Proofs of partial knowledge and simplified design of witness hiding protocols

R. Cramer, Ivan Damgard, B. Schoenmakers

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    Abstract

    Suppose we are given a proof of knowledge P in which a prover demonstrates that he knows a solution to a given problem instance. Suppose also that we have a secret sharing scheme S on n participants. Then under certain assumptions on P and S , we show how to transform P into a witness indistinguishable protocol, in which the prover demonstrates knowledge of the solution to some subset of n problem instances out of a collection of subsets defined by S . For example, using a threshold scheme, the prover can show that he knows at least d out of n solutions without revealing which d instances are involved. If the instances are independently generated, we get a witness hiding protocol, even if P did not have this property. Our results can be used to efficiently implement general forms of group oriented identification and signatures. Our transformation produces a protocol with the same number of rounds as P and communication complexity n times that of P . Our results use no unproven complexity assumptions.
    Original languageEnglish
    Title of host publicationAdvances in Cryptography - Eurocrypt'94 (Santa Barbara CA, USA, August 21-25, 1994)
    EditorsY. Desmedt
    Place of PublicationBerlin
    PublisherSpringer
    Pages174-187
    ISBN (Print)3-540-58333-5
    DOIs
    Publication statusPublished - 1994

    Publication series

    NameLecture Notes in Computer Science
    Volume839
    ISSN (Print)0302-9743

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