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A Protocol for Generating Random Elements with Their Probabilities

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Book cover Computing and Combinatorics (COCOON 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8591))

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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.

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Author information

Authors and Affiliations

  1. Department of Computer Science, ETH Zurich, 8092, Zurich, Switzerland

    Thomas Holenstein & Robin Künzler

Authors
  1. Thomas Holenstein
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  2. Robin Künzler
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Georgia State University, 34 Peachtree Street, Suite 1410, 30303, Atlanta, GA, USA

    Zhipeng Cai

  2. Department of Computer Science, Georgia State University, 34 Peachtree Street, Suite 1443, 30303, Atlanta, GA, USA

    Alex Zelikovsky

  3. Department of Computer Science, Georgia State University, 34 Peachtree Street, Suite 1449, 30303, Atlanta, GA, USA

    Anu Bourgeois

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Holenstein, T., Künzler, R. (2014). A Protocol for Generating Random Elements with Their Probabilities. In: Cai, Z., Zelikovsky, A., Bourgeois, A. (eds) Computing and Combinatorics. COCOON 2014. Lecture Notes in Computer Science, vol 8591. Springer, Cham. https://doi.org/10.1007/978-3-319-08783-2_17

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  • DOI: https://doi.org/10.1007/978-3-319-08783-2_17

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08782-5

  • Online ISBN: 978-3-319-08783-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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