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A Protocol for Generating Random Elements with Their Probabilities

  • Thomas Holenstein
  • Robin Künzler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8591)

Abstract

We give an AM protocol that allows the verifier to sample elements x from a probability distribution P, which is held by the prover. If the prover is honest, the verifier outputs (x,P(x)) with probability close to P(x).

In case the prover is dishonest, one may hope for the following guarantee: if the verifier outputs (x,p), then the probability that the verifier outputs x is close to p. Simple examples show that this cannot be achieved. Instead, we show that the following weaker condition holds (in a well defined sense) on average: If (x,p) is output, then p is an upper bound on the probability that x is output.

Our protocol yields a new transformation to turn interactive proofs where the verifier uses private random coins into proofs with public coins. The verifier has better running time compared to the well-known Goldwasser-Sipser transformation (STOC, 1986). For constant-round protocols, we only lose an arbitrarily small constant in soundness and completeness, while our public-coin verifier calls the private-coin verifier only once.

Keywords

Sampling Protocol Full Version Interactive Protocol Interactive Proof Soundness Condition 
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 International Publishing Switzerland 2014

Authors and Affiliations

  • Thomas Holenstein
    • 1
  • Robin Künzler
    • 1
  1. 1.Department of Computer ScienceETH ZurichZurichSwitzerland

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