Unconditionally secure homomorphic pre-distributed commitments

Authors:
Anderson C. A. Nascimento;Akira Otsuka;Hideki Imai;Joern Mueller-Quade
Affiliations:
Institute of Industrial Science, The University of Tokyo, Tokyo, Japan;Institute of Industrial Science, The University of Tokyo, Tokyo, Japan;Institute of Industrial Science, The University of Tokyo, Tokyo, Japan;Universitaet Karlsruhe, Institut fuer Algorithmen und Kognitive Systeme, Karlsruhe, Germany
Venue:
AAECC'03 Proceedings of the 15th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Year:
2003

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Abstract

In this paper we deal with unconditionally secure commitment schemes based on pre-distributed data. We provide bounds for the amount of data which has to be pre-distributed to the participants of the commitment, thus solving an open problem stated in the literature. We also introduce the issue of homomorphism in unconditionally secure commitment schemes. We provide a definition and a construction based on modules of mappings over finite rings. As an application of our constructions, we provide a new pre-distributed primitive which yields non-interactive unconditionally secure zero knowledge proofs of any polynomial relation among commitments.