret sharing turns out to have simplicity as its nice game-theoretic counterpart. It also follows that Perfect Secret Sharing Schemes do admit universal implementation procedures using 1-threshold schemes as elementary 'building blocks'.
Vannucci, S. (2001). On Perfect Secret Sharing Schemes and Coalitional Game Forms. In Theoretical Aspects of Rationality and Knowledge 2001 (TARK VIII) (pp. 183-192). SAN FRANCISCO : Morgan Kaufmann.
On Perfect Secret Sharing Schemes and Coalitional Game Forms
VANNUCCI, STEFANO
2001-01-01
Abstract
It is shown that Perfect Secret Sharing Schemes are Simple Weak Effectivity Functions. Namely for any finite set K of Keys and any finite set N of participants the set of all Perfect Secret Sharing Schemes having 0-normalized security level #K-1is characterized as the set of all Simple Weak Effectivity Functions on (N,K): perfection in secret sharing turns out to have simplicity as its nice game-theoretic counterpart. It also follows that Perfect Secret Sharing Schemes do admit universal implementation procedures using 1-threshold schemes as elementary 'building blocks'.
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https://hdl.handle.net/11365/424457
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