Classification of ideal homomorphic threshold schemes over finite Abelian groups

Authors:
Yair Frankel;Yvo Desmedt
Affiliations:
Department of EE & CS, University of Wisconsin, Milwaukee, Milwaukee, WI;Department of EE & CS, University of Wisconsin, Milwaukee, Milwaukee, WI
Venue:
EUROCRYPT'92 Proceedings of the 11th annual international conference on Theory and application of cryptographic techniques
Year:
1992

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Abstract

Threshold schemes allow any t out of l individuals to recompute a secret (key). General sharing schemes are a generalization. In homomorphic sharing schemes the "product" of shares of the keys gives a share of the product of the keys. We prove that there exist infinitely many Abelian groups over which there does not exist an ideal homomorphic threshold scheme. Additionally we classify ideal homomorphic general sharing schemes. We discuss the potential impact of our result on the construction of general sharing schemes.