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Proofs of Partial Knowledge and Simplified Design of Witness Hiding Protocols

  • Ronald Cramer
  • Ivan Damgård
  • Berry Schoenmakers
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 839)

Abstract

Suppose we are given a proof of knowledge \( \mathcal{P} \) in which a prover demonstrates that he knows a solution to a given problem instance. Suppose also that we have a secret sharing scheme \( \mathcal{S} \) on n participants. Then under certain assumptions on \( \mathcal{P} \) and \( \mathcal{S} \), we show how to transform \( \mathcal{P} \) 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 \( \mathcal{S} \). 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 \( \mathcal{P} \) 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 \( \mathcal{P} \) and communication complexity n times that of \( \mathcal{P} \). Our results use no unproven complexity assumptions.

Keywords

Access Structure Secret Sharing Scheme Monotone Formula Round Complexity Qualified Subset 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Ronald Cramer
    • 1
  • Ivan Damgård
    • 2
  • Berry Schoenmakers
    • 1
  1. 1.CWIDenmark
  2. 2.Aarhus UniversityDenmark

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