Proofs of partial knowledge and simplified design of witness hiding protocols

R. Cramer, Ivan Damgard, B. Schoenmakers

    Research output: Contribution to journalArticleAcademicpeer-review


    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 a subset of n problem instances corresponding to a qualified set of participants. 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, this can lead to witness hiding protocols, even if P did not have this property. 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
    Pages (from-to)111-127
    JournalCWI Quarterly
    Issue number2
    Publication statusPublished - 1995


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